Three-dimensional numerical simulations of strongly stratified flow past conical orography

Results from a series of numerical simulations of three-dimensional stably stratified flows past conical orography with unit slope are presented and a re compared directly with laboratory results from a stratified towing tank. The simulations are conducted with a finite-difference model (configured t o simulate flows in the towing tank) based on the inviscid nonhydrostatic e quations of motion in sigma (normalized pressure) coordinates. A free-slip lower boundary condition is implemented. The Rows studied have values of th e Froude number, F-h = U/Nh, between 0.1 and 0.8, where Li is the mean Row speed, N is the buoyancy frequency, and it is the mountain height. To excite unsteadiness in the simulations an asymmetric perturbation is app lied to the initial potential temperature (theta) field. The resulting vari ation of the temporally averaged drag coefficient with F-h is found to comp are reasonably well with the laboratory measurements and there is a general trend for the drag coefficient to decrease as F-h increases. For many of t he simulations the temporal evolution of the drag is highly unsteady: when F-h less than or equal to 0.3 the unsteadiness is quasiperiodic and is due to vortex shedding in the lee of the orography. The nondimensional vortex s hedding frequency is similar to that measured in the laboratory. Simulation s conducted without the initial theta perturbation do not exhibit vortex sh edding and in this case the drag is significantly reduced. The vorticity ge nerated in both the perturbed and unperturbed Rows is shown to be largely p erpendicular to the isentropic surfaces and hence potential vorticity anoma lies are present. These anomalies appear early on in the simulations and ar e caused by internal dissipation within the vortices due to numerical visco sity. Simple tests in which the free-slip lower boundary condition is repla ced with one containing a surface friction parametrization show that one of the main effects of friction is to suppress the vortex shedding. Further, the results indicate that in the laboratory an inviscid mechanism (in which vertical vorticity is generated via, the tilting of baroclinically generat ed horizontal vorticity) dominates over the generation of vertical vorticit y in the boundary layer. At F-h = 0.4 a local maximum occurs in the temporally averaged drag and thi s corresponds to the occurrence of wave breaking in the lee of the mountain . The wave-breaking process itself is highly unsteady and after continuous growth of the wave amplitude (and drag) convective instability eventually l eads to a complete collapse of the overturning region and a significant fal l in the drag. Further unsteadiness occurs at higher values of F-h when a rigid-lid upper- boundary condition is enforced: for 0.45 less than or equal to F-h less tha n or equal to 0.6 the evolution of the simulated drag is quasiperiodic and this is shown to be caused by the generation of an unsteady wave motion ups tream. Comparison with existing linear theory indicates that this is due to the existence of a wave mode whose horizontal group velocity is small but has a nonzero frequency. The effects of blockage, due to the presence of the towing-tank side walls, are investigated by enforcing radiative boundary conditions at the spanwis e lateral boundaries. As found in the towing-tank experiments, blockage eff ects are shown to significantly increase the drag coefficient and nondimens ional shedding frequency at low Froude numbers (F-h less than or similar to 0.4) and also alter the Froude number at which wave breaking occurs.