Global Calculation of Tidal Energy Conversion into Vertical Normal Modes

Abstract

A direct calculation of the tidal generation of internal waves over the global ocean is presented. The calculation is based on a semianalytical model, assuming that the internal tide characteristic slope exceeds the bathymetric slope (subcritical slope) and the bathymetric height is small relative to the vertical scale of the wave, as well as that the horizontal tidal excursion is smaller than the horizontal topographic scale. The calculation is performed for the M 2 tidal constituent. In contrast to previous similar computations, the internal tide is projected onto vertical eigenmodes, which gives two advantages. First, the vertical density profile and the finite ocean depth are taken into account in a fully consistent way, in contrast to earlier work based on the WKB approximation. Nevertheless, the WKB-based total global conversion follows closely that obtained using the eigenmode decomposition in each of the latitudinal and vertical distributions. Second, the information about the distribution of the conversion energy over different vertical modes is valuable, since the lowest modes can propagate over long distances, while high modes are more likely to dissipate locally, near the generation site. It is found that the difference between the vertical distributions of the tidal conversion into the vertical modes is smaller for the case of very deep ocean than the shallow-ocean depth. The results of the present work pave the way for future work on the vertical and horizontal distribution of the mixing caused by internal tides.

On the Consumption of Antarctic Bottom Water in the Abyssal Ocean

“…We note that both q and the vertical structure of local dissipation must vary regionally 272 depending on topographic and oceanographic conditions , St Laurent and Nash 2004, Polzin 2009, Nikurashin and Ferrari 2010a,b, Nikurashin and Legg 2011, 274 Waterman et al 2013, Falahat et al 2014 global averages should not strongly affect the general picture of the presented transformation estimates. On the other hand, because of the non-linear dependence on  , we will examine the 282 sensitivity of transformation rates to the vertical decay scale.…”

“…2013 and modelling Ferrari 2010a,b, Nikurashin et al 2014) results showing that the predicted energy fluxes (Scott et al 2011) tend to overestimate the water 254 column dissipation by about a factor of 3 to 10. Falahat et al (2014) calculated that, on a global average, the first two vertical normal modes take up 59 % of the energy flux into internal tides. Since near-field dissipation is thought to be quasi-258 negligible for the lowest two modes, this places an upper bound for q IT at 41 %.…”

Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?

“…Balmforth and Peacock (2009) modified the approach for studies of periodic supercritical topography in a uniformly stratified ocean of infinite depth, and Echeverri and Peacock (2010) advanced the Green function approach to handle two-dimensional topographies of arbitrary shape in a finite-depth ocean of arbitrary stratification, albeit assuming the WKB approximation. Most recently, Falahat et al (2014) performed global linear computations of tidal energy conversion by small-amplitude, subcritical topography without the WKB approximation, comparing how the accuracy depends on the topographic length scale.…”

“…Our conclusion is that WKB predictions can be quite sensitive to errors in the mode shapes, and given that the computational demands of the complete Green function method are significantly less than those of the numerical simulations (see section 3 for a quantitative comparison), the former should be used at all times, safe in the knowledge that this approach has now been thoroughly validated by direct comparison with numerical simulations. As a follow-up study, it would be intriguing to perform global estimates of internal tide generation along the lines of Falahat et al (2014) using the complete Green function approach, albeit in the twodimensional limit but with the capability to model supercritical topographies also.…”

Natural solutal convection in magnetic fluids: First-order phase transition aspect

“…The energy distribution among these vertical modes is highly variable in the oceans depending on the generation site. Previous analytical studies [5][6][7] have highlighted a strong relationship between vertical mode amplitudes and the topography shape of the generation site (height, width, slope). These analytical approaches rely on strong assumptions: linear approximation (weak wave amplitude limit), infinitesimal topography or subcritical topography, and "propagative" environment (ω < N(z) limit).…”