Internal wave stress‐shear correlations: A choice of reference frames

Abstract

A numerical simulation of internal waves using an eikonal approach is analyzed for a relation between the short wavelength, relatively high frequency waves, and the velocity and shear resulting from a background of low vertical wavenumber waves through which the short waves propagate. The background consists predominantly of quasi‐inertial motions. The results indicate a strong correlation between the horizontal group velocity of the short waves and the shear of the background when the short waves have been refracted to 10 meters or less in vertical wavelength. It appears that rapid refraction of the short waves to dissipative scales (< 5 m) then occurs as they become oriented with the shear. The directional anisotropy of the short high frequency waves at dissipation scales suggests an average u‐w correlation. Thus the high Reynolds stresses predicted by Müller [1976] are primarily associated with the shear of long wave inertial motions. In nature, the u‐w correlation would only be seen if the averaging is done in a reference frame that is allowed to rotate with the shear. A fixed frame averaging would give a near zero result, thus accounting for the absence of stress‐shear correlations in the fixed frame measurements of Ruddick and Joyce [1978]. Vertical profiler data of horizontal velocity are also examined for indications of a correlation in the short wave velocity field relative to the long wave shear and velocity fields. These observations are dominated by low frequency, quasi inertial oscillations. There is no consistent evidence of a directional anisotropy in the short wave field which is dependent on the long wave shear, but weak evidence of velocity polarization such that the long and short waves are polarized in the same direction.