scholarly journals LINEAR AND NONLINEAR EVOLUTION OF ISOLATED DISTURBANCES IN A GROWING THERMAL BOUNDARY LAYER IN POROUS MEDIA

2010 ◽  
Author(s):  
A. Selim ◽  
D. A. S. Rees ◽  
Kambiz Vafai
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Boundary Layer ◽  
Nonlinear Evolution ◽  
Linear And Nonlinear

Linear and nonlinear evolution of boundary layer instabilities generated by acoustic‐receptivity mechanisms

1996 ◽  
Vol 8 (6) ◽  
pp. 1415-1423 ◽  
Author(s):  
Kenneth S. Breuer ◽  
Elizabeth G. Dzenitis ◽  
Jonas Gunnarsson ◽  
Mats Ullmar
Keyword(s):  
Boundary Layer ◽  
Nonlinear Evolution ◽  
Linear And Nonlinear

Thermal Convection in Porous Media at High Rayleigh Numbers

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Daniel J. Keene ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Packed Bed ◽  
Horizontal Layer ◽  
Homogeneous Fluid ◽  
Fluid Systems ◽  
Dimensionless Groups ◽  
Rayleigh Numbers

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

Linear and nonlinear evolution of boundary layer instabilities generated by acoustic-receptivity mechanisms

1996 ◽  
Author(s):  
Kenneth Breuer ◽  
Margaret Grimaldi ◽  
Jonas Gunnarsson ◽  
Mats Ullmar
Keyword(s):  
Boundary Layer ◽  
Nonlinear Evolution ◽  
Linear And Nonlinear

Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 1. Linear and nonlinear instabilities

2008 ◽  
Vol 595 ◽  
pp. 379-408 ◽  
Author(s):  
XUESONG WU ◽  
JING ZHANG
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Gravity Waves ◽  
High Frequency ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Small Scale ◽  
S Waves ◽  
Viscous Instability ◽  
Linear And Nonlinear

In this paper, we consider a viscous instability of a stratified boundary layer that is a form of the familiar Tollmien–Schlichting (T-S) waves modified by a stable density stratification. As with the usual T-S waves, the triple-deck formalism was employed to provide a self-consistent description of linear and nonlinear instability properties at asymptotically large Reynolds numbers. The effect of stratification on the temporal and spatial linear growth rates is studied. It is found that stratification reduces the maximum spatial growth rate, but enhances the maximum temporal growth rate. This viscous instability may offer a possible alternative explanation for the origin of certain long atmospheric waves, whose characteristics are not well predicted by inviscid instabilities. In the high-frequency limit, the nonlinear evolution of the disturbances is shown to be governed by a nonlinear amplitude equation, which is an extension of the well-known Benjamin–Davis–Ono equation. Numerical solutions indicate that as a spatially isolated disturbance evolves, it radiates a beam of long gravity waves, and meanwhile small-scale ripples develop on its front to form a well-defined wavepacket. It is also shown that for jet-like velocity profiles, the standard triple-deck theory must be adjusted to account for both the displacement and transverse pressure variation induced by the inviscid flow in the main layer. The nonlinear evolution of high-frequency disturbances is governed by a mixed KdV–Benjamin–Davis–Ono equation.

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