Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Scattering of internal gravity waves<br />
A. Nye a and S.B. Dalziel a<br />
Internal gravity waves are generated by disturbances to continuous stable<br />
stratifications such as those found in the deep ocean. While reflection from smooth<br />
boundaries (i.e. boundaries that appear flat on the scale of the wavelength) may be well<br />
modelled through simple ray tracing, the same is not true when the boundaries<br />
contain features of a scale comparable with the wavelength. In such cases incident<br />
wave energy flux may be ‘scattered’ amongst different wavenumbers at boundaries<br />
and even reflected back along the path of the incident wave beam. The amplitude and<br />
steepness of the scattered waves will also differ from that of the incident beam.<br />
Consequently, subsequent propagation of scattered waves can result in breaking,<br />
turbulence and mixing. Such mixing is associated with higher wavenumbers because<br />
the corresponding waves have small length scales and may develop shear instabilities.<br />
This research aims to establish scattering behaviour of internal gravity waves<br />
incident on topography with length scales similar to those of incident waves.<br />
Numerical and experimental methods are used to investigate two-dimensional internal<br />
gravity waves with frequencies less than the buoyancy frequency interacting with<br />
topography.<br />
A two-dimensional inviscid numerical model had been developed to describe<br />
internal gravity waves propagating in a stable linear stratification. Waves are generated<br />
by fluxes varying sinusoidally in time over the surfaces of a square ‘source’. Structures<br />
of simulated wave beams are compared before and after incidence on various<br />
numerical topographies. Amplitudes of the scattered waves are used to determine the<br />
partitioning of incident energy flux between different wavenumbers and frequencies at<br />
the boundary. A complementing experimental investigation uses a “synthetic<br />
schlieren” 1 technique to observe scattering of internal gravity waves in a stable linear<br />
salt-stratified tank. Waves are produced by small amplitude vertical oscillation of axissymmetric<br />
cylinders of circular and square cross-section. These studies are intended<br />
as a comparison to theoretical work currently in progress.<br />
a DAMTP, University of Cambridge, U.K.<br />
1 Dalziel et al., Exp. Fluids 482, 51 (2003).<br />
145
Change language