Buoyancy frequency profiles and internal semidiurnal tide turning depths in the oceans
Résumé
We examine the possible existence of internal gravity wave "turning depths," depths below which the local buoyancy frequency N(z) becomes smaller than the wave frequency. At a turning depth, incident gravity waves reflect rather than reaching the ocean bottom as is generally assumed. Here we consider internal gravity waves at the lunar semidiurnal (M2) tidal frequency, ωM2. Profiles of N2(z) (the quantity in the equations of motion) are computed using conductivity, temperature, and depth data obtained in the World Ocean Circulation Experiment (WOCE). Values for N2(z) computed using Gibbs SeaWater routines in two thermodynamically equivalent expressions for N2(z) are found to yield values that are in excellent accord but differ significantly from N2(z) computed from often-used but inexact expressions that involve potential density. Uncertainties in N2(z) are estimated using a Monte Carlo method, where the data are averaged over a range in depth (80-200 m), which is determined by minimizing a cost function. Our principal result, reached from an analysis of all 18,000 WOCE casts, is that turning depths are common for zonal (east-west propagating) internal tides in the deep oceans. Inclusion of the full Coriolis effect (i.e., not making the so-called Traditional Approximation) leads to the conclusion that turning depths cannot occur for meridional and near-meridional internal tides, but the 'non-traditional' component has little impact on turning depths for internal tides that are near-zonal (i.e., propagating within about 30° of the east-west direction) at low and midlatitudes.