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Abstract
The stability properties of 24 experimentally generated internal
solitary waves (ISWs) of extremely large amplitude, all with minimum
Richardson number less than 1/4, are investigated. The study is
supplemented by fully nonlinear calculations in a threelayer fluid. The
waves move along a linearly stratified pycnocline (depth h_{2}) sandwiched between a thin upper layer (depth h_{1}) and a deep lower layer (depth h_{3}),
both homogeneous. In particular, the waveinduced velocity profile
through the pycnocline is measured by particle image velocimetry (PIV)
and obtained in computation. Breaking ISWs were found to have amplitudes
(a_{1}) in the range a_{1}>2.24 √h_{1}h_{2}(1+h_{2}/h_{1}), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 < h_{2}/h_{1} < 1 and 4.14 < h_{3}/(h_{1} + h_{2}) < 7.14 and stable waves for 0.36 < h_{2}/h_{1} < 3.67 and 3.22 < h_{3}/(h_{1} + h_{2}) < 7.25. Kelvin–Helmholtzlike billows were observed in the breaking cases. They had a length of 7.9h_{2}
and a propagation speed 0.09 times the wave speed. These measured
values compared well with predicted values from a stability analysis,
assuming steady shear flow with U(z) and ρ(z) taken at the wave maximum (U(z) horizontal velocity profile, ρ(z) density along the vertical z).
Only unstable modes in waves of sufficient strength have the chance to
grow sufficiently fast to develop breaking: the waves that broke had an
estimated growth (of unstable modes) more than 3.3–3.7 times than in the
strongest stable case. Evaluation of the minimum Richardson number (Ri_{min}, in the pycnocline), the horizontal length of a pocket of possible instability, with waveinduced Ri < 14, (L_{x}) and the wavelength (λ), showed that all measurements fall within the range Ri_{min} = −0.23L_{x}/λ + 0.298 ± 0.016 in the (L_{x}/λ, Ri_{min})plane. Breaking ISWs were found for L_{x}/λ > 0.86 and stable waves for L_{x}/λ < 0.86. The results show a sort of thresholdlike behaviour in terms of L_{x}/λ. The results demonstrate that the breaking threshold of L_{x}/λ
= 0.86 was sharper than one based on a minimum Richardson number and
reveal that the Richardson number was found to become almost
antisymmetric across relatively thick pycnoclines, with the minimum
occurring towards the top part of the pycnocline
Original language  English 

Pages (fromto)  129 
Number of pages  29 
Journal  Journal of Fluid Mechanics 
Volume  620 
Early online date  26 Jan 2009 
DOIs  
Publication status  Published  Feb 2009 
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 1 Finished

EP/F030622/1 Breaking characteristics: Breaking Characteristics of large amplitude internal solitary waves
Carr, M.
1/10/08 → 30/09/11
Project: Standard