Blocking in periodic valleys

Results are presented from a study of blocked flow (practically stagnant or recirculating light winds) in periodic valleys in thermally stably stratified ambient conditions. Inviscid and turbulent diffusion cases were modelled numerically to clarify the effects of turbulence on the blocking. The reflection of gravity waves from the top boundary of the hydrostatic model atmosphere was avoided by employing the radiation condition given by Klemp and Durran (1983). The dissipative numerical results are compared with new laboratory experiments which utilized the technique of Baines and Hoinka (1985) to simulate a semi-infinitely deep region.A criterion for the occurrence of blocked flow cannot be defined for the inviscid case except when the Froude number, Fr, based on the peak-to-trough ridge amplitude is less than about 0.4: then blocking is clearly identifiable before wave-breaking occurs. Breaking of waves is evident for Fr as large as 0.75, in agreement with analytical results given by Lilly and Klemp (1979).At small Froude number (Fr 0.5) in the dissipative flow simulations, blocked flow (stagnation) is present in the valleys, but a lee rotor (complete stagnation) is not evident. For order unity Froude numbers, blocking is a wave phenomenon, resulting from wave steepening and overturning or turbulent mixing. A finite thickness is brought to rest or participates in a recirculating flow when it first appears. A strong upward flow appears ahead of the rotor in the valleys, and the downslope wind over the windward side of the valleys is strengthened. Thus the present study shows that conditions for the onset of a rotor, and of stagnant flow, in periodic valleys are different.When blocked flow exists, the amplitudes of gravity waves in the upper layer are only 15% (Fr = 0.3) to 80% (Fr = 1.5) of those given by linear theory; this is supported by observations.