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Abstract
A numerical method that employs a combination of contour advection and pseudospectral techniques is used to simulate shearinduced instabilities in an internal solitary wave (ISW). A threelayer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steadystate, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ri_{c}) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ri_{c} = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of L_{x}/λ required for instability, where L_{x} is the length of the region in a wave in which Ri < 1/4 and λ is the halfwidth of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δ_{i}T_{w} (where δ_{i} is the growth rate of the instability averaged over T_{w}, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely L_{x}/λ ≥ 0.86 and δ_{i}T_{w > 5} , are shown to be valid only for a limited parameter range.
Original language  English 

Pages (fromto)  263288 
Journal  Journal of Fluid Mechanics 
Volume  683 
Early online date  22 Aug 2011 
DOIs  
Publication status  Published  25 Sept 2011 
Keywords
 Internal waves
 Solitary waves
 Stratified flows
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Dive into the research topics of 'Numerical simulation of shearinduced instabilities in internal solitary waves'. Together they form a unique fingerprint.Projects
 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