UC San Diego

Cross-shore exchange processes are of critical importance for coastal ecosystems such as coral reefs with implications for transport of nutrients, larvae and heat. We present an analytical study of two-dimensional flow in a wedge driven by a time-dependent surface heat flux as a model problem to understand buoyancy-induced cross-shore flow. Besides the turbulent Prandtl number and the Rayleigh number, both assumed to be of order unity, the solution is seen to depend on the geometry through a small parameter ß measuring the bottom slope. Following previous efforts (e.g. [1]) an analytic solution is sought in the asymptotic limit ß << 1 for a water layer bounded by an adiabatic bottom surface subject to a harmonic heat flux on the upper surface. The analysis reveals that the motion at leading order can be expressed as the sum of a harmonic component and a steady component, the latter driven by the nonlinear advection terms. This steady-streaming motion includes a nearshore and alongshore oriented vortex with associated counterclockwise recirculating motion that could have a signicant effect on the near-short transport dynamics.