Decimated Amplitude Equations in Turbulence Dynamics

1985 ◽  
pp. 91-135 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Amplitude Equations

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Chaotic Amplitude Dynamics for Parametrically Excited Systems With Quadratic Nonlinearities

1995 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Order Approximation ◽  
Amplitude Equations ◽  
Analytical Technique ◽  
First Order ◽  
Numerical Studies ◽  
Quadratic Nonlinearities ◽  
First Order Approximation

Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.

Amplitude equations for cellular instabilities

1992 ◽  
Vol 7 (1) ◽  
pp. 1-34 ◽  
Author(s):  
N. Damil ◽  
M. Potier-Ferry
Keyword(s):  
Amplitude Equations

Phase mixed rotating magnetoconvection and Taylor's condition I. Amplitude equations

1994 ◽  
Vol 77 (1-4) ◽  
pp. 209-230 ◽  
Author(s):  
Susan A. Ewen ◽  
Andrew M. Soward
Keyword(s):  
Amplitude Equations

A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations

1976 ◽  
Vol 66 (6) ◽  
pp. 1881-1885 ◽  
Author(s):  
G. B. Young ◽  
L. W. Braile
Keyword(s):  
Computer Program ◽  
Elastic Waves ◽  
Displacement Amplitude ◽  
Plane Interface ◽  
Angle Of Incidence ◽  
Amplitude Equations ◽  
Elastic Solids ◽  
Displacement Potential ◽  
Energy Equations ◽  
Sample Case

abstract A computer program is presented which calculates Zoeppritz's displacement amplitude coefficients, displacement potential coefficients, and Knott's energy coefficients for plane harmonic elastic waves of P or SV type incident on a plane interface between two isotropic, homogeneous elastic solids. A discussion of these three basic types of coefficients is included. Results of applying the program to a sample case are presented in the form of a graph of the energy coefficients computed for all possible wave types and over a range of angle of incidence of 0° to 90°.

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