Update on WP2 – plume modelling Ralph Burton, Stephen Mobbs, Alan Gadian 1

entrainment parameters Latest work has been a collaboration between the Leeds and Bristol groups: WRF and integral models: wind shear Entrainment in plume with shear: several relevant parameters: shear, N2, entrainment parameters Courtesy Mark Woodhouse This side to show that the latest work has been a direct collaboration between Leeds and Bristol groups. Leeds have been running a series of WRF runs specified by Bristol. The work is motivated by the problem of plume response to wind shear.

Courtesy Mark Woodhouse Theoretical models of dependence of plume height upon shear: different entrainment parameters H = plume height (shear) H0 = plume height (no shear) 𝛾 = shear (s-1) Courtesy Mark Woodhouse Here, various theoretical models are shown for h/ho vs shear/N. Bristol will know more about the specific details of the models but they have different levels of complexity (number of parameters), different approaches, etc. Bristol will know if details needed!! But the question is, what does WRF give? Variation in response – what does WRF give?

WRF setup No jet: surface heat flux only, set to give plume height of H0 = 10.5km Variable linear shear: 0 s-1 to 0.01s-1 Constant N = 0.01 High-resolution (100m) runs; 1.5 hour simulations. Example WRF cross-section through plume Here, details of the WRF simulations. N.B. no jet (no imposed W at surface), plume rises through buoyancy: so comparable with theoretical models. N.B. in this WRF example, what appears to be Kelvin-Helmholtz-type structures are appearing at the plume edge. This is for wind speed = 37.5m/s at 10km altitude.

WRF results with theory WRf results superimposed on Mark’s theory graph. There is some agreement (described on next slide), WRF results fit within the envelope of the theoretical approaches. N.B. last statement not true for shear/N > 0.7 but this represents very high wind speeds. (see next slide). N.B. plume height varies in WRF model, there are wavelike features, etc; so the standard deviation of plume height is shown also (error bars). WRF results for last 30 minutes of 1.5 hour simulation: mean±1s.d.

Preliminary conclusions WRF “agrees” with theoretical responses for shear/N < ~ 0.7 but does not follow a single theoretical model For 0.0 < shear/N <0.1 agrees best with Ooms model For 0.1< shear /N <0.5 agrees best with Devenish 3-parameter model. WRF differs from theoretical models for shear/N>0.7 -- but this represents very high background wind speeds (70m/s @10km) More work needed! More work needed on the determination of plume height in the WRF model but this is all very encouraging and a nice piece of work joining two work packages together.