J. C. R. Hunt

Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization

In flows around three-dimensional surface obstacles in laminar or turbulent streamsthere are a number of points where the shear stress or where two or more component,s of the mean velocity are zero. In the first part of this paper we summarize and extend the kinematical theory for the flow near these points, particularly by emphasizing the topological classification of these points as nodes or saddles. We show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes Σ N and the sum of the saddles Σ s satisfy \[ \Sigma_N -\Sigma_S = 0. \] If the obstacle has a hole through it, such as a passageway under a building, \[ \Sigma_N -\Sigma_S =-2. \] If the surface is a junction between two pipes, \[ \Sigma_N -\Sigma_S =-1. \] We also consider, in two-dimensional plane sections of the flow, the points where the components of the mean velocity parallel to the planes are zero, both in the flow and near surfaces cutting the sections. The latter points are half-nodes N′ or half-saddles S′. We find that \[ (\Sigma_N +{\textstyle\frac{1}{2}}\Sigma_{N^{\prime}}-(\Sigma_{S^{\prime}}+{\textstyle\frac{1}{2}}\Sigma_{S^{\prime}}) = 1-n, \] where n is the connectivity of the section of the flow considered. In the second part new flow-visualization studies of laminar and turbulent flows around cuboids and axisymmetric humps (i.e. model hills) are reported. A new method of obtaining a high resolution of the surface shear-stress lines was used. These studies show how enumerating the nodes and saddle points acts as a check on the inferred flow pattern. Two specific conclusions drawn from these studies are that: for all the flows we observed, there are no closed surfaces of mean streamlines around the separated flows behind three-dimensional surface obstacles, which con-tradicts most of the previous suggestions for such flows (e.g. Halitsky 1968); the separation streamline on the centre-line of a three-dimensional bluff obstacle does not, in general, reattach to the surface.

Saltating particles over flat beds

Measurements of ejection and impact velocities, trajectory lengths and maximum rise heights of sand grains (median diameters 118 and 188 μm) in saltation over a flat sand bed in a wind tunnel have been obtained from the digitization of multiple-image photo graphs. The mean angle of ejection is found to be about 30 o from the horizontal (rather than 90 o ) with mean vertical ejection velocity of about 2u * , where u * is the friction velocity. Trajectories of saltating grains have been computed, using the measurements of the initial ejection velocities and the mean velocity profile of the air flow.

Turbulent shear flow over slowly moving waves

We investigate the changes to a fully developed turbulent boundary layer caused by the presence of a two-dimensional moving wave of wavelength L = 2π/ k and amplitude a. Attention is focused on small slopes, ak , and small wave speeds, c , so that the linear perturbations are calculated as asymptotic sequences in the limit ( u * + c )/ U B ( L ) → 0 ( u * is the unperturbed friction velocity and U B ( L ) is the approach-flow mean velocity at height L ). The perturbations can then be described by an extension of the four-layer asymptotic structure developed by Hunt, Leibovich & Richards (1988) to calculate the changes to a boundary layer passing over a low hill. When ( u * + c )/ U B ( L ) is small, the matched height, z m (the height where U B equals c ), lies within an inner surface layer, where the perturbation Reynolds shear stress varies only slowly. Solutions across the matched height are then constructed by considering an equation for the shear stress. The importance of the shear-stress perturbation at the matched height implies that the inviscid theory of Miles (1957) is inappropriate in this parameter range. The perturbations above the inner surface layer are not directly influenced by the matched height and the region of reversed flow below z m : they are similar to the perturbations due to a static undulation, but the ‘effective roughness length’ that determines the shape of the unperturbed velocity profile is modified to z m = z 0 exp ( kc/u * ). The solutions for the perturbations to the boundary layer are used to calculate the growth rate of waves, which is determined at leading order by the asymmetric pressure perturbation induced by the thickening of the perturbed boundary layer on the leeside of the wave crest. At first order in ( u * + c )/ U B ( L ), however, there are three new effects which, numerically, contribute significantly to the growth rate, namely: the asymmetries in both the normal and shear Reynolds stresses associated with the leeside thickening of the boundary layer, and asymmetric perturbations induced by the varying surface velocity associated with the fluid motion in the wave; further asymmetries induced by the variation in the surface roughness along the wave may also be important.

UK-ADMS: A new approach to modelling dispersion in the earth's atmospheric boundary layer

The UK atmospheric dispersion modelling system is a computer code for modelling the dispersion of buoyant or neutrally buoyant gaseous and particulate emissions to the atmosphere. It comprises a number of individual modules, each dealing with either one aspect of the dispersion process or data input and output. Each module can be modified independently to keep it, and hence the whole model, scientifically up-to-date. Emissions can be of any duration. The effects of plume rise, wet and dry deposition, radio-active decay, hilly and variable roughness terrain, coastal regions and large buildings are allowed for. Fluctuations in concentration about the calculated mean are also modelled for time scales less than one hour. Output includes mean values, variances and percentiles of air concentration, dosage (time integrated concentration raised to some power), and deposition to the ground. For emissions of radio-active isotopes estimates can be made of the ground level gamma-radiation dose rate beneath the plume. A user interacts with the model via a system of menus based on Microsoft Windows so that it is easy to use.

Wakes behind two-dimensional surface obstacles in turbulent boundary layers

By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of height h ) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed that h [Gt ] δ, and that the wake can be divided into three regions. The velocity deficit − u is greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profile U ( y ) = U ∞( y − y 1 ) n / δ n , where n [Gt ] 1. In (M), assuming that an eddy viscosity (= KhU ( h )) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found that u ( x,y ) has the form

Structure of the temperature field downwind of a line source in grid turbulence

\frac{u}{U(h)} = \frac{ C }{Kh^2U^2(h)} \frac{f(n)}{x/h},\;\;\;\; {\rm where}\;\;\;\; \eta = (y/h)/[Kx/h]^{1/(n+2)}

The distortion of turbulence by a circular cylinder

, and the constant which defines the strength of the wake is

The drag on an undulating surface induced by the flow of a turbulent boundary layer

C = \int^\infty_0 y^U(y)(u-u_E)dy

Velocity fluctuations near an interface between a turbulent region and a stably stratified layer

, where u = u E ( x, y ) as y → 0 in region (E). In region (W), u ( y ) is proportional to In y. By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body. New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8 h . These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks. It is found that the theory describes the distribution of mean velocity reasonably well, in particular the ( x / h ) −1 decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as

Swirling recirculating flow in a liquid metal column generated by a rotating magnetic field

(\frac{x}{h})^{- \frac{3}{2}}