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Abstract Turbulent flows over a large surface area (S) covered bynobstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter areaAand a shelter volumeV. The individual sizes ofAandVwithout any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element ton/Selements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducingAorVwith each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction inAandVonly when the ratio ofn/Sis small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughoutS. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities. 

Empirical evidence is provided that within the inertial sublayer (i.e. logarithmic region) of adiabatic turbulent flows over smooth walls, the skewness of the vertical-velocity component$$S_w$$displays universal behaviour, being a positive constant and constrained within the range$$S_w \approx 0.1\unicode{x2013}0.16$$, regardless of flow configuration and Reynolds number. A theoretical model is then proposed to explain this behaviour, including the observed range of variations of$$S_w$$. The proposed model clarifies why$$S_w$$cannot be predicted from down-gradient closure approximations routinely employed in large-scale meteorological and climate models. The proposed model also offers an alternative and implementable approach for such large-scale models. 

The drag coefficient Cd for a rigid and uniformly distributed rod canopy covering a sloping channel following the instantaneous collapse of a dam was examined using flume experiments. The measurements included space x and time t high resolution images of the water surface h(x, t) for multiple channel bed slopes So and water depths behind the dam Ho along with drag estimates provided by sequential load cells. Using these data, an analysis of the Saint-Venant equation (SVE) for the front speed was conducted using the diffusive wave approximation. An inferred Cd=0.4 from the h(x, t) data near the advancing front region, also confirmed by load cell measurements, is much reduced relative to its independently measured steady-uniform flow case. This finding suggests that drag reduction mechanisms associated with transients and flow disturbances are more likely to play a dominant role when compared to conventional sheltering or blocking effects on Cd examined in uniform flow. The increased air volume entrained into the advancing wave front region as determined from an inflow–outflow volume balance partly explains the Cd reduction from unity. 

Abstract Turbulent mixing of scalars within canopies is investigated using a flume experiment with canopy‐like rods of heighthmounted to the channel bed. The data comprised a time sequence of high‐resolution images of a dye recorded in a plane parallel to the bed atz/h= 0.2. Image processing shows that von Kármán wakes shed by canopy drag and downward turbulent transport from upper canopy layers impose distinct scaling regimes on the scalar spectrum. Measures from information theory are then used to explore the dominant directionality of the interaction between small and large scales underlying these two spectral regimes, showing that the arrival of sweeps from aloft establishes an inertial‐range spectrum with forward “information” cascade. In contrast, wake growth with downstream distance leads to persistent upscale transfer (inverse cascade) of scalar variance, which hints at their nondiffusive character and the significance of the stem diameter as an active length scale in canopy turbulence. 

Abstract The effect of hydraulic resistance on the downstream evolution of the water surface profilehin a sloping channel covered by a uniform dense rod canopy following the instantaneous collapse of a dam was examined using flume experiments. Near the head of the advancing wavefront, wherehmeets the rods, the conventional picture of a turbulent boundary layer was contrasted to a distributed drag force representation. The details of the boundary layer around the rod and any interferences between rods were lumped into a drag coefficientC_d. The study demonstrated the following: In the absence of a canopy, the Ritter solution agreed well with the measurements. When the canopy was represented by an equivalent wall friction as common when employing Manning's formula with constant roughness, it was possible to match the measured wavefront speed but not the precise shape of the water surface profile. However, upon adopting a distributed drag force with a constantC_d, the agreement between measured and modeledhwas quite satisfactory at all positions and times. The measurements and model calculations suggested that the shape ofhnear the wavefront was quasilinear with longitudinal distance for a constantC_d. The computed constantC_d(≈0.4) was surprisingly much smaller than theC_d(≈1) reported in uniform flow experiments with staggered cylinders for the same element Reynolds number. This finding suggested that drag reduction mechanisms associated with unsteadiness, nonuniformity, transient waves, and other flow disturbances were more likely to play a role when compared to conventional sheltering effects.