Two-dimensional analytical model of dry air thermal convection

Abstract

In the present work, the steady-state stationary dry air thermal convection in a lower atmosphere has been studied theoretically. The thermal convection was considered without accounting for the Coriolis force, and with only the vertical temperature gradient. The stream function has been analytically obtained within the framework of two-dimensional thermal convection model in the Boussinesq approximation with velocity divergence taken as zero. It has been shown that the stream function is symmetrical about the horizontal and vertical. The expressions for the horizontal and vertical air velocity components have been obtained. The maximal vertical velocities level is in the center of the convective cell where the horizontal air velocity component is equal to zero. It has been shown that the air parcel’s rotation period during the thermal convection is determined by the Brunt–Vaisala frequency. The expression for the maximal air velocity vertical component has been found. The dependence of the maximal air velocity vertical component on the overheat function at ground surface and on the atmosphere instability has been demonstrated. The expression for the pressure disturbance has been obtained. It has been demonstrated that at the points with maximal pressure disturbance the vertical velocity is equal to zero and the horizontal velocity is maximal. It has been found that the convection cell size depends on the atmosphere stability state.