scholarly journals Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers

Fluids ◽  
2017 ◽  
Vol 2 (3) ◽  
pp. 39
Author(s):  
Tatyana Lyubimova ◽  
Igor Muratov
Keyword(s):  
Fluid Layer ◽  
Porous Layers ◽  
Instability Modes ◽  
Horizontal Fluid Layer ◽  
Two Fluid

scholarly journals An intrusion layer in stationary incompressible fluids Part 2: A solitary wave

2006 ◽  
Vol 17 (5) ◽  
pp. 577-595 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
GRAEME C. HOCKING
Keyword(s):  
Solitary Wave ◽  
Fluid Layer ◽  
Boundary Integral ◽  
Wave System ◽  
Fluid Interfaces ◽  
Weakly Nonlinear ◽  
System A ◽  
Horizontal Fluid Layer ◽  
Two Fluid ◽  
Intrusion Layer

The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg–de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces.

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

The Effect of Spatially Nonuniform Internal Heating on the Onset of Convection in a Horizontal Fluid Layer

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
A. V. Kuznetsov ◽  
D. A. Nield
Keyword(s):  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Source Strength ◽  
Linear Quadratic ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Special Cases ◽  
Basic Temperature ◽  
Horizontal Fluid Layer

In this paper, we investigated the onset of natural convection in a horizontal fluid layer due to nonuniform internal heat generation, which is relevant to a number of geophysical situations. We investigated a number of special cases, which we believe are paradigmatic. Those include linear, quadratic, concentrated, and exponential source strength distributions. Our results show that those situations that lead to a reduction/increase in the size of the region in which the basic temperature gradient is destabilizing lead to an increase/decrease in stability.

Stabilization of the No-Motion State of a Horizontal Fluid Layer Heated From Below With Joule Heating

1995 ◽  
Vol 117 (2) ◽  
pp. 329-333 ◽  
Author(s):  
J. Tang ◽  
H. H. Bau
Keyword(s):  
Joule Heating ◽  
Fluid Layer ◽  
Control Strategies ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Small Perturbations ◽  
Motion State ◽  
Conduction State ◽  
Rayleigh Numbers ◽  
Horizontal Fluid Layer

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Be´nard problem of an infinite fluid layer heated from below with Joule heating and cooled from above can be significantly increased through the use of feedback control strategies effecting small perturbations in the boundary data. The bottom of the layer is heated by a network of heaters whose power supply is modulated in proportion to the deviations of the temperatures at various locations in the fluid from the conductive, no-motion temperatures. Similar control strategies can also be used to induce complicated, time-dependent flows at relatively low Rayleigh numbers.

Throughflow effects on convective instability in superposed fluid and porous layers

1991 ◽  
Vol 231 ◽  
pp. 113-133 ◽  
Author(s):  
Falin Chen
Keyword(s):  
Porous Layer ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Single Layer ◽  
Layer Depth ◽  
Onset Of Convection ◽  
Precise Control ◽  
Porous Layers

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

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