Turbulence structure in thermal convection and shear-free boundary layers

Abstract

This paper is a study of turbulence near rigid surfaces, in the absence of any mean shear. Different sources of turbulence are considered, including thermal convection and grid turbulence. It is shown that, if a rigid boundary is introduced into the flow, then for short times the linear theory of Hunt & Graham (1978) reveals the common structure of these flows near the boundary, if the parameters used are the rate of energy dissipation per unit mass ε and the distance z from the surface. Over longer times nonlinear effects develop, such as large eddies straining smaller eddies near the boundary. Some new estimates are suggested here and compared with the computations of Biringen & Reynolds (1981) and experiments of Thomas & Hancock (1977).It is shown that calculations based on the linear theory agree well with many measurements of the vertical profiles of turbulence in thermal convection layers, including those of the vertical variance, the low-frequency end of the spectrum of the vertical turbulence (w), the integral scale of w, and two-point cross-correlations of w. (The latter was a prediction, subsequently tested by atmospheric measurements.) Some discussion of the reasons for this agreement are suggested. The observations of the effects of mean-velocity gradients near the surface are also shown to be consistent with the theoretical arguments proposed here.