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In this paper, a new analysis of the known topographic models of Rossby waves for piecewise exponential topography profiles is
performed. A mathematical method is proposed that allows us to find analytically the group velocity and variance. A numerical comparison is made of the relations presented in the study of Buchwald and Adams and the dependencies obtained within the framework of
a new analytical approach. Numerical comparative analysis showed that the discrepancy for the phase velocities lies in the range of five
percent. For group speeds, the discrepancy reaches nineteen percent for the first mode and decreases for higher mode numbers. We also
consider long-wave asymptotics of eigenfunctions. It is established that the long-wave limit for Rossby shelf waves has specifics: the longitudinal wave number tends to zero, and the transverse wave number reaches a certain finite positive constant, which is the greater the
higher the mode number. It is shown that in the long-wave limit, Rossby shelf waves transform into shelf topographic currents, while
there is a certain self-similarity for the phase and group velocities of shelf currents depending on the value of the topography gradient.
Translated title of the contributionGROUP VELOCITY AND DISPERSION OF BUCHWALD AND ADAMS SHELF WAVES. A NEW ANALYTICAL APPROACH
Original languageRussian
Pages (from-to)8-20
JournalФУНДАМЕНТАЛЬНАЯ И ПРИКЛАДНАЯ ГИДРОФИЗИКА
Volume16
Issue number2
StatePublished - 27 Jul 2023

    Research areas

  • Rossby waves, topographic waves, shelf waves, exponential profile, group velocity, dispersion, self-similarity, mesoscale eddies

ID: 107448606