The governing flow equations, which include the momentum and buoyancy/heat balance equations complemented by the continuity equation, are solved numerically in the Boussinesq approximation. The equations are written in a slope-following right-hand coordinate system. The solution is carried out by a numerical algorithm with a fourth-order finite differencing of advection and diffusion terms in the transport equations, and with the fourth-order Runge-Kutta scheme applied for the time integration. For the pressure, a fourth-order Poisson solver is used. Boundary conditions in the lateral (along- and cross-slope) directions are periodic. At large distance from the slope, free-flow conditions are imposed on the flow variables, with buoyancy going to zero. On the sloping surface, the no-slip and impermeability conditions are used for the velocity components, and the condition for the buoyancy is formulated in accordance with the prescribed thermal forcing type.
Every individual simulation starts with the generation of a slope-following daytime convective boundary layer (CBL) driven by either a positive surface buoyancy or buoyancy flux. In the presence of the southerly geostrophic wind, and under the combined effect of the upslope (anabatic) buoyant acceleration and the Coriolis force, the upslope component in the CBL flow develops by the end of the day. At that point, the surface buoyancy (or buoyancy flux) drops to some lower (negative in some cases) nighttime value. The adjustment of the boundary layer flow to such a change in surface forcing happens in a form of an oscillation that has both gravitational (buoyancy) and inertial (associated with weakened near-surface friction) components. The NLLJ, developing as a result of such oscillation, appears to be rather different to the traditional NLLJ typically considered in the flat-terrain context.
The obtained numerical results indicate that the shallow slope affects the flow structure of NLLJ in many different ways. Besides the pace of the jet development (which is faster if the slope is present) and the shape of the jet wind-speed profile (which is characterized by a sharper and larger-magnitude maximum in presence of the slope), the entire turbulence structure of NLLJ and its evolution in time are essentially influenced by the slope-related flow mechanisms. Instigated by the slope-related gravitational branch of the oscillation, a pronounced nighttime jet-like flow develops from the daytime tilted CBL in the absence of any geostrophic forcing. Another effect associated with the presence of the slope is the upslope advection of potential temperature in the near-surface region of the flow during the night. Under certain circumstances, this advection can reignite static instability in the weakly turbulent flow formed after the evening transition and lead to a complete remix of the lower portion of the boundary lay flow and associated drastic changes in the NLLJ shape and elevation. The type of prescribed surface forcing is found to affect the evolution of the turbulence structure of the NLLJ over sloping terrain much stronger than in the flat-terrain NLLJ. Also, the daytime flow preconditioning during the CBL stage, known to be the primary factor determining the subsequent NLLJ development, apparently plays even more important role in NLLJs over a slope due to the contribution of slope effects to the preconditioning.