A 2D Finite Volume Non-hydrostatic Atmospheric Model ...

Šª6.6 Thermal bubbleIn [11] Straka et al. present the numerical solution of a nonlinear density current in an otherwise homogeneousand isentropic atmosphere. This density current serves us as another test case. It is initiated asa cold blob of air that subsequently descends to the ground. The elliptic temperature perturbation isspecified byT e³´g h c Ld ‰ 1.0d š µ0.0 K if L 1.0115.0 K cos2if L 1.06.7Žwhere x c0.0 km , x r4.0 km , z c3.0 km and z r2.0 km. In the rest of the domain the potential temperatureis 300 K. The perturbation in the potential temperature resulting from (6.7) can be calculatedusing Š«ª the relation T where is the exner š e c function€ 1 €e š1° ±pp š 0§ and 1.4 is the d­¬¯® ® adiabatic²exponent. Table 6.4 gives the list of the parameters we use for our simulation. Figure 6.11 shows the solutionof the thermal bubble e simulation at times t 0,300,600and 900 seconds. According to [11] weuse a diffusion coefficient of 75 m 2 s 1 . Our simulation shows the typical development of three so calledKelvin-Helmholtz shear instability rotors during the period from 0 to 900 seconds described in [11].€parameter value unittime integration schemeatmosphereleapfrogisentropic--horizontal domain sizevertical domain sizehorizontal cell sizevertical cell sizenumber of horizontal grid cellsnumber of vertical grid cells30510010030050kmkmmm--undisturbed potential temperatureinitial vertical velocity3000Km/stime stepintegration timex-divergence damping coefficientz-divergence damping coefficientAsselin coefficientdiffusion constantx-computational mixing coefficientz-computational mixing coefficient0.1259000.020.020.1750.00050.0005ss---m²/s--number of steps between background5state calculationTable 6.4: List of used parameters for the thermal bubble simulation.35