TITLE

# The Evolution of General Three-Dimensional Disturbances in a Thermally Stratified Couette Flow

AUTHOR(S)
Balagondar, P. M.; Vijayalakshmi, A. R.
PUB. DATE
December 2007
SOURCE
Global Journal of Pure & Applied Mathematics;2007, Vol. 3 Issue 3, p399
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The evolution of general three-dimensional disturbances in a thermally stratified Couette flow is investigated with the help of initial-value problem approach. Using Boussinesq approximation, the disturbances satisfy a system of linear first-order partial differential equation which is solved subject to appropriate initial and boundary conditions using two-dimensional Fourier transformation and squire transformation. The governing stability equation is solved using both perturbation method and Fourier method. In the Fourier approach, the solution is obtained in terms of Bessel function. Perturbation solution is obtained for small values of Brunt Vï¿½isï¿½lï¿½ frequency. The terms in the perturbation series are obtained in terms of two representations of Green's function, one in the form of sine hyperbolic functions and the other in the form of Fourier sine series which represent the total energy and the energy of a single component respectively. In order to quantify disturbances amplitudes, a single measure which is basically the sum of the square of the L2 -norm of the Fourier transforms of the disturbances is used to analyze the temporal evolution of disturbances in the case of square wave pulse for velocity and temperature. Graphically it is found that the total energy and the sum of first five components of energy are almost same.
ACCESSION #
35155496

## Related Articles

• Existence of Solution for Four-Point Boundar Value Problems of Second-Order Impulsive Differential Equations (III). Li Ge // World Academy of Science, Engineering & Technology;Apr2011, Issue 52, p987

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory: Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. (E) where 0 < Î¾ â‰¤...

• Layer-adapted Methods for a Singularly Perturbed Singular Problem. Grossmann, Christian; Ludwig, Lars; Roos, Hans-Görg // Computational Methods in Applied Mathematics;2011, Vol. 11 Issue 2, p192

In the present paper we analyze linear finite elements on a layer-adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel...

• Local existence and blow up in a semilinear heat equation with the Bessel operator. Messaoudi, Salim A. // Nonlinear Studies;2003, Vol. 10 Issue 1, p59

Considers an initial one-point boundary value problem to the heat equation with a Bessel operator. Existence theorem of weak solutions for a related linear problem; Theory for ordinary differential equations; Information on semilinear problem.

• A transform method for linear evolution PDEs on a finite interval. FOKAS, S.; PELLONI, B. // IMA Journal of Applied Mathematics;Aug2005, Vol. 70 Issue 4, p564

We study initial boundary value problems for linear scalar evolution partial differential equations, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 < x < L}. We show that the solution can be expressed as an integral in the complex k-plane. This integral is defined in...

• On the existence and stability of a global subsonic flow in a 3D infinitely long cylindrical nozzle. XU, Gang; YIN, Huicheng // Chinese Annals of Mathematics;Mar2010, Vol. 31 Issue 2, p163

This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]: A flow through a duct should be considered as a...

• On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations. Asanova, A. T. // Journal of Mathematical Sciences;May2008, Vol. 150 Issue 5, p2302

We consider a family of two-point boundary-value problems for systems of ordinary differential equations with functional parameters. This family is the result of the reduction of a boundary-value problem with nonlocal condition for a system of second-order, quasilinear hyperbolic equations by...

• PERIODIC SOLUTIONS OF LIÃ‰NARD EQUATIONS WITH ASYMMETRIC NONLINEARITIES AT RESONANCE. ANNA CAPIETTO // Journal of the London Mathematical Society;Aug2003, Vol. 68 Issue 1, p119

The existence of $2\pi$-periodic solutions of the second-order differential equation $x''+f(x)x'+ax^+-bx^-+g(x)=p(t), \qquad n\in \mathbb{N},$ where $a, b$ satisfy $1/\sqrt{a}+1/\sqrt{b}=2/n$ and $p(t)=p(t+2\pi)$, \$t\in...

• THE LEVINSON-TYPE FORMULA FOR A BOUNDARY VALUE PROBLEM WITH A SPECTRAL PARAMETER IN THE BOUNDARY CONDITION. Mamedov, Khanlar R.; Menken, Hamza // Arabian Journal for Science & Engineering (Springer Science & Bu;Jan2009, Vol. 34 Issue 1A, p219

In the present paper, we consider a boundary-value problem generated by a second order differential equation and a spectral parameter dependent boundary condition on the half line. For this boundary-value problem, we define the scattering data, we prove the continuity of the scattering function...

• A Lyapunov-Type Function for Generalized Dynamical Systems Without Uniqueness. Filippov, A. F. // Differential Equations;Jun2003, Vol. 39 Issue 6, p901

Discusses the Lyapunov-type function for generalized dynamical systems without uniqueness. Autonomous systems of differential equations; General conditions providing the validity of the study's results.

Share