Wind Energy

18
Boundary-Layer Influence on Extreme Events
in Stratified Flows over Orography
Karine Leroux and Olivier Eiff
Summary We present a laboratory investigation of the boundary-layer effects
on mountain wave-breaking under conditions of uniform flow and stratification,
in particular the first complete up- and downstream velocity field revealing
upstream separation and blocking, wave breaking, downslope windstorms,
trapped lee-waves and rotors. Contrary to the slip condition on the obstacle
we show that the slip condition downstream only has a slight influence on
the flow dynamics. The results also reveal that the boundary layer developed
on the obstacle is controlled by the wave-field, independently of the Reynolds
number.
18.1 Introduction
Flow of stably density-stratified fluid over orography, such as mountains, generates
internal gravity waves. For strong enough stratifications, �i.e.
Froude
numbers FH = U0/N H < 1 where U0 is the wind speed, N = − g ∂ρ
ρ0 ∂z is
the Brunt–Väisälä frequency and H the mountain height, these waves can
attain sufficient amplitude to develop vertical isopycnals which leads to wavebreaking
at high altitudes. The ensuing (clear-air) turbulence is accompanied
by strong downslope windstorms, with speeds up to 50 m s−1 , as observed in
Colorado on 11 January 1972 [1].
Other orographic phenomena that can occur under stratified conditions
are trapped lee-waves (TLW) with embedded rotors. These have usually been
associated with inversions and non-uniform flow (e.g. [2]) and are not usually
linked to wave-breaking in uniform flow and stratification conditions. However,
even for uniform conditions, these phenomena were observed by Eiff
et Bonneton [3] when wave breaking occurs. Gheusi et al. [4] showed that
the physically correct no-slip condition on the obstacle yields TLWs and rotors
even for uniform conditions. In addition to showing that the maximum
downslope wind speed is reduced (3–2.5U0), the slip-condition helps to induce