Exact Solutions of a Fully Nonlinear Two-Fluid Model

TL;DR

This paper derives exact solutions for a nonlinear two-fluid model describing wave phenomena in layered fluids, revealing various wave types through analytical methods.

Contribution

It introduces a transformation that simplifies the model and provides a comprehensive set of explicit solutions for different wave forms.

Findings

Multiple families of exact solutions including periodic, solitary, and kink waves.

Reduction of model parameters from five to one for simplified analysis.

Analytical characterization of bidirectional traveling wave solutions.

Abstract

A nonlinear coupled Choi-Camassa model describing one-dimensional incompressible motion of two non-mixing fluid layers in a horizontal channel has been derived in Ref.1. An equivalence transformation is presented, leading to a special dimensionless form of the system, with the number of constant physical parameters reduced from five to one. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of exact closed-form solutions of the Choi-Camassa model are obtained, describing periodic, solitary, and kink-type bidirectional traveling waves.