Abstract
Abstract. An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. This analytical solution is one of the few available for wall-bounded buoyancy-driven flows. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free of errors in formulation of wall boundary conditions and to evaluate the relative performances of competing numerical algorithms. Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be for testing the no-slip, impermeable wall boundary conditions for the pressure Poisson equation. Examples of such tests are presented.
Highlights
In this paper we present an analytical solution of the Boussinesq equations for flows driven by a surface thermal forcing with large gradients in the horizontal
Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be as a test for surface boundary conditions in the pressure Poisson equation
Note the change in the scales of the x and the z axes between Figs. 4 and 2: the low-level thermal disturbance in the second test is much shallower than the disturbance in the first test. In this second test case we find dramatic differences between the inhomogeneous inhomogeneous Neumann condition (INC)-2 and homogeneous homogeneous Neumann condition (HNC)-2 cases
Summary
Thermal disturbances associated with variations in underlying surface properties can drive local circulations in the atmospheric boundary layer (Atkinson, 1981; Briggs, 1988; Hadfield et al, 1991; Segal and Arritt, 1992; Simpson, 1994; Mahrt et al, 1994; Pielke, 2001; McPherson, 2007; Kang et al, 2012) and affect the development of the convective boundary layer (Patton et al, 2005; van Heerwaarden et al, 2014). In this paper we present an analytical solution of the Boussinesq equations for flows driven by a surface thermal forcing with large gradients (step changes) in the horizontal. The solution can be used to verify that CFD codes for Boussinesq fluid system simulations are free of errors, and to evaluate the relative performances of competing numerical algorithms. Such verification procedures are important in the development of CFD models designed for research, operational, and classroom applications. Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be as a test for surface boundary conditions in the pressure Poisson equation.
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