Requirements for large-eddy simulation of surface wind gusts in a mountain valley

During the passage of a front, data from a light-weight cup anemometer and wind vane, sited in a steep-walled glacial valley of the Mt Cook region of the Southern Alps of New Zealand, were analysed to derive a power spectrum of the wind velocity for periods between 0.5 and 16 min. The energy spectrum roughly followed a -5/3 power law over the range of periods from 0.5-4 min — as might be expected in the case of an inertial subrange of eddies. However, any inertial subrange clearly does not extend to periods longer than this. We suggest that the observed eddies were generated in a turbulent wake associated with flow separation at the ridge crests, and large eddies are shed at periods of 4-8 min or more. A compressible fluid-dynamic model, with a Smagorinsky turbulence closure scheme and a "law of the wall" at the surface, was used to calculate flow over a cross section through this area in neutrally stratified conditions. A range of parameters was explored to assess some of the requirements for simulating surface wind gusts in mountainous terrain in New Zealand. In order to approximate the observed wind spectrum at Tasman aerodrome, Mount Cook, we found the model must be three-dimensional, with a horizontal resolution better than 250 m and with a Reynolds-stress eddy viscosity of less than 5 m² s^-1. In two-dimensional simulations, the eddies were too big in size and in amplitude and at the surface this was associated with reversed flow extending too far downstream. In contrast the three-dimensional simulations gave a realistic gusting effect associated with large scale "cat's paws" (a bigger variety of those commonly seen over water downstream of moderate hills), with reversed flow only at the steep part of the lee slope. The simulations were uniformly improved by better resolution, at all tested resolutions down to 250 m mesh size. The spectra of large eddies simulated in steep terrain were not very sensitive to the details of the eddy stress formulation. We suggest that this is because boundary-layer separation is forced in any case by terrain-induced pressure gradients.