Analyses of three-dimensional flow calculations in a driven cavity

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Abstract
Comprehensive numerical solutions of three-dimensional flows of an incompressible viscous fluid confined in a square cubic cavity are presented. The flow is maintained by the upper surface of the cavity, which slides in its own plane at a constant speed. Extensive numerical solutions to the governing Navier-Stokes equations were acquired over a wide range of the Reynolds numbers. Re ≤ 2000. The previous report depicted the global structures of these complex three-dimensional flows at varying Re. The preceding account demonstrated broad agreement between the numerical results and the available experimental observations in gross flow characteristics. The present paper continues to give expanded description of the flows, in particular, the detailed velocity profiles along the vertical and horizontal symmetry lines. The changes in the main character of flow with increasing Re are elaborated. The conspicuous three-dimensionalities, at high Re exemplified by substantial transverse gradients of the velocities, as a result of the Taylor-Görtler-like vortices and the comer vortices, are delineated. Taking advantage of the wealth of the numerical results, diagnostic studies of the major terms in the momentum equations are conducted. These studies reveal the dominant dynamic balances in various parts of the flow field. The characterizations of the three-dimensional nature of the flow, based on the present numerical results, are in accord with the prior experimental visualizations.