## An atmospheric mesoscale model: treatment of hydrostatic flows and application to flows with hydraulic jumps.(English)Zbl 0684.76018

Numerical methods in fluid mechanics, Proc. 7th GAMM-Conf., Louvain-La- Neuve/Belg. 1987, Notes Numer. Fluid. Mech. 20, 363-370 (1988).
Summary: [For the entire collection see Zbl 0652.00019.]
For numerical simulation of three-dimensional atmospheric flows at micro- and mesoscales a finite-difference method has been developed (program MESOSCOP). In its non-hydrostatic variant it requires the inversion of an elliptic (Poisson) equation. Here we describe an alternative which applies the hydrostatic approximation and thus avoids the elliptic equation. It has been found, however, that the hydrostatic version requires smaller time steps for stability. The method is applied to investigate the formation of hydraulic jumps in shallow nonlinear fluid flow over a mountain ridge on a rotating plane. By scale analysis and numerical experiments it is shown that the effect of rotation is negligible essentially if $$F^ 2/R_ 0$$ is small, where $$F$$ is the Froude number and $$R_ 0$$ the Rossby number.

### MSC:

 76B60 Atmospheric waves (MSC2010) 76M20 Finite difference methods applied to problems in fluid mechanics 86A10 Meteorology and atmospheric physics

Zbl 0652.00019

MESOSCOP