Formulations and Direct Numerical Simulation Methods for Effects of Coriolis Force, Latitude, and Stably Stratified Ambient on a Large-Scale Thermal Plume

Abstract

A thermal plume with (1) the Coriolis force depending on the latitude of the earth, (2) turbulence, (3) varying density and properties, (4) hydrostatic pressure of air column weight placed above a heated square, and (5) stably stratified ambient is first elucidated. The earth model is employed as an analytical model, time-dependent three-dimensional governing equations are formulated, and a direct numerical simulation (DNS) methodology is obtained. Then, the plume without the Coriolis force is computed, the grid dependence is discussed, and the computed results are compared with previous results. As a result, the formulations, numerical methods, and computed results are validated. At the North Pole, a laminar plume with the Coriolis force rises spirally with the earth's rotation in an anticlockwise direction. However, the turbulent plume with the Coriolis has a thin column rotating very quickly and spirally in the clockwise direction. The rotations and heights of laminar and turbulent plumes are suppressed by a stably stratified ambient and/or a decrease of latitude. With increasing Rayleigh number, the rotation direction in the plume is varied to clockwise in the turbulent state from anticlockwise in the laminar state. Whether the thermal flow is turbulent or not is determined by the slopes of power spectrum density (PSD) of time-series data of computed temperature, and a sufficient number of grids and time steps exist in the Kolmogorov microscale.