Durland Theodore S.

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Durland
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Theodore S.
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  • Article
    Another note on Rossby wave energy flux
    (American Meteorological Society, 2020-02-19) Durland, Theodore S. ; Farrar, J. Thomas
    Longuet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.
  • Article
    Long-distance radiation of Rossby Waves from the equatorial current system
    (American Meteorological Society, 2021-05-24) Farrar, J. Thomas ; Durland, Theodore S. ; Jayne, Steven R. ; Price, James F.
    Measurements from satellite altimetry are used to show that sea surface height (SSH) variability throughout much of the North Pacific Ocean is coherent with the SSH signal of the tropical instability waves (TIWs) that result from instabilities of the equatorial currents. This variability has regular phase patterns consistent with freely propagating barotropic Rossby waves radiating energy away from the unstable equatorial currents, and the waves clearly propagate from the equatorial region to at least 30°N. The pattern of SSH variance at TIW frequencies exhibits remarkable patchiness on scales of hundreds of kilometers, which we interpret as being due to the combined effects of wave reflection, refraction, and interference. North of 40°N, more than 6000 km from the unstable equatorial currents, the SSH field remains coherent with the near-equatorial SSH variability, but it is not as clear whether the variability at the higher latitudes is a simple result of barotropic wave radiation from the tropical instability waves. Even more distant regions, as far north as the Aleutian Islands off of Alaska and the Kamchatka Peninsula of eastern Russia, have SSH variability that is significantly coherent with the near-equatorial instabilities. The variability is not well represented in the widely used gridded SSH data product commonly referred to as the AVISO or DUACS product, and this appears to be a result of spatial variations in the filtering properties of the objective mapping scheme.