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

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.

Wave patterns generated by an axisymmetric obstacle in a two-layer flow

“…Some recent laboratory experiments have focused on such waves in a two layer flow, but they lack instantaneous 3D interface elevation measurements, the interface height being retrieved either from local probes [17,20] or from a vertical plane intersecting the interface [18]. In the present study, an optical stereoscopic technique is deployed to measure an instantaneous field of the elevation of an interface located between two layer of fluid.…”

“…1). These experiments were inspired by recent theoretical works [16,17,11] predicting the wave structure in similar flows where dispersive effects dominate over dissipative effects, as in many geophysical situations. Under certain conditions, for example when the flow speed is close to the gravity waves speed, these results lead to different predictions than previous work in the non-dispersive limit (e.g.…”

Transcritical rotating flow over topography

“…Figure 1 shows the interface displacement recorded during towing tank experiments (Johnson et al 2006) performed at the LEGI-Coriolis rotating tank facility in Grenoble. In the experiments, a surface-mounted obstacle is towed across the tank, exciting internal waves at the interface between two layers of fluid of contrasting density.…”

“…Figure 1(a) shows the interface elevations for an oblong obstacle towed at 10 cm s −1 in the absence of rotation. Figure 1(b) shows a similar experiment, but with the tank rotating with period 120 s, giving a Rossby radius of about 1 m. The experimental values of the non-dimensional parameters Froude number, obstacle height and rotation, defined in § 2.1, are approximately F = 1.1−1.3, M = 0.5 and B = 0.5 (in the rotating case), where the Froude number estimate is partly informed by comparing flow patterns in a number of experiments at different towing speeds with the flow patterns in the model calculations of Johnson et al (2006). Appreciable differences are apparent between the non-rotating and rotating flows.…”

Non-dispersive and weakly dispersive single-layer flow over an axisymmetric obstacle: the equivalent aerofoil formulation

“…For example, there are numerous observations of multiple solitary waves, which are a distinctively dispersive phenomenon, in the flow upstream of obstacles, both in atmospheric flows ahead of islands (Li et al 2004;Badgley, Miloy & Childs 1969;Burk & Haack 1999) and in laboratory experiments (Maxworthy, Dhieres & Didelle 1984;Johnson et al 2006). In order to describe such dispersive phenomena, the third important physical parameter in the problem, the ratio δ of the layer depth and the obstacle width, must be treated as non-zero.…”