Bifurcations and instabilities of stratified anabatic flows in idealized valleys*

Due to evening cooling of the atmospheric boundary layer, areas of complex terrain experience downslope, or katabatic, winds during the night time. In valleys, this process leads to the formation of a stably stratified cold pool at the base of the valley. Subsequently, morning heating will cause upslope, or anabatic flows, leading to the destruction of the stratified layer. However, the specific dynamics of these stratified anabatic flows in valleys are not well understood. This study investigates stably stratified anabatic flows in an idealized valley geometry using local and bi-global linear stability analysis (LSA) as well as direct numerical simulations (DNS) for extensive validation of the results. Through LSA, we observe a unique series of bifurcations, which includes a pair of pitchfork bifurcations, followed by a Hopf bifurcation that initiates a three-dimensional unsteady flow in the idealized valley. We also observe a unique three-dimensional instability which returns to a two-dimensional state in DNS, when control parameters are sufficiently low. Finally, we classify each flow regime by a unique set of novel dimensionless parameters.