Amplitude equations for a system with thermohaline convection

TL;DR

This paper derives amplitude equations for thermohaline convection near bifurcation points using multiple scale expansion, revealing complex Ginzburg-Landau, Newell-Whitehead, and $\

Contribution

It introduces specific amplitude equations and analytic coefficient expressions for thermohaline convection near critical points, including asymptotic forms and soliton structures.

Findings

Amplitude equations include Ginzburg-Landau, Newell-Whitehead, and $\

Reduced equations describe dark soliton structures at high frequencies

Analytic expressions for coefficients are provided for different bifurcation scenarios.

Abstract

The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and an equation of the $\phi^4$ type, respectively, were obtained. Analytic expressions for the coefficients of these equations and their various asymptotic forms are presented. In the case of Hopf bifurcation for low and high frequencies, the amplitude equation reduces to a perturbed nonlinear Schr\"odinger equation. In the high-frequency limit, structures of the type of "dark" solitons are characteristic of the examined physical system.