Kholoud Alzahrani

Unstability for the governing non-hydrostatic equations of Mesoscale with thermal forcing

In this talk we will prove that the governing non-hydrostatic equations of Mesoscale taking into account the presence of thermal forcing, the background profile around which the equations are linearized is unstable. The idea, first we linearize The general set of equations describing fluid motion in a two-dimensional, non-hydrostatic, non-rotating and Boussinesq Mesoscale atmosphere with thermal forcing, and then, we will reduce the linearized set of equations, finally, we use a smooth shear background profile, an ansatz and then make use of the continued fractions to construct an unstable mode.