Mathematical Physics, Analysis and Geometry

, Volume 13, Issue 4, pp 331–355

Mechanism of Energy Transfers to Smaller Scales Within the Rotational Internal Wave Field


DOI: 10.1007/s11040-010-9083-x

Cite this article as:
Ibragimov, R.N. Math Phys Anal Geom (2010) 13: 331. doi:10.1007/s11040-010-9083-x


We discuss the effect of the earth rotation on the two-triad interaction and the oceanic energy distribution processes that occur between five coupled internal gravity waves. The system we study is a two-triad test wave system consisting of an initial wave of the tidal M2 frequency interacting with four recipient waves forming two resonant triads. It is shown that the general mechanism of an arbitrarily large number of internal wave interactions can be described by a three classes of interactions which we call the sum, middle and difference interaction classes. The four latitude singularities are distinguished for the particular case of five interacting waves and all three classes of resonant interactions are studied separately at those critical values. It is shown that the sum and difference interaction classes represent the latitude-inferior and latitude-predominant classes respectively. The phenomenon of coalescence of the middle and difference interaction classes is observed along latitude 48.25° N. It shown that at this value of latitude, the coalescence phenomenon provides the analogy between rotating and reflecting internal waves from slopes.


Critical latitudeResonant interactionsInternal wavesEnergy spectrum

Mathematics Subject Classifications (2010)


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at Brownsville & Texas Southmost CollegeBrownsvilleUSA