Neutrally- and stably-stratified boundary layers adjustments to a step change in surface roughness

Abstract

In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development in the log-law region shows good agreement with the diffusion model proposed by Panofsky and Dutton (Atmospheric turbulence, Wiley, New York, 1984) provided that a modified origin condition is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes $$n\approx 0.8$$ n ≈ 0.8 ). For the stably-stratified boundary layers, n is found to further reduce as the bulk Richardson number, $$\textrm{Ri}_\textrm{b}$$ Ri b , increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers. Graphical abstract

Statistical properties of neutrally and stably stratified boundary layers in response to an abrupt change in surface roughness

“…Further details on their dimension and spacing are discussed in Ding et al. (2023), where this set-up was first used. The resulting roughness lengths, evaluated with the methodology described in § 2.3, are for the upstream and for the downstream surface in neutral conditions, respectively.…”

“…The incoming flow is in a state of equilibrium, as discussed in Ding et al. (2023), and its friction velocity, , is determined at . With regards to the downstream surface, the friction velocity is determined by the mean value of the local friction velocity in the range based on the observation that the local friction velocity becomes invariant with fetch for .…”

“…2018; Ding et al. 2023), which is troublesome to explain/reproduce with these early analytical models. Progress in interpreting the appearance of small values includes the study of a flow from a rough to a smooth surface by Li et al.…”

“…In addition, Ding et al. (2023) incorporated the decay laws of the diffusion and the vertical advection terms into the original diffusion model to interpret the small exponent that arises for both neutrally and stably stratified boundary layers developing from a rough to a much rougher surface.…”

“…2018; Ding et al. 2023), hence the slow growth rates of stable IBLs. However, the statistical properties during the development of stably stratified IBLs remain largely unexplored and their dynamics is poorly understood.…”