Turbulent thermal convection in a finite domain: Part II. Numerical results

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Abstract
A pseudospectral method is used to solve the Boussinesq equations for a fully inhomogeneous turbulent flow. The numerical data are analyzed using the empirical eigenfunction technique. As a result of the underlying inhomogeneity of the flow, the eigenfunctions (structures) are inhomogeneous in all three directions. This is the first instance in which fully three‐dimensional empirical eigenfunctions have been calculated. The generated basis set is extremely efficient at depicting the flow. The first eigenfunction captures almost 60% of the average energy. The eigenfunctions are an optimal basis for capturing the energy of the flow and more than 95% of the energy is captured by the first 100 eigenfunctions. Ten classes of eigenfunctions are present and examples of each are shown. The average Nusselt number for the bounded geometry is found to be lower than that for a correspondong homogeneous case and the physics causing this decrease is analyzed and discussed.

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