An analytical study of thermal turbulence
Abstract
The turbulent natural convection induced in an initially quiescent, horizontally unbounded layer of fluid by a heat flux antiparallel to the direction of gravity is considered. The basic approach used is that of the statistical theory of turbulence. Since the flow is neither isotropic nor homogeneous, a new, generalized symmetry assumption is introduced. When applied to the Boussinesq equations this leads to a number of new results for the kinematics of the correlation tensors. Phenomenological arguments are used to study the vertical profile of mean temperature. A new logarithmic relation is found which shows better agreement in certain regions with reported experimental data than any previous theories. In addition, an approximate method is presented which predicts the entire profile and satisfies the boundary conditions exactly. The hierarchy of dynamical equations is derived for both twopoint, twotime and onepoint, onetime correlations. A linearized method is proposed for the solution of the twopoint, twotime equations. The onepoint, onetime equations are used to investigate the energetics and vorticity dynamics of the flow.
 Publication:

Ph.D. Thesis
 Pub Date:
 1974
 Bibcode:
 1974PhDT........43G
 Keywords:

 Convective Flow;
 Heat Flux;
 Turbulent Flow;
 Boundary Conditions;
 Boundary Layer Flow;
 Boussinesq Approximation;
 Temperature Profiles;
 Fluid Mechanics and Heat Transfer