The University of Southampton
University of Southampton Institutional Repository

Internal wave reflection and scatter from sloping rough topography

Thorpe, S.A. (2001) Internal wave reflection and scatter from sloping rough topography Journal of Physical Oceanography, 31, (2), pp. 537-553. (doi:10.1175/1520-0485(2001)031<0537:IWRASF>2.0.CO;2).

Record type: Article


Internal gravity waves propagating in a uniformly stratified ocean are scattered on reflection from a rough inclined boundary. The boundary is inclined at angle ? to the horizontal and the roughness is represented by superimposed sinusoidal ripples of amplitude A and steepness S with crests inclined at angle to a horizontal line on the slope. The incident internal waves, of amplitude a and steepness s, propagate in a constant stability frequency ocean toward the boundary at azimuthal angle ?I and at an angle, ? > ?, to the horizontal. They have a wavelength R times that of the sinusoidal roughness. Effects of the earth’s rotation are neglected. To order aS, there are three scattered components: the “primary” component, identical to that reflected from a plane slope with inclination ?, and scattered “sum” and “difference” components. These scattered components have wavenumber components in the plane of the slope equal to the sum and difference of the internal wave’s wavenumber components and those of the sinusoidal topography. It is found that the directional scatter, measured as the angle between the primary reflected wavenumber component on the inclined plane and that of the scattered wave components, is particularly large for topographic angle near 90°, and when the incident wave’s azimuth angle ?I is near zero or 180°. The wavenumbers of the scattered waves, especially those of difference scattered waves, may be an order of magnitude larger than the primary reflected waves when R is large, in particular when the internal wave upslope wavenumber at zero azimuth exceeds the wavenumber of the roughness. The amplitude of the scattered waves is generally largest for “sum” scattered waves and when and ?I are small. The amplitude of the largest scattered waves increases as ? increases from 2.5° to 7.5°, typical of oceanic slopes, with ? ? ? maintained constant (at 5°) and 0.05 R 0.8. The shear in the scattered waves scales with the steepness of the roughness, and is of comparable size to that in the reflected waves when R is large (i.e., typically R 0.4 with ? = 5°); scattering of the longer incident internal waves by topography contributes to the mean magnitude of the (variable) shear near sloping boundaries. The flux of energy carried by the scattered waves as a fraction of the flux incident on the boundary is largest when R is smallest and when ? is near ?. In consequence the effect of scattering by rough topography is likely to contribute to the processes dominant when short waves are incident on a sloping boundary at, or near, critical slope (when ? = ?). The ratio of the scattered flux to that of the primary reflected wave component increases by factors of 3 to 7 as ? increases from 2.5° to 7.5° with ? ? ? = 5° and 0.05 R 0.8; a greater proportion of the incident flux is scattered on the larger slopes. The likelihood of resonant interactions is enhanced by topographic scattering; not only is it possible for the incident and reflected waves to interact resonantly, but the incident and scattered waves may also interact. Conditions for resonance depend on ?, ?, ?I, , and R. Resonance becomes less likely as R increases with other values kept constant, and impossible at second order when ? > 30°.

Full text not available from this repository.

More information

Published date: 2001


Local EPrints ID: 7929
ISSN: 0022-3670
PURE UUID: ef243ded-7389-44d8-b41d-ad7905895a5d

Catalogue record

Date deposited: 04 Aug 2004
Last modified: 17 Jul 2017 17:13

Export record



Author: S.A. Thorpe

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.