Abstract
The anelastic system of equations is used to investigate shallow convection as a function of time in a two-dimensional region subjected to differential heating along the bottom. Incompressibility is assumed and a stream of function is defined in the usual manner. The stream function and the deviation of potential temperature are each represented by a Fourier series and the system of equations is transformed to the spectral domain. This procedure results in coupled sets of ordinary differential equations to be solved for the fields of stream function and temperature deviations. The Fourier series were truncated to obtain a two-by-two and three-by-three system of equations. Numerical computations were performed for both systems using the same surface heating and the circulation and thermal fields were printed out at the end of 15 min, 30 min, 45 min, and 60 min. A comparison of the results of the two-by-two system with the results of the three-by-three system showed close agreement. The wind field and the pattern of temperature deviations closely approximated a realistic physical situation.
Conley, John Landis (1971). A spectral approach to convection. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -170214.