Abstract The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence ...

It is shown that the anelastic Oberbeck-Boussinesq system is a small Mach, small Péclet and small Froude number limit of the complete Navier-Stokes-Fourier system for gases with large specific heat at constant volume. This result is obtained on an arbitrary large time interval. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Li...

Gravity waves arise in gravitationally stratified compressible flows at low Mach and Froude numbers. These waves can have a negligible influence on the overall dynamics of the fluid but, for numerical methods where the acoustic waves are treated implicitly, they impose a significant restriction on the time step. A way to alleviate this restriction is to filter out the modes corresponding to the...

A condition is derived for the hydraulic criticality of a 2-layer flow with transverse variations in both layer velocities and thicknesses. The condition can be expressed in terms of a generalized composite Froude number. The derivation can be extended in order to obtain a critical condition for an N-layer system. The results apply to inviscid flows subject to the usual hydraulic approximation ...