Impact of Wave Interference on the Consistency Relations of Internal Gravity Waves near the Ocean Bottom

Abstract

Consistency relations of internal gravity waves (IGWs) describe ratios of cross-spectral quantities as functions of frequency. It has been a common practice to evaluate the measured or simulated signals (e.g., time series of velocity, density, etc.) against the consistency relations, as a way to determine whether an oceanic field of interest is comprised of IGWs. One such study is carried out in Nelson et al. (JGR Oceans, 125(5), 2020, e2019JC015974), which certifies that the ocean interior field in a numerical simulation of a region southwest of Hawaii is dominated by IGWs, through evaluating the consistency relations derived from time series at a depth of 620 m. However, we find that when the same procedure is applied at greater depths (e.g., 2362 m, 3062 m, and 4987 m), a clear deviation of the simulated signal from the classical consistency relations is observed. In this paper, we identify the reason for the unexpected deviation and show that it is a general phenomenon due to interference of low vertical modes under the reflection by the ocean bottom. We further derive a new set of formulae to characterize the consistency relations of these low modes and validate these formulae using model output.