The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

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Local and global instabilities in spatially developing flows

▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...

Turbulent flows over rough walls

Publisher Summary This chapter discusses the heat transfer and the hydraulic resistance of single tubes, and the banks of tubes of various arrangements in flows of gases and viscous liquids. The focus is on the important problems of the heat transfer and the hydraulic resistance of tubes, in particular with the heat transfer of single tubes, banks of tubes, and systems of tubes in crossflow. The chapter also highlights the influence of the physical properties of fluids on heat transfer. Extensive experimental data will be analyzed and will include investigations of banks of tubes of various arrangements, and a single tube in crossflow in the range of Prandtl number from 0.7 to 500 and that of Reynolds number from 1 to 2xl0 6 .

Heat Transfer from Tubes in Crossflow

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices We also discuss the physics of wind-blown sand and dune formation on Venus and Titan

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The physics of wind-blown sand and dust

CFD simulation of the atmospheric boundary layer: wall function problems

An experimental investigation of the flow around surface-mounted cubes in both uniform, irrotational and sheared, turbulent flows is described. The shear flow was a simulated atmospheric boundary layer with a height ten times the body dimension. Measurements of body surface pressures and mean and fluctuating velocities within the wake are presented. In the latter case a pulsed-wire anemometer was used extensively since the turbulent intensities were much too high for effective use of more standard instrumentation. The clear effects of upstream turbulence and shear on the wake flow are described, comparisons with the somewhat sparse measurements of previous workers are made and the relevance of recent theoretical attempts to describe the flow, as opposed to numerical calculation techniques to predict it, is briefly discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112077000172

The flow around a surface-mounted cube in uniform and turbulent streams

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves. The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.

Near Wall Flow over Urban-like Roughness

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant ‘dispersive stress’ whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

Mean Flow and Turbulence Statistics Over Groups of Urban-like Cubical Obstacles

Using a numerical weather forecasting code to provide the dynamic large-scale inlet boundary conditions for the computation of small-scale urban canopy flows requires a continuous specification of appropriate inlet turbulence. For such computations to be practical, a very efficient method of generating such turbulence is needed. Correlation functions of typical turbulent shear flows have forms not too dissimilar to decaying exponentials. A digital-filter-based generation of turbulent inflow conditions exploiting this fact is presented as a suitable technique for large eddy simulations computation of spatially developing flows. The artificially generated turbulent inflows satisfy the prescribed integral length scales and Reynolds-stress-tensor. The method is much more efficient than, for example, Klein’s (J Comp Phys 186:652–665, 2003) or Kempf et al.’s (Flow Turbulence Combust, 74:67–84, 2005) methods because at every time step only one set of two-dimensional (rather than three-dimensional) random data is filtered to generate a set of two-dimensional data with the appropriate spatial correlations. These data are correlated with the data from the previous time step by using an exponential function based on two weight factors. The method is validated by simulating plane channel flows with smooth walls and flows over arrays of staggered cubes (a generic urban-type flow). Mean velocities, the Reynolds-stress-tensor and spectra are all shown to be comparable with those obtained using classical inlet-outlet periodic boundary conditions. Confidence has been gained in using this method to couple weather scale flows and street scale computations.

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Efficient Generation of Inflow Conditions for Large Eddy Simulation of Street-Scale Flows

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 103 and 5 106, based on the free stream velocity and the obstacle height. Re = 5 × 103 data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.

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Ian P. Castro

Papers

The flow around a surface-mounted cube in uniform and turbulent streams

Near Wall Flow over Urban-like Roughness

Mean Flow and Turbulence Statistics Over Groups of Urban-like Cubical Obstacles

Efficient Generation of Inflow Conditions for Large Eddy Simulation of Street-Scale Flows

LES and RANS for turbulent flow over arrays of wall-mounted obstacles