Abstract
A nonlinear equation of the Korteweg–de Vries equation usually describes internal solitary waves in the coastal ocean that lead to an exact solitary wave solution. However, in any real application, there exists the Earth’s rotation. Thus, an additional term is required, and consequently, the Ostrovsky equation is developed. This additional term is believed to destroy the solitary wave solution and form a nonlinear envelope wave packet instead. In addition, an internal solitary wave is commonly disseminated over the variable topography in the ocean. Because of these effects, the Ostrovsky equation is retrieved by a variable-coefficient Ostrovsky equation. In this study, the combined effects of both background rotation and variable topography on a solitary wave in a two-layer fluid is studied since internal waves typically happen here. A numerical simulation for the variable-coefficient Ostrovsky equation with a variable topography is presented. Two basic examples of the depth profile are considered in detail and sustained by numerical results. The first one is the constant-slope bottom, and the second one is the specific bottom profile following the previous studies. These indicate that the combination of variable topography and rotation induces a secondary trailing wave packet.
Highlights
The classical example of an equation yielding solitary wave equations is the Korteweg–de Vries (KdV) equation
We examine the generation of the internal solitary waves in the two-layer fluid flow over a varying topography region in the presence of the background rotation
The aim of this paper is to distinguish the formation of the solitary waves as it propagates through the varying depth region in two-layer fluid in the presence of the rotational effect
Summary
The classical example of an equation yielding solitary wave equations is the Korteweg–de Vries (KdV) equation. The KdV Equation (1), which is acknowledged as a model for weakly nonlinear long waves, was first derived by Korteweg and de Vries [1] by conducting long one-dimensional wave generating at a constant depth of a shallow water channel. They found solitary wave solutions [2]. A( x, t) is denoted as the amplitude of the wave, while x and t are space and time variables Both μ and λ are the coefficients of the nonlinear and dispersive terms, respectively, which are determined by the characteristics of the distinct physical system. The detailed analysis and Fluids 2020, 5, 140; doi:10.3390/fluids5030140 www.mdpi.com/journal/fluids
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