Bounds on the heat transport in a horizontal fluid layer with stress-free boundaries

1997 ◽  
Vol 48 (2) ◽  
pp. 310-324
Author(s):  
N. K. Vitanov ◽  
F. H. Busse
Keyword(s):  
Heat Transport ◽  
Fluid Layer ◽  
Free Boundaries ◽  
Horizontal Fluid Layer

Instabilities of convection rolls with stress-free boundaries near threshold

1984 ◽  
Vol 146 ◽  
pp. 115-125 ◽  
Author(s):  
F. H. Busse ◽  
E. W. Bolton
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Limited Range ◽  
Finite Domain ◽  
Free Boundaries ◽  
Prandtl Numbers ◽  
The Stability ◽  
Convection Rolls ◽  
Horizontal Fluid Layer

The stability properties of steady two-dimensional solutions describing convection in a horizontal fluid layer heated from below with stress-free boundaries are investigated in the neighbourhood of the critical Rayleigh number. The region of stable convection rolls as a function of the wavenumber α and the Rayleigh number R is bounded towards higher α by the monotonic skewed varicose instability, while towards low wavenumbers stability is limited by the zigzag instability or by the oscillatory skewed varicose instability. Only for a limited range of Prandtl numbers, 0·543 < P < ∞, does a finite domain of stability exist. In particular, convection rolls with the critical wavenumber αc are always unstable.

Non-linear Convection with Free Boundaries

1970 ◽  
Vol 1 (8) ◽  
pp. 381-382 ◽  
Author(s):  
J. O. Murphy
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Solution ◽  
Extreme Values ◽  
Fluid Layer ◽  
Free Boundaries ◽  
Non Linear ◽  
Basic Equations ◽  
Horizontal Fluid Layer ◽  
Astrophysical Situation

In an IAU Symposium report, Spiegel has made mention of the basic reasons for the astrophysical interest in the problem of non-linear convection of a horizontal fluid layer heated from below. Unfortunately the two important parameters of this problem—the Prandtl number P and the Rayleigh number R take on ‘extreme’ values in the astrophysical situation and this presents immediate difficulties as far as the numerical solution of the basic equations go.

scholarly journals Marangoni Convection In A Relatively Hotter Or Cooler Liquid Layer With Free Boundaries

2013 ◽  
Vol 18 (2) ◽  
pp. 581-588 ◽  
Author(s):  
A.K. Gupta ◽  
R.G. Shandil
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Slip Boundary Condition ◽  
Driving Mechanism ◽  
Free Boundaries ◽  
Slip Boundary ◽  
Thermally Conducting ◽  
Horizontal Fluid Layer

In this paper, we study the onset of cellular convection in a horizontal fluid layer heated from below, with a free-slip boundary condition at the bottom when the driving mechanism is surface tension at the upper free surface, in the light of the modified analysis of Banerjee et al. (Jour. Math. & Phys. Sci., 1983, 17, 603). This leads to a formulation of the problem which depends upon whether the liquid layer is relatively hotter or cooler. It is found that the phenomenon of surface tension driven instability problems should not only depend upon the Marangoni number which is proportional to the maintained temperature differences across the layer but also upon another parameter that arises due to variation in the specific heat at constant volume on account of the variations in temperature. Numerical results are obtained for the problem wherein the lower free boundary is perfectly thermally conducting.

scholarly journals A nonlinear model for rotationally constrained convection with Ekman pumping

2016 ◽  
Vol 798 ◽  
pp. 50-87 ◽  
Author(s):  
Keith Julien ◽  
Jonathan M. Aurnou ◽  
Michael A. Calkins ◽  
Edgar Knobloch ◽  
Philippe Marti ◽  
...  
Keyword(s):  
Heat Transport ◽  
Boundary Layers ◽  
Fluid Layer ◽  
Plane Layer ◽  
Linear Stability Theory ◽  
Reduced Model ◽  
Ekman Pumping ◽  
Free Boundaries ◽  
Nonlinear Feedback ◽  
Thermal Wind

A reduced model is developed for low-Rossby-number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominantly aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need to resolve the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping (which correlates positively with interior convection) allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer, the nonlinear feedback from Ekman pumping would be able to generate heat transport that diverges to infinity at finite Rayleigh number. This layer arrests this blowup, resulting in finite heat transport at a significantly enhanced value. With increasing buoyancy forcing, the heat transport transitions to a more efficient regime, a transition that is always achieved within the regime of asymptotic validity of the theory, suggesting that this behaviour may be prevalent in geophysical and astrophysical settings. As the rotation rate increases, the slope of the heat transport curve below this transition steepens, a result that is in agreement with observations from laboratory experiments and direct numerical simulations.

Onset of thermal convection in a horizontal fluid layer under ramp heating

2002 ◽  
Author(s):  
Dae Jun Yang ◽  
Jake Kim ◽  
Chang Kyun Choi ◽  
In Gook Hwang
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Horizontal Fluid Layer
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