Abstract
The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.
Highlights
Besides wind-driven upwelling in the Southern Ocean, interior mixing has been identified as a major contributor to maintaining the global ocean circulation (e.g. Munk & Wunsch 1998; Talley 2013, and references therein)
In order to determine suitable numerical parameter settings for realistic topography, we choose a region of interesting topography that involves no land points and is large enough to incorporate a reasonable number of circular patches for a variety of parameters: spanning 30.85–55.83◦ W and 10.83–35.83◦ N, it covers an area of 2.78 × 103 km in latitudinal and 2.55 × 103 km in longitudinal direction over the Mid-Atlantic Ridge (MAR)
The main difference from previously applied schemes is that the energy conversion is derived from the far-field energy flux instead of an integral over the sources
Summary
Besides wind-driven upwelling in the Southern Ocean, interior mixing has been identified as a major contributor to maintaining the global ocean circulation (e.g. Munk & Wunsch 1998; Talley 2013, and references therein). Bell 1975b; Nycander 2005; Falahat et al 2014b) and if they do, they describe the modal structure of the internal tide field only in approximate form (Vic et al 2018) To close this gap and to help improve mixing parametrisations based on internal wave dynamics, we here present a new semi-analytical method to calculate both the horizontal direction and the magnitude of the energy flux from the barotropic tide into the different vertical modes, taking the full vertical structure of the stratification into account. Falahat et al (2014b), on the other hand, based their global calculations on the approach by LSY02 and solved the vertical eigenvalue problem for the first 10 internal tide modes They compared their results to those of Nycander (2005) and found that the two methods diverged most strongly in the upper ocean, with the global integrals of the energy conversion rate differing by 16 %. The focus of this paper is on the introduction of the new method and its evaluation; global calculations of the angular energy flux into vertical modes using realistic topography, tidal velocities and stratification will be presented in a follow-up publication
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