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

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.

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

Linear and nonlinear evolution of alpha-particle driven gap modes

1995 ◽  
Vol 37 (11A) ◽  
pp. A279-A290 ◽  
Author(s):  
S Briguglio ◽  
C Kar ◽  
F Romanelli ◽  
G Vlad ◽  
F Zonca
Keyword(s):  
Alpha Particle ◽  
Nonlinear Evolution ◽  
Linear And Nonlinear

scholarly journals Solving Boundary-Layer Problems by Residual-Power-Series Method

2016 ◽  
Vol 8 (3) ◽  
pp. 68
Author(s):  
Mohd Taib Shatnawi
Keyword(s):  
Boundary Layer ◽  
Power Series ◽  
Nonlinear Boundary ◽  
Power Series Method ◽  
Boundary Layer Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Linear And Nonlinear ◽  
Boundary Layer Problems ◽  
Residual Power

<p><span lang="EN-US">In this paper, the so-called residual-power-series (RPS) method is presented for solving nonlinear boundary-layer equations. The RPS method provides a single unified treatment for the linear and nonlinear terms in the equations. The accuracy and efficiency of the RPS method is demonstrated for both a single and a system of two coupled boundary-layer equations on an unbounded domain.</span></p>

scholarly journals Reconnection in Sheared Magnetic Fields in Space and Astrophysics

1985 ◽  
Vol 107 ◽  
pp. 61-81
Author(s):  
James F. Drake
Keyword(s):  
Energy Dissipation ◽  
Magnetic Fields ◽  
Nonlinear Evolution ◽  
Magnetic Energy ◽  
Coronal Loops ◽  
Theoretical Understanding ◽  
Physical Mechanisms ◽  
Linear And Nonlinear

The current theoretical understanding of the linear and nonlinear evolution of resistive tearing instabilities in sheared magnetic fields is reviewed. The physical mechanisms underlying this instability are emphasized. Some of the problems which are encountered in developing a model of magnetic energy dissipation in coronal loops are discussed and possible solutions are suggested.

scholarly journals Analysis of the atmosphere behaviour in the proximities of an orographic obstacle

1995 ◽  
Vol 2 (1) ◽  
pp. 30-48 ◽  
Author(s):  
E. Hernández ◽  
J. Díaz ◽  
L. C. Cana ◽  
A. García
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Critical Points ◽  
Complex Terrain ◽  
Laboratory Experiments ◽  
Real Experiment ◽  
The Real ◽  
Linear And Nonlinear ◽  
Atmospheric Variables

Abstract. The atmospheric behaviour near an orographic obstacle has been thoroughly studied in the last decades. The first papers in this field were mainly theoretical, being more recent the laboratory experiments which represented that behaviour in ideal conditions. The numerical simulations have been addressed lately thanks to the development of computers. But the study of meteorology in complex terrain has lacked experiments in the atmosphere to understand the real influence the relief has on it. In this paper the problem has been considered from the last perspective, and so, seasons of measure of the atmospheric variables within the boundary layer have been organized with the goal of checking existing theories and bringing right conclusions from real experiment in the atmosphere. Controverted aspects of linear and nonlinear theories, as the location of critical points upwind and downwind of an orographic obstacle, will be analyzed. The results obtained show a large adequacy between the forecasted behaviour and the experimentally detected.

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