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Title: Early spring turbulent mixing in an ice-covered Arctic fjord during transition to melting Article Type: Research Paper
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Keywords: mixing; turbulence; fast ice; fjords; Arctic; Svalbard; Van Mijenfjorden Corresponding Author: Dr. Ilker Fer, PhD
Corresponding Author's Institution: University of Bergen First Author: Ilker Fer, Dr.
Order of Authors: Ilker Fer, Dr.; Karolina Widell Manuscript Region of Origin:
Abstract: Observations are presented of currents, hydrography and turbulence in a jet-type tidally-forced fjord in Svalbard. The fjord was ice covered at the time of the experiment in early spring 2004. Turbulence measurements were conducted by both moored instruments within the uppermost 5 m below the ice and a microstructure profiler covering 3-60 m at 75 m depth. Tidal choking at the mouth of the fjord induces a tidal jet advecting relatively warmer water past the measurement site and dominating the variability in
hydrography. While there was no strong correlation with the observed hydrography or mixing and the semi- diurnal tidal cycle, when conditionally sampled for tidal jet events, the mean structure in dissipation and work done under the ice and the mixing in the water column corresponded to the time development of inflow events. Observed levels of dissipation of turbulent kinetic energy per unit mass, 1.1x10-7 W kg-1, and eddy diffusivity, 7.3x10-4 m2 s-1, were comparable to direct measurements at other coastal sites and shelves with rough topography and strong forcing. During spring tides, an average upward heat flux of 5 W m-2 in the
under-ice boundary layer was observed. Instantaneous (1-h averaged) large heat flux events were
correlated with periods of large inflow, hence elevated heat fluxes were associated with the tidal jet and its heat content. Vertical heat fluxes are derived from shear-probe measurements by employing a novel model for eddy diffusivity (Shih et al., 2005). When compared to direct heat flux measurements using the eddy correlation method, the upper 3-10 m averaged heat flux estimates from the microstructure profiler agreed with the direct measurements averaged at 1 and 5 m below the ice to within 10%. During the experiment destabilizing buoyancy fluxes were recorded close to the ice, but overall, turbulence production was
dominated by shear. A scaling for dissipation employing production by both stress and buoyancy (Lombardo and Gregg, 1989) was found to be appropriate for the under-ice boundary layer.
1 2
Early spring turbulent mixing in an ice-covered Arctic fjord 3
during transition to melting 4
5 6 7
Ilker Fer 1*and Karolina Widell 1, 2 8
9 10
1 Bjerknes Centre for Climate Research and Geophysical Institute, University of Bergen.
11
2 University Centre in Svalbard, Longyearbyen, Norway 12
13 14 15 16 17 18 19 20 21 22
* Corresponding author:
23
Dr. Ilker Fer 24
Geophysical Institute, University of Bergen 25
Allégaten 70, N-5007 26
Bergen, Norway 27
E-mail : [email protected] 28
Phone : +47 5558 2580 29
Fax : +47 5558 9883 30
Manuscript
Click here to download Manuscript: Fer_Widell_text.pdf
Abstract 1
Observations are presented of currents, hydrography and turbulence in a jet-type tidally- 2
forced fjord in Svalbard. The fjord was ice covered at the time of the experiment in early 3
spring 2004. Turbulence measurements were conducted by both moored instruments within 4
the uppermost 5 m below the ice and a microstructure profiler covering 3-60 m at 75 m depth.
5
Tidal choking at the mouth of the fjord induces a tidal jet advecting relatively warmer water 6
past the measurement site and dominating the variability in hydrography. While there was no 7
strong correlation with the observed hydrography or mixing and the semi-diurnal tidal cycle, 8
when conditionally sampled for tidal jet events, the mean structure in dissipation and work 9
done under the ice and the mixing in the water column corresponded to the time development 10
of inflow events. Observed levels of dissipation of turbulent kinetic energy per unit mass, 11
1.1×10-7 W kg-1, and eddy diffusivity, 7.3×10-4 m2 s-1, were comparable to direct 12
measurements at other coastal sites and shelves with rough topography and strong forcing.
13
During spring tides, an average upward heat flux of 5 W m-2 in the under-ice boundary layer 14
was observed. Instantaneous (1-h averaged) large heat flux events were correlated with 15
periods of large inflow, hence elevated heat fluxes were associated with the tidal jet and its 16
heat content. Vertical heat fluxes are derived from shear-probe measurements by employing a 17
novel model for eddy diffusivity (Shih et al., 2005). When compared to direct heat flux 18
measurements using the eddy correlation method, the upper 3-10 m averaged heat flux 19
estimates from the microstructure profiler agreed with the direct measurements averaged at 1 20
and 5 m below the ice to within 10%. During the experiment destabilizing buoyancy fluxes 21
were recorded close to the ice, but overall, turbulence production was dominated by shear. A 22
scaling for dissipation employing production by both stress and buoyancy (Lombardo and 23
Gregg, 1989) was found to be appropriate for the under-ice boundary layer.
24
Keywords and regional terms 1
mixing; turbulence; fast ice; fjords; Arctic; Svalbard; Van Mijenfjorden 2
1. Introduction 3
During winter and early spring, the surface ice cover over seasonally frozen Arctic fjords 4
prevents energy input from the wind and low run-off significantly reduces the estuarine 5
circulation. Remaining major sources of energy for mixing are convection induced by salt 6
rejection from the ice, the response to the atmospheric disturbances in the ice free coastal 7
waters at the entrance to the fjord, and the tidal motions. In a sill fjord, the energy can be 8
extracted from the barotropic tide through processes including friction against boundaries, 9
baroclinic wave drag, tidal jets and high-frequency internal waves (Farmer and Freeland, 10
1983; Stigebrandt and Aure, 1989). The progressive internal waves generated at a sill can 11
break at the sloping sides of a fjord contributing to the vertical mixing of the fjord basin 12
(Stigebrandt, 1976). Tidal jets occur when the constriction at the mouth of a fjord is such that 13
the tidal flow is too fast for internal wave generation. Recently, Inall et al. (2004) reported on 14
the energy budget of a jet-type fjord, where 16% of the incident barotropic tidal energy was 15
extracted. The fjord, in neaps, was favorable to internal wave generation and the loss due to 16
baroclinic wave drag increased by three fold with respect to springs. The transfer processes 17
governing the vertical distribution of mass, heat, and momentum are crucial for deep water 18
renewal, nutrient transfer into the surface layer and, in ice-covered fjords, for heat supply 19
towards the ice.
20
The sea ice provides a stable platform from which highly accurate oceanic turbulence 21
flux measurements can be made using eddy-correlation methods. Such experiments were 22
conducted in the past three decades following the seminal work of McPhee and Smith (1976) 23
contributing to our understanding of the under-ice boundary layer and the oceanic boundary 24
layer, in general. Such direct flux measurements are rare in the ice-free ocean (Fleury and 25
Lueck, 1994; Moum, 1996). Instead, fluxes are inferred from shear, conductivity or 1
temperature variances resolved at dissipation scales by sensors mounted on profiling or towed 2
instruments (Gregg, 1987; Moum et al., 2002) or on manned or autonomous underwater 3
vehicles (Osborn and Lueck, 1985; Fer et al., 2002; Thorpe et al., 2003) and using 4
challengeable assumptions (e.g. isotropy, homogeneity, simplification of turbulent budget 5
equations).
6
The majority of under-ice turbulence measurements were conducted from drifting 7
pack-ice (e.g., McPhee, 1992; McPhee and Martinson, 1994; McPhee and Stanton, 1996) 8
under conditions covering near-neutral, stabilizing and de-stabilizing surface fluxes. Studies 9
from land-fast ice (fast ice, hereinafter) were made in the Canadian Arctic, e.g. in Resolute 10
Passage (Shirasawa and Ingram, 1997), in Hudson Bay (Shirasawa and Ingram, 1991), and in 11
Barrow Strait at ∼160 m water depth (Crawford et al., 1999), as well as from an artificially 12
constructed growing thin sea ice pool in Saromo-ko Lagoon in Japan (Shirasawa et al., 1997).
13
Among the relevant work, only McPhee and Stanton (1996) and Crawford et al. (1999) 14
obtained both types of oceanic turbulence measurement: 1) time series of direct turbulent 15
fluxes at several vertical levels under the ice 2) vertical profiles of turbulent structure through 16
microstructure shear and/or temperature. Here we report on measurements of both types 17
under fast ice in a tidally-active Arctic fjord at a depth of about 75 m, much shallower than 18
the site studied by Crawford et al. (1999). Following Turner (1973), who differentiated 19
between “external mixing” induced by surface and bottom generated turbulence and “internal 20
mixing” induced by processes typically in the pycnocline away from the boundaries, we 21
might expect the external and internal mixing to interact and cover a much larger portion of 22
the water column compared to deeper waters. The level of mixing across the pycnocline is 23
particularly important in supplying nutrient rich water into the surface layer as well as for 24
supplying heat towards the ice contributing to its thermodynamic balance.
25
Due to their accessibility and relatively stable ice conditions, Arctic fjords offer suitable 1
laboratories for studies on first year sea ice. The field experiment described here was 2
conducted in Van Mijenfjorden in the Svalbard archipelago as part of an atmosphere-ice- 3
ocean interaction study aiming at processes that govern the growth and decay of sea-ice. The 4
focus of this paper is to describe the oceanographic context throughout the experiment, report 5
on nearly full water column turbulence observations, identify processes responsible for 6
mixing and compare microstructure profile and eddy-correlation measurements in early 7
spring 2004.
8
The structure of the paper is as follows. We describe the site and experiments in section 9
2, together with the data sampling and reduction processes for different types of turbulence 10
measurement. The oceanic background including tides, currents and the hydrography during 11
the time of the observations are given in section 3. The mixing in the water column, heat 12
fluxes under the ice and evolution in a tidal cycle are described in section 4. Discussion in 13
section 5 addresses eddy diffusivity estimates and comparison with other work conducted 14
under-ice, in the ice-free open ocean and on shelves. A summary and concluding remarks are 15
given in section 6.
16
2. Experimental methods and data reduction 17
2.1. Experiment 18
The experiment was conducted over the ice-covered Van Mijenfjorden on the island of 19
Spitzbergen in the Svalbard archipelago (Figure 1). The 110 m deep fjord is about 68 km 20
long and 10 km wide. Observations were made for 18 days from 11 March 2004 at a station 21
established over 1.2 m thick, undeformed ice on the 75-m isobath, about 10 km from the 22
mouth of the fjord, which is partially blocked by an island.
23
During the experiment the atmospheric conditions were relatively mild and the ice 1
gradually warmed, with a heat conduction of about 6 W m-2 in the lower part of the ice 2
inferred from the vertical temperature gradient measured by thermistors embedded in the ice 3
(Widell et al., 2006). The melting season typically begins in May-June.
4
The instrumentation deployed comprised two Aanderaa current metres (RCM) 5
nominally at 10 and 50 m below the ice, two sets of turbulence instrument clusters (TIC, 6
section 2.1.1 ) nominally at 1 and 5 m below the ice and a microstructure profiler (MSS, 7
section 2.1.2) profiling between about 3 m under the ice to 60 m depth. The RCMs sampled 8
the horizontal current every 10 min between 12 – 29 March 2004. The three sets of data used 9
in this study were collected from hydroholes approximately forming a triangle with sides 50 10
m (MSS-TIC), 130 m (RCM-TIC), and 100 m (MSS-RCM), with MSS station located at 77°
11
43.0′N and 15° 10.5′E. The bulk of the data presented is from 21-29 March when MSS was 12
deployed. The time convention used is such that day of year (doy) 0.5 corresponds to UTC 13
noon at 1 January 2004 and 21 March 2004 starts at doy = 80. A more detailed account on the 14
complete TIC record is presented in Widell et al. (in prep.).
15
2.1.1 Moored turbulence measurement and processing details 16
Time series of temperature, T, conductivity, C, and three orthogonal components of 17
velocity were acquired and averaged at 2 Hz by instruments clustered at nominally 1 m and 5 18
m below the ice. In addition to the slow time-response but relatively accurate conductivity 19
units (SBE4C) installed at both levels, a fast-response dual-needle conductivity sensor 20
(SBE7) was mounted at 1 m. Temperature and 3-D velocity were measured at approximately 21
the same point by fast response SBE3F sensors and 5 MHz SonTek ADVOcean Doppler 22
current meters.
23
Salinity, S, is calculated in practical salinity units (psu) using the measured T, C, and 24
pressure at the measurement level. Turbulent fluxes are calculated at 15-min intervals by the 25
eddy-correlation method. At each segment the velocity components are aligned with the 1
streamline such that u, v, and w are the longitudinal, transverse and vertical (positive 2
upwards) components and 〈v〉 and 〈w〉 vanish. Here and in the following angle brackets 3
denote averaging1. Fluctuating quantities, denoted by prime, are obtained by linearly 4
detrending each segment. Fluxes are obtained by zero-lag covariances invoking Taylor’s 5
frozen turbulence hypothesis. Turbulent heat flux is FH = ρCP〈w′T′〉, in units of Wm-2, where 6
ρ is the density and CP is the specific heat of seawater. Reynolds stress per unit mass is τr = 7
〈u′w′〉 + i〈v′w′〉, expressed in complex notation where i = (-1)1/2, and local friction speed is u*
8
= |τr|1/2. The salinity flux QS = 〈w′S′〉, in units of psu m s-1, is resolved only at 1 m below the 9
ice where the fast response conductivity sensor was mounted. The low-response conductivity 10
units do not sufficiently resolve the inertial subrange and underestimate salt fluxes by 11
typically 25% (McPhee and Stanton, 1996). QS is sensitive to the absolute salinity and is 12
calculated after careful in situ calibration of fast response conductivity sensor. The calibration 13
is conducted, as detailed in Widell et al. (2006), every 15 minutes against the relatively 14
accurate SBE4C.
15
2.1.2 Turbulence profiler measurement and processing details 16
The microstructure data were collected at 1024 Hz using a loosely-tethered free-fall MSS 17
profiler (Prandke and Stips, 1998) equipped with airfoil shear probes and fast response 18
conductivity and temperature (FP07) sensors. The profiler comprises an acceleration sensor 19
and conventional conductivity-temperature-depth (CTD) sensors for precision measurements.
20
Microstructure data are processed as described in Fer (2006). The dissipation rate of turbulent 21
kinetic energy per unit mass, ε in units W kg-1, is calculated using the isotropic relation 22
2
7.5 uz
ε = ν , where ν is the viscosity of seawater (∼1.9×10-6 m2 s-1 for the cold temperatures 23
recorded in this study), and uz is the shear of the horizontal small-scale velocity. The 24
instrument fall speed (∼0.6 m s-1) is used to convert from frequency domain to vertical 25
1 Throughout the paper 〈.〉 is used interchangeably denoting MSS-set averages, survey-means, 15-min averaged
wavenumber domain using Taylor’s hypothesis, and the shear variance, u2z , is obtained by 1
iteratively integrating the reliably resolved portion of the shear wavenumber spectrum of 2
half-overlapping 1-s segments. Narrow band noise peaks induced by a probe guard are above 3
the wavenumber range chosen for the analysis. Typical commonly accepted uncertainty in 4
shear-probe ε measurements is a factor of two (Moum et al., 1995). Dissipation data in the 5
upper 3-4 m (2-3 m below ice) are unreliable due to the initial adjustment to the free-fall.
6
The profiles of precision CTD (corrected against available SeaBird 19 SeaCat CTD 7
profiles) and ε are produced as 10 cm and 50 cm vertical averages, respectively. A sequence 8
of 4-7 microstructure profiles (set hereafter) was acquired typically around 11:00 and 16:00 9
UTC between doy = 80-85 and doy = 87-89. The duration of each set was less than 0.5 h. A 10
set ensemble of 50-cm vertical bin averaged dissipation profile thus consists of 8-14 data 11
points when both shear probes acquired acceptable data.
12
The diapycnal eddy diffusivity is estimated using Kρ = 2ν(ε/νN2)1/2, valid for ε/νN2 >
13
100 (Shih et al., 2005). Here and throughout the buoyancy frequency, N=(-g/ρ ∂ρ/∂z)1/2, is 14
calculated using Thorpe-ordered σθ profiles (Thorpe, 1977) with density gradient obtained 15
from the slope of linear fits of σθ against depth in 4-m sliding boxcar windows. The 16
application of this model differs from the common practice of using Kz ≤ Γε/N2 (Osborn, 17
1980), with a typical value of Γ = 0.2 and is discussed in section 5.1.
18
3. Oceanic background: Tides, currents and hydrography 19
The island, Akseløya, across the mouth of the fjord restricts the exchange between the 20
basin and outer coastal water masses to between two sounds: Akselsundet in the north and 21
Mariasundet in the south (Figure 1). The majority of the exchange takes place at the deeper 22
(sill depth of 34 m) and wider (1.1 km) Akselsundet. The inflowing current is influenced by 23
the Atlantic water and is typically warmer than the basin water. The fjord, at the time of the 24
measurements, is completely covered by ice which prevents energy input from the wind.
1
Current measurements and numerical model results reported by Bergh (2004) yield a pattern 2
consisting of tidal motion with superimposed cyclonic circulation. There is in-fjord flow 3
along the southern coast (crossing our measurement site) nearly at all times compensated by a 4
dominant out-fjord flow along the northern coast, creating a net cyclonic circulation. At the 5
main entrance, Akselsundet, flow is in-fjord during floods and out-fjord during ebbs, 6
reaching maximum velocities of about 1.5 m s-1 and 2.5 m s-1, respectively. During floods, 7
tidal choking (Stigebrandt, 1980) creates tidal jets with estimated total volume flux of about 8
(20-30)x103 m3s-1, and energy of order 1013 J (Bergh, 2004). The jet loses only about 1% of 9
its energy to friction (bottom and ice) and is therefore the main driving force for the mean 10
circulation. The loss in generating mid-column turbulence, however, was not evaluated.
11
The current recorded by RCMs are rotated into along and across principal axis (PA) 12
components where PA aligned at 53° clockwise from north, approximately along the 13
coastline. At the station, there is inflow, i.e. into the fjord, at all times. Along PA current (Ua) 14
accounted for more than 98% of the total variance and when averaged over the total duration 15
of 16.85 days Ua = 13.8 cm s-1 at both 10 m and 50 m depth. The major/minor axis half 16
lengths are 6.8/3.1 cm s-1 at 10 m and 8.3/2.8 cm s-1 at 50 m, respectively.
17
Harmonic analysis of hourly averaged currents recorded by the RCMs resolved the 18
semidiurnal constituents (M2 and S2) with signal-to-noise ratio greater than 2 at both depths.
19
The tidal amplitude along the PA is UM2 = 0.04 (±0.02) m s-1 at 50 m for the dominant M2 20
constituent. The corresponding tidal excursion amplitude, UM2/ωM2, is 285 (±142) m using 21
the M2 frequency ωM2 = 1.4052×10-4 s-1. Note that at this latitude the inertial frequency f = 22
1.425×10-4 s-1 is slightly larger than ωM2 and cannot be distinguished in the harmonic 23
analysis. At both levels the resolved semidiurnal components accounted for only ∼18% of the 24
along PA variance. Most of the turbulence profiling was conducted during spring tides 25
(Figure 2a). Low-passed currents show low-frequency oscillations, particularly during the 1
first part of MSS-sets around doy 82-83, when a strong reversal decreases Ua to nearly nil.
2
Although the measurements at 10 and 50 m suggest a strongly barotropic structure, the 3
horizontal velocity structure for second to fourth baroclinic modes (Figure 3b) shows nearly 4
equivalent contributions at the measurement depths, hence we cannot exclude baroclinicity.
5
A composite θ-S diagram for all 12 MSS sets show significant variability, although 6
within a narrow range of θ - S values, not directly associated with the tidal cycle (Figure 4, 7
section 4.3). The temperatures are always less than -1.7 °C, but are above the freezing point.
8
The spring profiles (sets 1-9) are relatively warmer as a consequence of warmer inflow 9
brought in by the tidal jet. During neaps (the later MSS sets 10-12), the nearly mixed water 10
column is rapidly stratified (set 12). The profiles do not show an obvious mixing line between 11
two water masses and suggest that the hydrography at the site is mainly determined by the 12
dominating advective inflow properties. The salinity is the stratifying agent at all times and 13
the conditions are stable to double-diffusion. When derived over all profiles the survey-mean 14
buoyancy frequency is 〈N2〉1/2 = 1.8×10-3 s-1 or ∼ 1 cycle per hour (cph, 1 cph = 2π/3600 s-1).
15
The depth of surface mixed layer (D) calculated using the split-and-merge method (Thomson 16
and Fine, 2003) is ∼9 m on the average and varies between 3 m (doy = 83.45) and 30 m (doy 17
= 83.68) 18
The frequency spectra of the horizontal current are calculated for 3.56 day windows 19
(fft length of 512) as the sum of the clockwise (CW) and counterclockwise (CCW) rotary 20
component spectra ΦCW and ΦCCW (Gonella, 1972). The spectra show a shoulder extending 21
between the harmonic MK3 up to 0.4 cph, particularly at 10 m depth about 9 m below the ice 22
(Figure 5). The spectral noise level at 50 m is about 1 (cm s-1)2/cph (slightly lower at 10 m), 23
and when integrated over 0.1-2 cph frequency band, corresponds to a horizontal velocity 24
error less than 1.5 cm s-1, in the rms sense.
25
The energy levels are slightly elevated above the Garrett-Munk level (Garrett and 1
Munk, 1972; Munk, 1981) derived using so-called GM79 form presented in Levine et al.
2
(1997) using the survey-mean N. Although there are no exceptional peaks at tidal-interaction 3
frequencies (e.g., M4, M6, etc), the shoulder at the internal wave continuum is possibly due to 4
non-linear internal wave interaction mechanisms at this coastal site covered by a “rigid lid”.
5
A nearly-linear interaction between a single harmonic, e.g. M2, would result in more peaked 6
higher harmonics (e.g., M4 and M6). We lack full-water column coverage of the current and 7
cannot delineate the barotropic and baroclinic components. However, the frequency spectrum 8
of the “rotary coefficient”, CR (Gonella, 1972) 9
CR(ω) = [ΦCW(ω) - ΦCCW(ω)] / [ΦCW(ω)+ ΦCCW(ω)] (1) 10
can be used as an indicator for internal wave polarization (van Haren, 2003, 2004). For purely 11
rectilinear motion CR = 0, whereas CR = 1 indicates a circular motion. In the internal wave 12
continuum between the inertial frequency, f, and the buoyancy frequency, N, free internal 13
waves are described by 14
R 2 2
C ( ) 2 f
f ω = ω
ω + (2)
15
The frequency spectra of CR (Eq.(1)) are shown together with the rotary energy ratio for 16
linear internal waves (Eq.(2)) in Figure 5c-d. At both levels (at 10 and 50 m), the polarization 17
within the semi-diurnal band and lower frequencies was weak, suggesting motions of 18
barotropic nature. Elevated CR follows the shape expected from linear internal waves starting 19
from frequencies of M4 (at 10m) and MK5 (at 50m) upto N ( 1 cph). We conclude the 20
frequencies larger than about M4 are associated with possibly non-linear internal waves. The 21
total mean horizontal kinetic energy per unit mass, HKE = ½(u2+v2), is 1.3×10-2 J kg-1 22
averaged over both depths. Assuming that the frequency band between ωM4 and N is 23
associated with baroclinic energy, we integrate (between ωM4 and N) the HKE spectrum 24
(1/2(ΦCW + ΦCCW)) averaged over both depths to obtain 5×10-4 J kg-1, i.e. ∼4% of the total 1
HKE. The linear internal wave speed for the first baroclinic mode, derived from set-mean 2
MSS N2-profiles varies between 2 and 5 cm s-1. 3
4. Mixing levels 4
4.1. Mixing in the water column 5
The dissipation in the water column was typically characterized by enhanced values 6
close to the ice decreasing with distance from the ice to background values of order 10-8 W 7
kg-1 (Figure 6). Among the microstructure profiles, those conducted on doy = 84.4 was at the 8
time of maximum inflow (larger currents occurred, however, not at the time of MSS profiles, 9
Figure 7a) and the whole water column was exceptionally turbulent (Figure 6e). Over all 10
MSS sets, the buoyancy Reynolds number, or turbulent activity index Reρ = ε/νN2, spanned 11
five orders of magnitude between 4×102 and 4.7×107 with a survey-mean of 〈Reρ〉 = 1.5×105 12
and all values above the threshold of about 200 when local isotropy is believed to be achieved 13
(Yamazaki and Osborn, 1990). The maximum likelihood estimator (mle) from lognormal 14
distribution (Baker and Gibson, 1987) of dissipation is 〈ε〉= 1.1×10-7 W kg-1 with 95%
15
confidence intervals of 9.8×10-8 – 1.2 ×10-7 W kg-1. The values of eddy diffusivity ranged 16
from 7×10-5 to 2×10-2 m2 s-1 with mle of 〈Kρ〉 = 7.3×10-4 m2 s-1 and 95% confidence intervals 17
of 6.9 – 7.8 ×10-4 m2 s-1. The values of ε and Kρ are reduced by 44% and 22%, respectively, 18
when the profiles at doy = 84.4 are not included. The survey-mean values are 10-100 times 19
greater than typical values found in the open ocean thermocline (Gregg, 1998) and are 20
comparable to other shelf studies (section 5.4). The depth averaged total horizontal energy 21
density, 1.3×10-2 J kg-1, would be dissipated in 1.5 days, using ε = 10-7 W kg-1. 22
The heat flux, FH = -ρCP 〈dT/dz〉 〈Kρ〉, profiles are calculated from MSS-sets at 5-m 23
moving vertical intervals using only the portions when the vertical temperature gradient was 24
greater than twice its error estimate. The time development of mixing and heat flux in the 1
water column is shown in Figure 7 together with the hydrography, the observed currents and 2
a representative background bulk shear, Sh = ((∂u/∂z)2+ (∂v/∂z)2)1/2, calculated using the 3
RCM currents at 10 and 50 m. Relatively warm patches of water advected by the tidal jet lead 4
to upward heat fluxes of up to 20 W m-2. Below a depth comparable to the sill depth at 5
Akselsundet, the temperature typically decreases with depth, yielding negative heat fluxes of 6
comparable magnitude.
7
Sequences from two selected MSS sets are shown in detail in Figure 8. Both sets were 8
collected during spring tides, but that on doy 82.6 was during ebb and with the lowest 9
recorded Ua whereas that on doy 84.4 was during flood and with the largest recorded Ua
10
(Figure 2). The time interval between profiles of each set is about 5 min, however, both the 11
temperature profiles and the microstructure vary substantially. During ebb with low Ua, the 12
microstructure shear is relatively quiescent, but intermittent events (such as that at ∼25 m at 13
profile 4) occur which cannot be tracked between subsequent profiles. A mean vertical 14
temperature gradient persists in the upper and lower 20 m of the temperature profiles towards 15
warmer, nearly well-mixed mid-column water. This warm core has low small scale 16
temperature gradient but is capped by relatively turbulent layers at the top and bottom.
17
During spring tide and large Ua, the temperature profiles are more irregular and variable. In 18
mid-column, warm water appears to advect through the sequence of profiles, mixing the cold 19
core at profile 1 (note the activity in T and dT/dz at profile 2) to a nearly homogeneous 20
column by profile 4 and further leaving a signature of temperature maximum at about 35 m.
21
Compared to doy 82.6, microstructure shear is elevated throughout the water column, and 22
particularly in the upper layers close to the ice due to TKE produced by swifter current at the 23
under ice boundary. Despite the increase in shear levels, the temperature gradient is not 24
exceptionally elevated at doy 84.4, and we note, in general, that patches of turbulent activity 1
in shear and temperature do not often correspond.
2
4.2. Under-ice boundary heat fluxes 3
Under-ice boundary layer heat fluxes were directly measured by TICs as 15-min 4
covariances at 1-m and 5-m below the ice. Here we present hourly averages over both depths, 5
representative of the heat fluxes in the boundary layer and compare to that derived from 6
profiler measurements within 10-m below the ice (Figure 9). The sub-set of FH time series 7
covering the MSS deployment period ranges from -8 to 41 W m-2, with a time average of 5 W 8
m-2, towards the ice (Figure 9). This is comparable to the mean conductive heat flux of ∼6 W 9
m-2 in the lower part of the ice. Large heat flux events correlate with the periods of large Ua
10
(compare Figure 7a and Figure 9), which can be associated with the tidal jet and its heat 11
content. MSS-set averaged FH in the upper 10 metres below the ice agree satisfactorily with 12
the direct measurements (Figure 9). Due to under-sampling in time, the majority of large heat 13
flux events are not captured by the profiling. When the data point when the temperature 14
gradient was not significantly different than its error estimate is ignored (filled square in 15
Figure 9), the agreement between MSS-derived FH and the TIC segments closest to the MSS 16
deployment is within 10%. We emphasize that we use the Kρ model suggested by Shih et al.
17
(2005). When the Osborn model is employed, the MSS overestimates FH by a factor 17, on 18
average.
19
4.3. Evolution in tidal cycle 20
The mean evolution in one semidiurnal tidal cycle is derived as follows. Using the 21
harmonic tidal analysis results, we assign the corresponding phase of the dominant lunar 22
semidiurnal tide, φM2 at each measurement time (every 1 h for tide prediction, 15-min for TIC 23
sampling, 10 min for RCMs, and the mean deployment time of each MSS set). All ensembles 24
covering the full φM2 are then averaged in 20° bins of φM2. For typically log-normal variable 1
such as ε, the mle value with 95% confidence intervals is calculated. Figure 10 shows the 2
mean cycle for selected parameters. The floods, defined as in-fjord (Utide > 0), are 3
approximately when φM2<90° and φM2>270°. The scatter in Figure 10a represents individual 4
M2 cycles and cover the spring-neap range. The mean structure of 40-m Sh2 is of comparable 5
magnitude to N2 at times of MSS-sets, however, the structure in Figure 10b is informative but 6
not conclusive. Mean vertical gradients of salinity and temperature (shown as contributions to 7
the density gradient, αdT/dz and βdS/dz, Figure 10c) do not have a clear signature suggesting 8
advection by the tidal cycle. Throughout the survey the contribution of temperature to the 9
density is negligible and salinity is the stratifying agent. The mean dissipation inferred from 10
the inertial subrange of the vertical velocity fluctuation spectrum derived from TICs is lower 11
at 5 m than at 1 m, consistent with a decrease in shear production of TKE with increasing 12
distance from wall. The rate of working by the Reynolds stress at 1 m below the ice, ρu*3, is 13
at least an order of magnitude less than the water column (3-60 m) integrated dissipation rate 14
with no apparent tidal cycle.
15
The lack of strong correlation between the mixing variables and the inferred M2-cycle 16
at the measurement site, as well as the fact that the resolved tidal components accounted for 17
only 18% of the variability (section 3), leads us to examine the mean structure at a window 18
centered at the time of maximum inflow events. The along PA current data at 50 m is low- 19
passed with a cut-off period of 6 h and de-meaned time series is used to detect times of 20
maximum flow (assigned t = 0) within each zero (here defined as 2 cm s-1) crossing. In total, 21
24 such events are detected (circles in Figure 2b) and ensembles of relevant data within ±6 h 22
of each event are extracted. Only 7 of 12 MSS-sets were within this time window. The 23
average structure is summarized in Figure 11. On the average, the maximum Ua develops 24
from and decays to ∼10-15 cm s-1 within t = ±2 h when it reaches a peak value of ∼30 cms-1. 25
The dissipation inferred from TICs at both levels and the work under ice at 1-m show 1
significant correlation with the ensemble-mean Ua cycle, with an asymmetric structure 2
increasing in the 2 hours before t=0 and decaying slowly in the subsequent 4 hours. Although 3
not significant at 95% confidence level, the shear is slightly elevated at t= -2 h when 4
acceleration commences, and shear overcomes stratification at t ∼ ±2 h.
5
5. Discussion 6
5.1. Eddy diffusivity and mixing efficiency 7
An upper limit for diapycnal eddy diffusivity, Kρ, is routinely estimated from shear- 8
probe dissipation measurements using the Osborn model Kz ≤ Γ〈ε〉/〈N2〉 (Osborn, 1980), 9
using a typical value of Γ = 0.2 (Moum, 1996). The parameter Γ is related to the flux 10
Richardson number, or mixing efficiency, Rf as Γ = Rf/(1-Rf). The mixing efficiency is 11
defined as Rf = FB/PS, where FB is the buoyancy flux and PS is the TKE production by mean 12
shear. The buoyancy flux is FB = -PB = g/ρ〈w′ρ′〉, where PB is the TKE production by 13
buoyancy, and assuming a steady-state TKE balance of the form PS + PB = ε, Rf = FB/(FB+ε), 14
i.e. the ratio of energy loss by working against the stratification to the rate of production by 15
the Reynolds stress in a shear flow. Ellison (1957) found theoretically that a critical 16
maximum value at which the turbulence persists is Rf = 0.17, giving Γ = 0.2. Reports from 17
oceanographic observations are in the range Rf =0-0.3 (Ruddick et al., 1997) and recent 18
studies indicate Rf = 0.11 (St. Laurent and Schmitt, 1999; Arneborg, 2002). Accordingly, the 19
estimates for Γ are highly variable leading to large uncertainties in application of the Osborn 20
model.
21
Recent laboratory results (Barry et al., 2001) and direct numerical simulations (Shih et 22
al., 2005) showed that for Reρ <1000 the Osborn model using Γ = 0.2 overestimated the 23
measurements by a factor of 2, and for larger Reρ the discrepancy systematically increased.
24
For our survey mean Reρ ∼ 105, the expected discrepancy is a factor of 32, much larger than 1
the typical factor 4 uncertainty assigned to Kρ inferred from the Osborn model (Oakey, 2
1982). When compared with diffusivities (or heat fluxes) from direct eddy-correlation 3
measurements, the Osborn model over-estimated the measurements by a factor 8 in the 4
thermocline at the equator (Moum, 1990) and by a factor of 20 in an estuary (Etemad- 5
Shadidi and Imberger, 2005). Shih et al.’s (2005) data for Reρ=ε/νN2 > 100 were best 6
explained by the diapycnal eddy diffusivity Kρ = 2ν(ε/νN2)1/2, providing for a novel model 7
independent of the mixing efficiency.
8
The excellent agreement between the direct measurements of the heat flux and that 9
derived from MSS measurements using the Shih et al. (2005) model is encouraging and 10
contributes to the model’s validation in an oceanographic setting (section 4.2). Our data set, 11
however, does not allow for more general conclusions.
12
Using the salt and heat fluxes measured at 1-m below ice, we can calculate the 13
buoyancy flux FB = g/ρ〈w′ρ′〉 ≡ g [β〈w′S′〉 - α〈w′T′〉], and together with the measured 14
dissipation we obtain Rf = FB/(FB+ε), for a steady state TKE budget. Another estimate of 15
shear production is the Reynolds stress squared divided by the eddy viscosity, or using PS = 16
u*3/λ, where λ is the mixing length scale of turbulence at the measurement level. This gives 17
Rf = FB/ (u*3/λ). The mixing length is estimated from the wavenumber corresponding to the 18
peak in the variance- preserving w′ spectrum (McPhee, 1994). The values of Rf are obtained 19
using both methods. Negative values of Rf indicate a destabilizing buoyancy flux whereas 20
those between -1 and 0 indicate that production is dominated by shear. Alternatively, a 21
measure of the effect of surface buoyancy flux is the Monin-Obukhov length, LMO = 22
u*3/(κFB), where κ = 0.4. As defined, L<0 indicates a destabilizing buoyancy flux, and 23
identifies a length scale when the buoyancy terms and shear production terms are of similar 24
ensembles with simultaneous FB, ε and λ values, only two values of Rf were greater than zero 1
with values 1.9 and 129 and two were less than -1 (-1.7 and -2.8). Using the remaining 228 2
data points the histograms (for –Rf and –LMO, to be able to plot in a log10 base) are presented 3
in Figure 12. The distributions are nearly log-normal, which is consistent with previously 4
reported data for stable conditions (Peters and Gregg, 1988; Ruddick et al., 1997). The mle 5
values are -0.11 and -0.13. For comparison oceanic values of stably stratified shear-generated 6
turbulence are 〈Rf〉 = 0.11 (Peters and Gregg, 1988), 〈Rf〉 = 0.15 (Ruddick et al., 1997) and 7
〈Rf〉 = 0.11 (St. Laurent and Schmitt, 1999). At 1m 〈LMO〉 = -14.8 giving z/-LMO <<1, hence 8
production is dominated by shear. As discussed in Widell et al. (2006), the slightly 9
destabilizing buoyancy flux at 1 m is due to salt release from warming sea ice. Such coherent 10
brine plumes were observed throughout the spring tides when the oceanic heat flux induced 11
by the tidal inflow was significant. No signature of the plumes, however, was found at TIC at 12
5 m, indicating that the negative buoyancy fluxes and the illustrated Rf and LMO in Figure 12 13
are only representative of the surface layer under the ice. The background stratification in the 14
water column is stable and overall turbulence production is dominated by shear, so we can 15
use the Shih et al. (2005) model devised for stable stratification with some confidence.
16
5.2. Comparison with relevant work under ice 17
Crawford et al. (1999) reported on turbulence measurements in the mixed layer under 18
first-year fast ice in Barrow Strait during April-May 1995. Their measurements comprise 19
upper 110m (45 m above sea bed) microstructure profiles as well as TICs deployed in the 20
under-ice boundary layer. They found energetic turbulence associated with strong currents 21
(sometimes in excess of 20 cm s-1) during springs and an eddy diffusivity proportional to 22
current speed with values up to 2×10-2 m2 s-1, on the average. A strong asymmetry in eddy 23
diffusivity (up to a factor 7) was observed associated with advection of horizontal salinity 24
(density) gradients during the tidal cycle. During the part of the tidal cycle when the mixed 1
layer salinity is decreasing, they identified advection as a process which can create conditions 2
similar to destabilizing buoyancy flux as if freezing was occurring (the advection close to the 3
ice is retarded due to friction and low salinity water deeper is horizontally advected 4
generating effectively unstable conditions). This is an important observation suggesting an 5
alternative discussion for destabilizing buoyancy fluxes recorded in our survey. We did not 6
measure the horizontal density gradients, however, the vertical salinity gradients contributing 7
most to the density structure did not show a clear relation with the tidal cycle (Figure 10).
8
The time evolution of salinity measured by TICs represents the horizontal gradients in the 9
along-stream direction, however, no indication of tidal advection of salinity gradients was 10
seen.
11
The under-ice studies by Shirasawa and co-authors (Shirasawa and Ingram, 1991, 12
1997; Shirasawa et al., 1997) were done using eddy-correlation techniques, similar to TIC 13
deployment, typically 0.5 – 0.7 m below ice undersurface, with focus on the ocean-ice heat, 14
momentum, exchange. For Resolute Passage they reported a mean oceanic flux of 32 Wm-2 15
towards the ice over 12 day sampling period, with a mean eddy viscosity (KM ∼ O(Kρ)) of 16
∼10-3 m2 s-1, based on measured friction speed of 5.6×10-3 m s-1 and assuming neutral scaling.
17
The growing thin ice experiment in Saroma-ko Lagoon was of 1 day duration and similar 18
upward heat fluxes (33 W m-2) during non-convective period in the day more than doubled 19
during ice-growth in the night (KM = 3.9×10-4 to 6.5×10-4 m2 s-1).
20
In the outer (Ekman) part of neutrally stratified planetary boundary-layer under 21
drifting sea ice, the eddy diffusivity has been found to scale as Kρ = 0.02u*2
/f, where f is the 22
Coriolis parameter (e.g., McPhee and Martinson, 1994). Using eddy-correlation 23
measurements of heat flux and turbulent stress and the vertical profiles of temperature and 24
velocity, McPhee (1992) reported eddy diffusivities as high as 1.5×10-1 m2 s-1 in the Ekman 25
layer under drifting ice encountering strong tidal forcing over the Yermak Plateau slope in 1
Fram Strait. In the Ekman layer underneath drifting pack ice during a storm in the Weddell 2
Sea, an eddy diffusivity of around 0.019 m2s-1 was reported in McPhee and Martinson (1994).
3
McPhee and Stanton (1996) reported Kρ = 5.5×10-2 m2 s-1 at depths of around 10 m 4
underneath a freezing lead. These results show how forcing by surface buoyancy fluxes 5
during freezing substantially changes the scales of turbulence in the under-ice boundary 6
layer.
7
The short-term (hourly) heat flux magnitudes presented here of around 2 to >30 Wm- 8
2, are roughly comparable to the short-term variability reported in the studies mentioned 9
above. The mean value corresponds fairly well to that encountered underneath drifting ice in 10
the Arctic. Maykut and McPhee (1995) computed the oceanic heat flux from water 11
temperature and drift speed measurements from the AIDJEX experiment in 1975, estimating 12
an annual mean of around 5 W m-2 with maximum values in summer in excess of 40 W m-2. 13
Their observations further indicated that in the central Arctic, incoming shortwave radiation 14
is the major source of heat to the oceanic heat flux, rather than diffusion from warm water 15
below. During the year-long SHEBA campaign, the oceanic heat flux as estimated from ice 16
temperature and ice mass balance measurements was found to vary over different ice types 17
with a mean for an undeformed multi-year floe of 7.5 W m-2 (Perovich and Elder, 2002).
18
Based on drifting buoy temperature and salinity data and u* computed from satellite ice drift 19
data, Krishfield and Perovich (2005) estimated a basin-wide annual mean value for the Arctic 20
ocean of 3-4 W m-2. 21
Our data were collected in March when the sun angle was low with short daylight, and 22
there were no openings in the ice except at the fjord mouth. We therefore do not expect 23
significant radiative contributions to the under-ice heat balance. The hydrographic data and 24
turbulence measurements indicate that the bulk of the oceanic heat supply stems from upward 1
mixing from the core of inflowing water.
2
5.3. Comparison with ice-free ocean surface boundary layer 3
Heat, momentum, and gas exchange between the ocean surface and atmosphere are 4
governed by a combination of processes that can be categorized by those affecting the upper 5
surface layer (e.g., precipitation, surface gravity wave breaking, temperature ramps), those 6
extending below or covering a significant portion of the mixed layer (e.g., convective plumes 7
and Langmuir circulation) and those with manifestations at the base of the mixed layer 8
(inertial shear, Kelvin-Helmholtz instability, internal gravity waves) (Thorpe, 1995; Garrett, 9
1996; Moum and Smyth, 2001). Anis and Moum (1995) compiled a summary of aquatic 10
surface layer dissipation observations including their measurements. The dissipation rates 11
were sometimes predicted well by law-of-the-wall stress scaling, εs = u*3/κz (κ=0.4 is von- 12
Karman constant), whereas in other cases there was a discrepancy of more than an order of 13
magnitude, suggested to be due to surface wave-related turbulence. Using data from shear- 14
probe equipped Autosub running at horizontal transects in the upper surface layer, Thorpe et 15
al. (2003) identified breaking waves, bubble clouds, Langmuir circulation and temperature 16
ramps as the principal processes of mixing in the near-surface layer of the ocean. Below a 17
depth of about six times the significant wave height, vertical mixing due to strong Langmuir 18
cells dominated the production of turbulence. The presence of sea ice partially insulates the 19
surface layer from such processes (e.g. surface wave breaking, Langmuir circulation).
20
However underice topography with a broad spectrum of roughness features from millimeter 21
to order 10 m pressure ridge keels can be another source of energy.
22
Using neutrally buoyant floats at an open ocean site in winter but with weak buoyancy 23
forcing, D’Asaro (2001) measured the vertical velocity variance 〈w′2〉 in the surface layer and 24
times those measured (approximately unity) for both smooth and rough wall boundary layers 1
driven by shear alone in laboratory experiments (Hinze, 1975) as well as in the under ice 2
boundary layer (McPhee and Smith, 1976). He attributed this enhanced turbulent vertical 3
kinetic energy to surface wave breaking or Langmuir circulation. By regressing 〈w′2〉 on 4
locally measured u*2, we obtain 95% confidence intervals for 〈w′2〉/ u*2
of [1.3 1.4] at 1 m and 5
[1.6 1.7] at 5 m below the ice in Van Mijenfjorden. At 1 m, TIC is within the constant stress 6
layer and local u* is representative of the interface value, however at 5 m the above ratio is 7
biased high since we use the local value and the expected decay of u* with distance from the 8
wall. Employing u* at 1 m, the ratio 〈w′2〉/ u*2 at 5 m is between 1.2 and 1.3. The 10%
9
increase at 1 m can be associated with the buoyancy input from salt release from the warm 10
ice (Widell et al., 2006), which is negligible compared to the TKE production by shear 11
(Figure 12). Although the processes suggested by D’Asaro are not at play under fast ice, our 12
observations at 1 m are 30-40% above unity, approximately half the elevation observed in the 13
open ocean boundary layer.
14
When both wind stress and convection are present, Lombardo and Gregg (1989, LG89) 15
found that the dissipation rate profiles in the oceanic mixed layer were well described when 16
scaled by 1.76εs + 0.58FB, where εs = u*3/κz is the law-of-the-wall scaling as above and FB is 17
the surface buoyancy flux. Their dissipation profiles in the mixed layer collapsed to ε/(1.76εs 18
+ 0.58FB) = 0.84. Using the stress and buoyancy flux recorded by TIC at 1 m we evaluate 19
LG89 scaling for both eddy-correlation and MSS measurements (Figure 13). Lacking the 20
mixed layer depth information at the time of each 15-min TIC segment, we normalized the 21
vertical axis for the survey mean D = 9 m for the TIC data. Long time series acquired by the 22
TICs lead to an appropriate averaging over the spring-neap cycle as well as over intermittent 23
turbulent structure and give a statistically significant estimate of the scaling. The MSS 24
profiles, on the other hand, are undersampled in time and are not appropriately representative 25
of the mean turbulent structure. The upper TIC and the MSS estimates at the corresponding 1
level fairly agree both with each other and with LG89 scaling within the measurement 2
uncertainties. The lower TIC at 5 m is slightly above but acceptably close to ε/(1.76εs + 3
0.58FB) = 0.84, suggesting LG89 scaling, on the average, is appropriate for the under-ice 4
boundary layer. Below z/D > 0.25, MSS measurements indicate dissipation 2-5 times greater 5
than that predicted by LG89. The elevated stirring is possibly to due to “interior” mechanisms 6
and episodic events contributing to the TKE production which cannot be explained by 7
boundary layer processes, however when sufficient averaging is performed (see TIC at 5 m), 8
the LG89 scaling nearly holds.
9 10
5.4. Comparison with other shelf studies 11
In contrast to the open ocean, there have been few studies reporting on direct turbulence 12
measurements on fjords and shelves. Observations in the Puget Sound fjord, Seattle (WA, 13
USA), show mixing levels 〈Kρ〉 = 1.8 - 67×10-4 m2s-1, dominated by the passage of a mid- 14
depth density intrusion, possibly related to a strongly advected non-linear tide (Mickett et al., 15
2004). Enhanced turbulence was associated with shear instabilities as well as double- 16
diffusive layers observed in the warm core of the intrusion. Direct measurements in 17
Storfjorden (Svalbard) in September 2003 (Fer, 2006) showed high levels of background 18
diffusivity of order 10-4 m2 s-1 which increased by a factor 10 within the density driven 19
bottom-attached overflow of dense, brine enriched fjord waters produced in winter.
20
Studies of mixing on shelves cover processes associated with the bottom boundary layer 21
(Dewey and Crawford, 1988; Nash and Moum, 2001; Perlin et al., 2005), energetic tidal 22
flows (Rippeth et al., 2003) internal tide, linear and non-linear internal waves and solitons 23
(Sandstrom and Oakey, 1995; Inall et al., 2000; Lien and Gregg, 2001; Rippeth and Inall, 24
2002; MacKinnon and Gregg, 2003; Moum et al., 2003) and near inertial waves (MacKinnon 25
and Gregg, 2005a). Over smooth continental shelf topography dissipation rate measurements 1
and dye-release experiments show 〈Kρ〉 = 0.1 - 5×10-5 m2s-1, away from the surface and 2
bottom mixed-layers (Sandstrom and Oakey, 1995; Sundmeyer and Ledwell, 2001;
3
Lozovatsky and Fernando, 2002; MacKinnon and Gregg, 2003; Ledwell et al., 2004), 4
comparable to the open-ocean thermocline. Rough topography and strong forcing, however, 5
enhance turbulent mixing on the shelf and diffusivities typically cover the range 10-4 – 10-2 6
m2s-1, due to processes associated with proximity to the shelf break, locally generated tides 7
and non-linear internal waves, enhanced energy of high baroclinic modes, instability of low 8
baroclinic modes, shear from near-inertial waves, enhanced bottom drag etc. (Inall et al., 9
2000; Nash and Moum, 2001; Mickett et al., 2004; Carter et al., 2005; MacKinnon and 10
Gregg, 2005a-b). The survey mean 〈Kρ〉 = 7.3×10-4 m2s-1 observed in Van Mijenfjorden falls 11
within this range, but, however, approaches the higher end considering the fact that all cited 12
work employed the Osborn model.
13
6. Summary and concluding remarks 14
We described the oceanographic context and reported on water column turbulence 15
observations in early spring 2004 in fast ice covered Van Mijenfjorden. Turbulence 16
measurements were conducted using both moored instruments within the uppermost 5 metres 17
below the ice, and a microstructure profiler covering 3-60 m at a water depth of 75 m. While 18
the turbulent fluxes obtained using the eddy correlation technique (moored instruments) 19
provided excellent sampling in time and covered the spring-neap cycle, the microstructure 20
profiles were few and did not resolve the different phases of the tide. Background currents 21
recorded at two levels, 10 m and 50 m, under the ice allowed for neither a detailed analysis of 22
the shear structure nor partitioning of energy into baroclinic modes, but nevertheless gave a 23
description of the bulk currents and tides. A comparison of the rotary spectral ratio with that 24
expected from linear internal waves suggested that the frequencies higher than M4 could be 25
associated with possibly non-linear internal waves which comprised ∼4% of the total 1
horizontal kinetic energy.
2
The fjord is characterized as jet-type and tidal choking at the mouth of the fjord induces 3
a tidal jet advecting relatively warmer water past the measurement site and dominating the 4
variability in hydrography. The resolved semidiurnal tidal components accounted for only 5
∼18% of the current variance and there was no strong correlation with the observed 6
hydrography or mixing and the M2 cycle. When conditionally sampled for tidal jet events, the 7
mean structure in dissipation and work done under the ice and the mixing in the water column 8
corresponded to the time development of inflow events.
9
Observed levels of dissipation, 〈ε〉= 1.1×10-7 W kg-1, and diffusivity, 〈Kρ〉 = 7.3×10-4 m2 10
s-1, are comparable to direct measurements at other coastal sites and shelves with rough 11
topography and strong forcing. During springs, an average upward heat flux of 5 W m-2 in the 12
under-ice boundary layer was observed. Instantaneous (1-h averaged) large heat flux events 13
were correlated with the periods of large inflow events, hence elevated heat fluxes were 14
associated with the tidal jet and its heat content. The upper 3-10 m averaged heat flux 15
estimates from microstructure profiler agreed within 10% with the direct measurements 16
averaged at 1 and 5 m below the ice. In deriving heat fluxes from microstructure profiles a 17
novel model for Kρ (Shih et al., 2005) was employed and our results contributes to the 18
model’s validation, however, better sampled field surveys are merited to draw concrete 19
conclusions.
20
During the experiment destabilizing buoyancy fluxes were recorded at 1 m close to the 21
ice, due to salt release from warm sea ice- especially during the spring tides when the oceanic 22
heat flux induced by the tidal inflow was significant. Overall, turbulence production was 23
found to be dominated by shear. A scaling of the form ε/(1.76εs + 0.58FB) (Lombardo and 24
Gregg, 1989) was found to be appropriate for the under-ice boundary layer when judged from 25
well-sampled eddy-correlation results. Microstructure profiles indicated dissipation 2-5 times 1
greater than that predicted by ε/(1.76εs + 0.58FB) = 0.84. Because profile data lack the 2
appropriate averaging, the discrepancy is possibly due to bias by episodic events contributing 3
to the TKE production.
4 5
Acknowledgements 6
IF is supported by the ProClim project grant 155923/700. KW is supported through AiO 7
project. The authors thank Peter M. Haugan, Miles McPhee, and Frank Nilsen for crucial 8
input to the AiO project and the experiments. IF thanks Alastair D. Jenkins for reading the 9
manuscript. This is publication number XXX of the Bjerknes Centre for Climate Research.
10
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