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Numerical Simulation of Three-Dimensional, Shape-Preserving Convective Elements

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  • 1 National Center for Atmospheric Research, Boulder, Colo. 80302
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Abstract

The motions resulting from the sudden release of a fixed amount of buoyancy in an incompressible fluid are simulated. Solutions are allowed to reach a steady state in the finite computed volume by the introduction of a dynamical stretching of the coordinate system. Fully nonlinear, transformed, and finite-differenced Navier-Stokes equations are integrated in time over a three-dimensional grid. It is shown that a steady-state solution to the transformed equations is equivalent to a self-preserving solution in real space. Physically realistic results are presented for a range of Reynolds numbers between 10 and 100. In a strongly diffusive regime the simulation agrees with an existing theoretical solution. Reynolds numbers of order 50 are sufficient to reproduce many of the features of laboratory experiments.

Abstract

The motions resulting from the sudden release of a fixed amount of buoyancy in an incompressible fluid are simulated. Solutions are allowed to reach a steady state in the finite computed volume by the introduction of a dynamical stretching of the coordinate system. Fully nonlinear, transformed, and finite-differenced Navier-Stokes equations are integrated in time over a three-dimensional grid. It is shown that a steady-state solution to the transformed equations is equivalent to a self-preserving solution in real space. Physically realistic results are presented for a range of Reynolds numbers between 10 and 100. In a strongly diffusive regime the simulation agrees with an existing theoretical solution. Reynolds numbers of order 50 are sufficient to reproduce many of the features of laboratory experiments.

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