On the breaking and broadening of internal solitary waves propagating in stratified fluid

h

h

2

1

a

y x

!(y)(y) !(y)

0 0.5 1 1.5 1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Camera 1−2 Camera 2−3 Theory

−0.1 0 0.1 0.2

−2.5

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−0.2 0 0.2 0.4 0.6

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−0.5 0 0.5

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−1 0 1

−2

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−1 0 1

−2

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−1 0 1

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−1 0 1

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−1 0 1

−2

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−1 0 1

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−1 0 1

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−1 0 1

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−1 0 1

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−1 0 1

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−1 0 1

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−1

−0.5 0 0.5 1

−1 0 1

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−1

−0.5 0 0.5 1

−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2

−2.5

−2

−1.5

−1

−0.5 0 0.5

−1 −0.5 0 0.5 1 1.5 2

−2.5

−2

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−1

−0.5 0 0.5 1

−1 −0.5 0 0.5 1 1.5 2

−2.5

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−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

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−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

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−1

−0.5 0 0.5 1

−2 −1 0 1

−2

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−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

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−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−2 −1 0 1

−2

−1.5

−1

−0.5 0 0.5 1

−250 −20 −15 −10 −5 0 5

10 15

−200 −15 −10 −5 0 5

5 10 15

−25 −20 −15 −10 −5 0 5 10 15 20

0 5 10 15

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

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−1 0 1

−0.5 0 0.5 1 1.5

−2

−1 0 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

−1.5

−1

−0.5 0 0.5 1

−2 0 2

−2

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−0.5 0 0.5 1

−2 0 2

−2

−1.5

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−0.5 0 0.5 1

−2 0 2

−2

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−0.5 0 0.5 1

−2 0 2

−2

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−0.5 0 0.5 1

−2 0 2

−2

−1.5

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−0.5 0 0.5 1

−2 0 2

−2

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−0.5 0 0.5 1

−2 0 2

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−2 0 2

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−2 0 2

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−1

−0.5 0 0.5 1

−20 −10 0 10 20 30

−10

−5 0 5 10 15

5 10 15 20 25 30 35 40 45

0 5 10 15 20 25

Vorticity, on the surface, v=200dm³

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

−100 −8 −6 −4 −2 0 2 4 6 8 10 0.2

0.4 0.6 0.8 1 1.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

5 7.5 10 12.5 15

−1.5 −1 −0.5 0 0.5 1 1.5 2

−5

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−1.5 −1 −0.5 0 0.5 1 1.5 2

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0 2 4 6 8 10

−1

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0 2 4 6 8 10

−1

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−0.2 0