The cross-slope transport of momentum by internal waves generated by alongslope currents over topography

Abstract

The alongslope currents flowing over topography of sufficiently small length scale, typically less than 10 km, on the continental slopes generate internal lee waves. These carry their momentum predominently toward shallower water, that is up the slope toward and across the shelf break, and onto the continental shelf, at least when, in summer, stratification permits their propagation. Analytical results show that even when the lee waves are generated with a component of their group velocity directed toward deeper water, reflection at the sloping seabed may lead to a turning toward shallower water. A numerical model is used to examine internal wave propagation and to quantify the flux of their momentum across the shelf break. In the conditions considered here with f/N ≪ 1 and slope angle, α, near 5 deg, the flux is parameterized by a stress (momentum flux per unit vertical area along the shelf break) per unit length downslope, τ*, given by τ* = kρ0VNh2 cos4(β + β0), where ρ0 is the mean water density, V is the mean alongslope flow over the slope, N is the buoyancy frequency in the vicinity of the shelf break, f is the Coriolis parameter, and h2 and βare the mean square amplitude of the topography of wavenumber l, such that Vl/N < 1, and its mean orientation relative to the upslope direction, respectively. The constant β0 is 7 ± 2 deg, and the formula is only valid if β < 60 deg. A value of k of about 9 (±4) × 10-6 m-2 is suggested, with values near 1.3 × 10-5 m-2 when the topography is dominated by wavelengths less than 4πV/N, or 5 × 10-6 m-2 when they exceed 20V/N. This flux represents a transfer of momentum to the shelf currents in a direction contrary to the current over the slope that generates the internal waves. The magnitude of the flux is usually dominated by conditions near the top of the continental slope. Timescales of about 5 days are associated with this transfer on 5 deg slopes with 10-m high topography when N ≈ 10-2 s-1.