Cross-shelf variations of near-inertial current oscillations

Observations and numerical simulations show that cross-shelf variations of current oscillations at near-inertial frequencies increase exponentially in amplitude from nearshore to waters with depths of 100–200 m. An assessment of a semi-analytical theory of the cross-shelf variation of near-inertial current oscillations (Chen and Xie, 1997, Journal of Geophysical Research 102(C7), 15,583–15,593) indicates that, although instructive, the theory does not capture all the elements seen in numerical simulations. Here a purely analytical approach is taken. It assumes only that the cross-shelf currents are of the form AB cos ft, where B is an amplitude modifier (a function of the distance offshore) and f is the Coriolis parameter. The solution to the governing equations gives B=1−e−x/L, where x is the distance offshore and L is a radius of deformation length scale. The solutions show that exponentially increasing current oscillations over continental shelves are actually a form of inertial-gravity waves. In non-equatorial regions, the effect of the sea surface pressure gradient is found to be in phase with that of the Coriolis effect but with a much larger magnitude over the inner continental shelves. The kinematic boundary condition results in the oscillating sea level setup and setdown, the resulting pressure gradient drives the oscillatory cross-shelf currents over the inner continental shelf, and the Coriolis effect results in a corresponding oscillatory flow in the longshore direction. One of the more notable findings is that the length scale L, referred to here as the inertial-gravity barotropic radius of deformation, is found to be significantly larger than the classical barotropic radius of deformation.