Inversion Effects on Lee-wave Rotors Simon Vosper, Stephen Mobbs, Ralph Burton Institute for Atmospheric Science University of Leeds, UK

UK Met Office BLASIUS model Dry Boussinesq equations of motion using a first-order (mixing-length) turbulence closure scheme Free-slip and no-slip (via a log-law formulation) lower- boundary conditions 2 dimensional bell-shaped ridge Upstream wind independent of height, apart from within the boundary layer in the no-slip case Upstream stratification neutral in a layer immediately above the ground, capped by a sharp temperature inversion Above inversion buoyancy frequency independent of height (N=0.01 s -1 ) Range of inversion strengths (measured by the difference in potential temperature across the inversion Δ θ) and inversion heights, z i Numerical Model

No slip case. Horizontal flow speed shaded, potential temperature contoured at 1K intervals. F i =0.6, z i =800 m, H=400 m Closed Rotors

No slip case. Horizontal flow speed shaded, potential temperature contoured at 1K intervals. F i =0.4, z i =800 m, H=400 m Stationary Hydraulic Jump

No Slip Case Closed rotors Stationary hydraulic jumps Free Slip Case No closed rotors Stationary hydraulic jumps

Regime Diagram – No slip Case Solid line – critical F i trapped lee waves (linear theory)

10 min wind vectors, 9 February 2001, East Falkland

High degree of spatial variability during rotor streaming Suggests the use of wind variances in rotor diagnostics Calculate instantaneous spatial standard deviation of wind at stations downwind of orography σ given by Rotor diagnostics σ and σU Energy argument suggests that closed rotors can occur if Analysis of Observations of Rotor Streaming

Time series of rotor diagnostics

Regime Diagram – Observations Solid line - R=1

Mean Speed-up and Rotors U up is wind speed upstream of mountains U is mean wind speed over 8 stations downwind of mountains

Regime Diagram – Observations Idealised modelling demonstrates connection between rotor streaming and trapped lee waves on inversion Needs no-slip boundary condition Correlation between inversions observed downwind of mountains and rotors is low Rotor activity (spatial variability of wind) directly proportional to mean speed-up