Internal wave beam propagation in non-uniform stratifications

Abstract

In addition to being observable in laboratory experiments, internal wave beams are reported in geophysical settings, which are characterized by non-uniform density stratifications. Here, we perform a combined theoretical and experimental study of the propagation of internal wave beams in non-uniform density stratifications. Transmission and reflection coefficients, which can differ greatly for different physical quantities, are determined for sharp density-gradient interfaces and finite-width transition regions, accounting for viscous dissipation. Thereafter, we consider even more complex stratifications to model geophysical scenarios. We show that wave beam ducting can occur under conditions that do not necessitate evanescent layers, obtaining close agreement between theory and quantitative laboratory experiments. The results are also used to explain recent field observations of a vanishing wave beam at the Keana Ridge, Hawaii.

Propagating and evanescent internal waves in a deep ocean model

“…Sutherland & Yewchuk (2004); Gregory & Sutherland (2010) performed experimental tests with a focus on the reflection and transmission of internal waves through weakly stratified regions. Mathur & Peacock (2009 verified their theory with experiments focused on the interaction of internal wave beams with sharp density gradients and finite-width transition regions, as a model of the upper-ocean and thermocline.…”

“…While their theory gives analytic expressions for the vertical velocity field, the derivation requires that the wavelength and beam width be small compared to the length scale characterizing the stratification, which is the case examined here. Recent studies (Nault & Sutherland 2007;Mathur & Peacock 2009 have developed theories for the propagation of internal waves in nonuniform stratifications that do not require these assumptions. Sutherland & Yewchuk (2004); Gregory & Sutherland (2010) performed experimental tests with a focus on the reflection and transmission of internal waves through weakly stratified regions.…”

New wave generation

“…A full understanding of the generation mechanism has yet to be achieved, however, and laboratory experiments using the Thomas-Stevenson beam profile impinging on a thermocline could provide significant insight. Indeed, the interaction of wave beams with nonlinear features in the density stratification is of widespread interest (Mathur & Peacock 2009), since this is also relevant to how and where atmospheric internal waves break and deposit their momentum (Nault & Sutherland 2007). In regards to ocean mixing problems, an open issue is to determine the fate of the internal tide which, among other things, can be scattered by topography (Johnston & Merrifield 2003;Ray & Mitchum 1997).…”

“…This scenario, which is possible because the direction of wave propagation is set by the dispersion relation (1.1), has two major advantages over the other possibility of a generator tilted in the direction of wave propagation Mathur & Peacock 2009). First, it is far more convenient because it requires no mechanical components to orient the camshaft axis and no change of orientation for different propagation angles.…”

“…The maximum horizontal displacement of each plate is set by the eccentricity of the corresponding cam, and the spatio-temporal evolution is defined by the phase progression from one cam to another and the rotation speed of the camshaft. So far, this novel configuration has been used to study plane wave reflection from sloping boundaries (Gostiaux 2006), diffraction through a slit (Mercier et al 2008) and wave beam propagation through nonuniform stratifications (Mathur & Peacock 2009). Despite Plates are vertically stacked on an eccentric camshaft.…”