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

TL;DR

This study investigates how wave interference near the ocean bottom affects the expected consistency relations of internal gravity waves, revealing deviations caused by low mode interference and proposing new formulas to account for this effect.

Contribution

The paper identifies the impact of wave interference on IGW consistency relations near the ocean bottom and introduces new formulas to accurately characterize low mode effects.

Findings

Deviations from classical consistency relations occur at greater depths.

Wave interference from low vertical modes causes these deviations.

New formulas successfully model the consistency relations considering interference.

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.