TwoPoint Closure Study of Covariance Budgets for Turbulent RayleighBenard Convection
Abstract
Statistical properties of turbulent RayleighBenard convection in a laterallyperiodic domain between free slip boundaries are investigated in the parameter range Pr(, )< O(1), R (TURN) (24)R(,c), and aspect ratio (eta) (TURN) 4(eta)(,c). Ensemblemean dynamics of this system are studied by means of a nonMarkovian twopoint closure obtained from the Direct Interaction Approximation by application of a two time perturbation formalism and nonequilibrium fluctuationdissipation relation. The computations are economized by use of Pade approximation methods to estimate the modal response function and triad relaxation time. Comparisons at the level of second and third order moments are made between the closure predictions and averages obtained from Direct Spectral Simulation (DSS) solutions of the full NavierStokesBoussinesq equations. The finalstate convective heat flux and volumeintegrated kinetic energy and thermal variance are predicted to O(5%) accuracy with the closure model, which contains no adjustable constants or functions. At Rayleigh numbers near the convective threshold (<2R(,c)),(, )characteristic correlation times for the vertical velocity and temperature fields grow to(, )>O(10) vertical thermal diffusion times. Evidence is given that the twotime perturbation formalism furnishes an efficient iteration scheme for estimating statistically steady dynamics in this parameter regime. Vertical profiles are constructed of the final state covariance budgets for R = 2R(,c); these agree at the 510% level with budgets computed from horizontal averages of the DSS solutions. In the kinetic energy budget, the term arising from correlation between buoyancyinduced pressure and vertical velocity dominates the total transport term at all depths in the convecting layer. In the other secondmoment budgets, triple correlations arising from the eddy flux of thermal variance and vertical heat flux play essential roles at nearly all levels.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT........47D
 Keywords:

 DIA;
 Physics: Fluid and Plasma