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  • FLUID MECHANICS AND HEAT TRANSFER  (5)
  • 1980-1984  (3)
  • 1975-1979  (2)
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  • 1
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    Time-dependent solutions of multimode convection equations (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 125; Dec. 198
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  • 2
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    Single-mode theory of diffusive layers in thermohaline convection (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 125; Dec. 198
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  • 3
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    Nonlinear modal analysis of penetrative convection (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Geophysical and Astrophysical Fluid Dynamics; 22; 1-2,; 1982
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  • 4
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    Modal equations for cellular convection (1975)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 68; Apr. 29
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  • 5
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    Numerical solutions of single-mode convection equations (1977)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 79; Jan. 20
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