Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Ginzburg-Landau equation Related Publications

2 Ginzburg-Landau Model for Curved Two-Phase Shallow Mixing Layers

Authors: Andrei A. Kolyshkin, Irina Eglite

Abstract:

Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained.

Keywords: mixing layer, shallow water equations, Ginzburg-Landau equation, weakly nonlinear analysis

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1 Ginzburg-Landau Model : an Amplitude Evolution Equation for Shallow Wake Flows

Authors: Andrei A. Kolyshkin, Imad Chaddad

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory

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