The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

TL;DR

This study investigates how rotation and shoaling effects influence solitary wave behavior over variable topography, revealing that shoaling can counteract decay caused by rotation, with implications for internal waves in coastal zones.

Contribution

It analyzes the interplay between rotation and shoaling effects on solitary waves using the Ostrovsky equation with variable coefficients, supported by numerical modeling and real oceanic parameter estimates.

Findings

Shoaling can suppress decay of solitary waves caused by rotation.

Two bottom profiles analyzed: constant slope and constant amplitude.

Predicted stable soliton dynamics are relevant for internal waves in coastal zones.

Abstract

This paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For solitary waves moving toward the beach, the terminal decay caused by the rotation effect can be suppressed by the shoaling effect. Two basic examples of a bottom profile are analyzed in detail and supported by direct numerical modelling. One of them is a constant-slope bottom and the other is a specific bottom profile providing a constant amplitude solitary wave. Estimates with real oceanic parameters show that the predicted effects of stable soliton dynamics in a coastal zone can occur, in particular, for internal waves.