Diurnal variations of the Ekman layer in a Rossby wave

Co-authors: Jason Chiappa and David B Parsons

An analytical model is presented for temporal variations of the Ekman layer in a zonally-propagating barotropic Rossby wave under fair-weather conditions. The flow is periodic in the zonal direction (x) and doubly-periodic in time. Temporal periodicities arise from a pressure gradient force that supports the Rossby wave (period is an integral number of days) and a diurnally-varying eddy viscosity that increases abruptly at each sunrise and decreases abruptly at each sunset to (crudely) model the turbulence intensities during the morning and evening transitions. The governing equations are the Reynolds-averaged Boussinesq-approximated horizontal equations of motion on a mid-latitude beta plane, linearized about a uniform westerly current. The governing parameters are latitude, wavelength, wave amplitude, wave frequency (or westerly current speed), daytime and nighttime values of eddy viscosity, duration of daylight, and a constant used to parameterize momentum-damping by inertia-gravity waves. The analytical solution produces nocturnal low-level jets and frictionally-induced ascent/subsidence (Ekman pumping and suction). Diurnal variations of the eddy viscosity result in a secondary maximum of ascent during the nighttime. Of particular interest are the amplitude, location, and timing of the peak vertical motion (which may play a role in nocturnal convective initiation) and the possibility of resonance when a harmonic of the Rossby wave frequency equals the diurnal frequency.