Seminar
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| Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
On Dispersion Improvements and Kelvin-Helmholtz Instability for Long Internal Gravity Waves
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
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 appears. With 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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