Diurnally-varying Ekman layer in a Rossby wave

Weak but persistent synoptic-scale ascent may play a role in the initiation or maintenance of nocturnal convection over the central United States. An analytical model is used to explore the nocturnal low-level jets (NLLJ) and ascent that develop in an idealized diurnally-varying frictional (Ekman) boundary layer in a neutrally stratified barotropic environment when the flow aloft is a zonally-propagating Rossby wave. Steady-periodic solutions are obtained of the linearized Reynolds-averaged Boussinesq-approximated equations of motion on a beta plane with an eddy viscosity that is specified to increase abruptly at sunrise and decrease abruptly at sunset. Rayleigh damping terms are used to parameterize momentum loss due to radiation of inertia-gravity waves. The model-predicted vertical velocity is (approximately) proportional to the wavenumber and wave amplitude. There are two main modes of ascent in mid-latitudes, an afternoon mode and a nocturnal mode. The latter arises as a gentle but persistent surge induced by the decrease of turbulence at sunset, the same mechanism that triggers inertial oscillations in the Blackadar theory of NLLJs. If the Rayleigh damping terms are omitted, the boundary layer depth becomes infinite at three critical latitudes, and the vertical velocity becomes infinite far above the ground at two of those latitudes. With the damping terms retained, the solution is well-behaved. Peak daytime ascent in the model occurs progressively later in the afternoon at more southern locations (in the northern hemisphere) until the first (most northern) critical latitude is reached; south of that latitude the nocturnal mode is dominant.