A mixing-length formulation for the turbulent Prandtl number in wall-bounded flows with bed roughness and elevated scalar sources

Abstract

Turbulent Prandtl number distributions are measured in a laboratory boundary layer flow with bed roughness, active blowing and sucking, and scalar injection near the bed. The distributions are significantly larger than unity, even at large distances from the wall, in apparent conflict with the Reynolds analogy. An analytical model is developed for the turbulent Prandtl number, formulated as the ratio of momentum and scalar mixing length distributions. The model is successful at predicting the measured turbulent Prandtl number behavior. Large deviations from unity are shown in this case to be consistent with measurable differences in the origins of the momentum and scalar mixing length distributions. Furthermore, these deviations are shown to be consistent with the Reynolds analogy when the definition of the turbulent Prandtl number is modified to include the effect of separate mixing length origin locations. The results indicate that the turbulent Prandtl number for flows over complex boundaries can be modeled based on simple knowledge of the geometric and kinematic nature of the momentum and scalar boundary conditions.

Settlement rates of macroalgal algal propagules: Cross‐species comparisons in a turbulent environment

“…However, at close proximity to the substratum, the shape of surrounding organisms is also likely to influence small-scale turbulence and diffusive processes that can affect the path of propagules through the viscous sub-layer (Crimaldi et al 2002;Reidenbach et al 2006b;Stevens et al 2008). Consequently, over intertidal reefs of high structural complexity shear-layer vortices may dominate, as has been shown for wave-dominated flat reefs (Falter et al 2004), seagrass beds (Cornelisen and Thomas 2004), and coral reefs (Reidenbach et al 2006a).…”

“…Laboratory vs. field conditions-In a natural intertidal setting, fine-scale turbulence is likely to be affected by substratum topography and roughness elements produced by reef biota, but at larger scales the shape of the nearshore environment is likely to be more important (Crimaldi et al 2006;Monismith et al 2006;Reidenbach et al 2006a). However, at close proximity to the substratum, the shape of surrounding organisms is also likely to influence small-scale turbulence and diffusive processes that can affect the path of propagules through the viscous sub-layer (Crimaldi et al 2002;Reidenbach et al 2006b;Stevens et al 2008).…”

“…The sinking of propagules should be Stokesian because a variant of Re p* , which replaces the friction velocity scale with a sinking speed, results in the buoyancy particle Reynolds number (Re p 5 U s d/v , 1); these are very small and so viscosity controls the flow (Crimaldi et al 2002;Stevens et al 2008). Under these conditions, assuming the particles are spherical in nature, the sinking velocity of the propagules, U s , is determined by a balance of buoyancy and viscosity and is given by…”

“…Due to their small size, the transport of these often nonmotile propagules is largely a passive process determined by the movement of the water mass (Butman 1987;Mullineaux and Butman 1991;Crimaldi et al 2002). However, as propagules approach the viscous sub-layer next to all settlement surfaces, the physical properties of the propagules themselves can affect settlement success (Stevens et al 2008).…”

A physical picture of the mechanism of turbulent heat transfer from the wall

“…Turbulent transport results using the DNS/LST method published previously from our research group in plane channel flow [16][17][18][19] and in plane Couette flow [20,21] [22], the turbulent Prandtl number can be calculated by finding the ratio of the turbulent length scales.…”