Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects

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 f̃ 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 f̃ ; 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 neartotal 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.