  We investigate the instabilities and transition mechanisms of Boussinesq
stratified boundary layers on sloping boundaries when subjected to oscillatory
body forcing parallel to the slope. Such conditions are typical of the boundary
layers generated by low wavenumber internal tides sloshing up and down
adiabatic abyssal slopes in the absence of mean flows, high wavenumber internal
tides, and resonant tide-bathymetry interactions. We examine flows within a
region of non-dimensional parameter space typical of the mid- to low-latitude
oceanic $M_2$ tides on hydraulically smooth abyssal slopes by direct numerical
simulation. We find that at low Reynolds numbers transition-to-turbulence
pathways arise from both shear and gravitational instabilities, and we find
that the boundary layers are stabilized by increased outer boundary layer
stratification during the downslope oscillation phase. However, if rotation is
significant (low slope Burger numbers) we find that boundary layer turbulence
is sustained throughout the oscillation period, resembling Stokes-Ekman layer
turbulence. Our results suggest that oscillating boundary layers on smooth
abyssal slopes created by low wavenumber $M_2$ tides do not cause significant
irreversible turbulent buoyancy flux (mixing) and that flat-bottom dissipation
rate models derived from the tide amplitude are accurate within an order of
magnitude.
