Internal tide generation by arbitrary two-dimensional topography

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. To date, analytical models of internal tide generation by two-dimensional ridges have considered only idealized shapes. Here, we advance the Green function approach to address the generation of internal tides by two-dimensional topography of arbitrary shape, employing the Wentzel-Kramers-Brillouin (WKB) approximation to consider the impact of non-uniform stratifications. This allows for a more accurate analytical estimation of tidal conversion rates. Studies of single and double ridges reveal that the conversion rate and the nature of the radiated internal tide can be sensitive to the topographic shape, particularly around criticality and when there is interference between wave fields generated by neighbouring ridges. The method is then applied to the study of two important internal tide generation sites, the Hawaiian and Luzon Ridges, where it captures key features of the generation process. 1. Introduction Oceanic internal tides are internal wave fields of tidal period. They are produced by barotropic tidal flow over topography, with steep, large-amplitude, nominally two-dimensional topographic features being particularly significant generators (Egbert & Ray 2000; Rudnick et al. 2003; Simmons, Hallberg & Arbic 2004). While some of the internal tidal energy produced by these ridges is believed to go into local mixing near the topography, the consensus is that for tall ridges a majority of the generated energy is radiated away, to participate in processes such as wave–wave interactions and reflections from the continental shelf (Ray & Mitchum 1997; Garrett & Kunze 2007; Echeverri et al. 2009). At the Mendocino Escarpment, for instance, field studies reveal that turbulent dissipation over the top of the topography accounts for only 1 % of the energy flux in the internal tides (Althaus, Kunze & Sanford 2003), and at Kaena Ridge in Hawaii the corresponding values are 5–25 % (Klymak, Pinkel & Rainville 2008). Given the significant contribution to global internal tide generation by nominally two-dimensional topography, there has been a substantial effort to develop analytical models that reasonably predict internal tide conversion rates by such features. An early approach (Baines 1973) uses the method of characteristics, although this technique has proven challenging to implement. The approach of Bell (1975) uses Fourier methods to model internal …