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Discover the significance of Nh/U, non-dimensional mountain heights, and orographic wind flows with statistical products and physical insights. Explore neutral flows over hills, stable flows over mountains, and the impact of the Coriolis force on airflow patterns. Learn how surface friction affects mountain waves and the implications for wind forecasting.
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Airflow over and around hills and mountains Haraldur Ólafsson University of Iceland Icelandic Meteorological Office haraldur@vedur.is
WHY INTERESTING FOR FORECASTERS? • STATISTICAL PRODUCTS • EXPERIENCE / PHYSICAL INSIGHT LOGICAL OROGRAPHIC WINDS ARE IN GENERAL POORLY OR NOT AT ALL RESOLVED BY THR NWP MODELS FORECASTERS MUST RELY ON
Key non-dimensional number Nh/U (Non-dimensional mountain height or inverse Froude nember) N={g/T ∂T/∂z } ½ Brunt-Väisälä frequency or stability N is often 10 -2 s -1 h : mountain height u : upstream wind speed U h Flow over mountains
What is Nh/U? • Non-dimensional wavelenght • Potential energy / kinetic energy Next slides: Flow with Nh/U = 0 Flow with 0 < Nh/U < 1 Flow with Nh/U >1.5
NEUTRAL FLOWS (OVER HILLS)Nh/u=0 GENTLE SLOPES STEEP SLOPES U/UO U/UO Boundary-layer separation STREAMLINES STREAMLINES
WIND SPEED IN MOUNTAIN WAVES ρn-5 ρn-2 ρn Umax where the air descends Nh/u > 0
UMAX Z Nh/U = 0 UMIN UMIN NEUTRAL FLOW (HILLS) T Nh/U > 0 UMIN UMAX Z T STABLE FLOW (MOUNTAINS)
FLOW OVER MOUNTAINS { Nh/U } > { Nh/U } C { Nh/U } C = (mountain shape,∂/∂ z (U,N),...) ≈ 1.5 => Blocked flows FAST Dense Air SLOW WAKE SLOW L H L BLOCKING B = ½ ρ u2 + P + gρz = constant In blocking: P ↑ => U ↓
For L<100 km (Ro>1) Corner wind DV/dt =1/ρVP-fV + F H L Gap wind L H Tip jet / corner wind
Two examples of simulated wind in the vicinity of Reykjavík • Weak ENE • Strong NE
Eastnortheasterly winds in Reykjavík – moderate wind speed (ca. 6 m/s) Nh/U ~2.0 Veðurstofa
Eastnortheasterly winds in Reykjavík – moderate wind speed (ca. 6 m/s) Nh/u ~0.5 Veðurstofa
If the airmass is stable almost all the time and mountain (gravity) waves form in a stable airmass that impinges a mountain why are there not strong waves all the time?
Surface friction is wave-destructive! No surface friction Surface friction
Isentropes in two numerical simulations (K) Very amplified waves Little wave activity in the troposphere A stable layer
Impact of scale / the Coriolis force Ro = U/fL U : upstream wind speed f : the Coriolis parameter L : length scale If L = 100 km, U = 10 ms-1 and f = 10-4 s-1 Ro = 1 => Significant impact of the Coriolis force on the flow very fast deceleration fast Ro = 1: L L H slow less deceleration fast
The mountain wind forecasting diagram Red=speed upBlue=slow down T 10 Ro=U/fL 1 0.1 0.1 1 10 ĥ=Nh/U