The nonlinear temporal evolution of a disturbance to a stratified mixing layer

Using a nonlinear critical layer analysis, Goldstein & Leib (1988) derived a set of nonlinear evolution equations governing the spatial growth of a two-dimensional instability wave on a homogeneous incompressible tanh y mixing layer. In this study, we extend this analysis to the temporal growth of the García model of an incompressible stratified shear layer. We consider the stage of the evolution in which the growth first becomes nonlinear, with the nonlinearity appearing inside the critical layer. The Reynolds number is assumed to be just large enough so that the unsteady, nonlinear and viscous terms all enter at the same order of magnitude inside the critical layer. The equations are solved numerically for the inviscid case.

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Nonlinear evolution of singular disturbances to a tanh3y mixing layer

The ANZIAM Journal ◽

10.1017/s1446181100012608 ◽

2002 ◽

Vol 43 (3) ◽

pp. 409-427

Author(s):

S. Saujani ◽

J. Drozd ◽

R. Mallier

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Nonlinear Evolution ◽

Mixing Layer ◽

Nonlinear Effects ◽

Critical Layer ◽

Linear Basis ◽

Layer Analysis ◽

Derivatives Of ◽

Non Equilibrium

AbstractWe consider the nonlinear evolution of a disturbance to a mixing layer, with the base profile given by u0(y) = tanh3y rather than the more usual tanh y, so that the first two derivatives of u0 vanish at y = 0. This flow admits three neutral modes, each of which is singular at the critical layer. Using a non-equilibrium nonlinear critical layer analysis, equations governing the evolution of the disturbance are derived and discussed. We find that the disturbance cannot exist on a linear basis, but that nonlinear effects inside the critical layer do permit the disturbance to exist. We also present results of a direct numerical simulation of this flow and briefly discuss the connection between the theory and the simulation.

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Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i3.470 ◽

2015 ◽

Vol 11 (3) ◽

pp. 3134-3138 ◽

Cited By ~ 3

Author(s):

Mostafa Khater ◽

Mahmoud A.E. Abdelrahman

Keyword(s):

Elliptic Function ◽

Traveling Wave ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Traveling Wave Solutions ◽

Expansion Method ◽

Mathematical Physics ◽

Nonlinear Evolution Equations ◽

Jacobian Elliptic Function ◽

Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity andÂ reliability of the method are tested by its applications to the Couple Boiti-Leon-PempinelliÂ System which plays an important role in mathematical physics.

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