Consistency relations for internal waves

Abstract

A complete set of linearly independent relationships among the different cross spectral components obtained from pairs of moored instruments is derived which can be utilized to test whether or not the observed fluctuations within the internal wave frequency band represent a field of propagating internal waves. A further complete set of relationships is derived which enables to test whether or not the internal wave field is horizontally isotropic and (or) vertically symmetric. These relations are compared with corresponding relations for alternative models (standing internal wave modes, three-dimensional isotropic turbulence) and their capability to discriminate between the various models is investigated. The tests are applied to a set of data for which it is found that the observed fluctuations are consistent with both propagating and standing internal waves whereas isotropic turbulence must be rejected for the most part of the internal wave frequency band.