Further Aspects of Transitions in Two-Dimensional Thermal Convection

Marina Zivković Department of Earth and Atmospheric Sciences, Purdue University, Indiana

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Ernest M. Agee Department of Earth and Atmospheric Sciences, Purdue University, Indiana

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Abstract

In this paper we present the results of numerical investigation of a two-dimensional nonlinear set of Boussinesq equations governing Bénard–Rayleigh convection using spectral representation in the horizontal direction and finite-difference formulation in the vertical direction. Integrations were characterized by high resolution (up to 171 horizontal modes on 32 levels in the vertical direction) and large domain size (ten linear cells were represented). The results presented were obtained for moderate values of Rayleigh number (1150 < Ra < 33 000) that was varied in a near continuous fashion.

It is found that two-dimensional heat flux transitions lead to simulations of various temporal states when sufficient resolution and high aspect-ratio domain of integration are used. The change of slope of the time-averaged logarithmic heat flux curve (log Nu) is simulated in a gradual manner by means of a series of bifurcated solutions.

This study demonstrates that transition from steady to time-dependent convection in two-dimensional simulations is the generic property of the Boussinesq equations. The findings highlight the roles of scale truncation and large domain aspect-ratio in simulations of self-organizing properties of thermal convection. They also provide useful information for the application of nonlinear spectral models to the study of organized convection.

Abstract

In this paper we present the results of numerical investigation of a two-dimensional nonlinear set of Boussinesq equations governing Bénard–Rayleigh convection using spectral representation in the horizontal direction and finite-difference formulation in the vertical direction. Integrations were characterized by high resolution (up to 171 horizontal modes on 32 levels in the vertical direction) and large domain size (ten linear cells were represented). The results presented were obtained for moderate values of Rayleigh number (1150 < Ra < 33 000) that was varied in a near continuous fashion.

It is found that two-dimensional heat flux transitions lead to simulations of various temporal states when sufficient resolution and high aspect-ratio domain of integration are used. The change of slope of the time-averaged logarithmic heat flux curve (log Nu) is simulated in a gradual manner by means of a series of bifurcated solutions.

This study demonstrates that transition from steady to time-dependent convection in two-dimensional simulations is the generic property of the Boussinesq equations. The findings highlight the roles of scale truncation and large domain aspect-ratio in simulations of self-organizing properties of thermal convection. They also provide useful information for the application of nonlinear spectral models to the study of organized convection.

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