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Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects
Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, The Netherlands
Abstract. Weakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component
of the earth
rotation vector (referred to as "non-traditional'') is taken into
account. Uniformity in one of the horizontal directions is
assumed. It is shown that solutions can be as readily derived with as
without ; hence there is no need to make the so-called
Traditional Approximation. Examples of reflecting internal-wave beams
are presented for super-inertial, inertial and sub-inertial
frequencies. The problem of resonant and non-resonant forcing of the
second harmonic is studied for single plane waves; unlike under the
Traditional Approximation, the problem of reflection from a horizontal
bottom no longer forms a singular case. Non-traditional effects are
favourable to resonant forcing at near-tidal rather than near-inertial
frequencies, and generally increase the intensity of the second
harmonic. Strong stratification tends to suppress non-traditional
effects, but a near-total suppression is only attained for high values
of stratification that are characteristic of the seasonal thermocline;
in most parts of the ocean, non-traditional effects can therefore be
expected to be important.Full Article (PDF, 1108 KB)
Citation: Gerkema, T.: Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects, Nonlin. Processes Geophys., 13, 265-273, 2006. Bibtex EndNote Reference Manager
