Multiple steady states and symmetry-breaking in stratified anabatic flows in idealized valleys

Due to evening cooling of the atmosphere, sloping terrain experiences downslope, or katabatic, winds during the nighttime, which lead to the formation of stably stratified cold pools in the base of valleys. Subsequently, morning heating causes upslope, or anabatic, flows, leading to the destruction of the stratified layer. However, the specific dynamics of these stratified anabatic flows in valleys is not well understood. In this study, we characterize the full structure of steady laminar anabatic flows in a stably stratified V-shaped valley using a dynamical systems approach. Our approach is based on the discovery of a quiescent conduction state from which a unique asymmetric nested-pitchfork bifurcation emerges. With sufficient surface heating, the conduction state bifurcates into two possible states, including symmetric and asymmetric steady state profiles. The asymmetric state manifests as a mirror image pair with clockwise and counterclockwise central circulations, while the symmetric state gives rise to upslope and downslope convection patterns, which do not satisfy the same mirror image reflection. Linear modal analysis and numerical simulations show that these two symmetric states are linearly unstable and will transition to the asymmetric state under the slightest perturbation.