Orographically generated nonlinear waves in rotating and non-rotating two-layer flow

E.R Johnson,J Sommeria,O.J Rump,G.G Vilenski,J.G Esler

doi:10.1098/rspa.2005.1550

Abstract

This paper reports experimental observations of finite amplitude interfacial waves forced by a surface-mounted obstacle towed through a two-layer fluid both when the fluid is otherwise at rest and when the fluid is otherwise rotating as a solid body. The experimental apparatus is sufficiently wide so that sidewall effects are negligible even in near-critical flow when the towing speed is close to the interfacial long-wave speed and the transverse extent of the forced wavefield is large. The observations are modelled by a simple forced Benjamin–Davis–Acrivos equation and comparison between integrations of both linear and nonlinear problems shows the fundamental nonlinearity of the near-critical flow patterns. In both the experiments and integrations rotation strongly confines the wavefield to extend laterally over distances only of order of the Rossby radius and also introduces finite-amplitude sharply pointed lee waves in supercritical flow.

Highlights

Among the many observations of cloud patterns near orography, some stand out as showing stationary disturbances upwind of the orography. Johnson & Vilenski (2004) ( ‘JV’ here) reproduce a NASA photograph of Guadalupe Island, Baja California taken during the Gemini-V flight and described by Stevenson (1969)
The flow is governed by the forced rotating KP (rKP) equation
A similar interpretation is possible and the cross-stream development of the interface displacement observations of figure 4b is closely modelled by the temporal development of a solution of the one-dimensional unforced rotating BDA equation

Summary

Introduction

Among the many observations of cloud patterns near orography, some stand out as showing stationary disturbances upwind of the orography. Johnson & Vilenski (2004) ( ‘JV’ here) reproduce a NASA photograph of Guadalupe Island, Baja California taken during the Gemini-V flight and described by Stevenson (1969). The flow is governed by the forced rKP (frKP) equation They describe weakly nonlinear supercritical solutions showing how steady oblique solitary waves, unattenuated in non-rotating flow, decay with distance from the obstacle and how they can be interpreted in terms of the temporal decay of solitary waves in the one-dimensional problem described by Grimshaw et al (1998a). These effects appear here in both the experimental and model results.

Experimental set-up

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Findings

Discussion and conclusions