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The purpose of this work is to study an example of low Mach (Froude) number limit of compressible o ws 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 inuence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low Mach number limit for standart compressible o ws given in P.{L. Lions's book that means with constant viscosity coecien ts.

An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit