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Home » Applied fluids: On dispersion improvements and Kelvin-Helmholtz instability for long internal gravity waves

Seminar

Applied fluids: On dispersion improvements and Kelvin-Helmholtz instability for long internal gravity waves March 12, 2021 (08:30 AM PST - 09:30 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Didier Clamond (Universite de Nice Sophia Antipolis)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

 

 

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To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract: 


We consider 2D irrotational flows of incompressible fluids stratified  in two homogeneous shallow layers, bounded below by a horizontal impermeable  bottom and above by a rigid lid.  We focus on the "fully-nonlinear weakly-dispersive"  Serre-like approximation obtained assuming long wavelength (compared to both  layer thicknesses), but without assuming small amplitude.

 

Serre's equations have several drawbacks. First, they are inaccurate for relatively  short waves. Second, even for weakly sheared currents, Kelvin-Helmholtz  instabilities  appear. Third, they do not admit physically relevant solutions such as `slug' or `plug' flows. We propose here modified Serre-like equations to address these 

shortcomings. 

 

The modified Serre equations have improved dispersion properties. In presence of weak  sheared current, no Kelvin--Helmholtz instability appearsWith strong sheared current,  Kelvin-Helmholtz instabilities appear at low frequencies, that is consistent with the long wave approximation. For steady waves, the modified Serre equations admit slug-like solutions.  

 

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