The behaviour of an inviscid, lock-released gravity current which propagates over a horizontal porous boundary in either a rectangular or an axisymmetric geometry is analysed by both shallow-water theory and ‘box-model’ approximations. It is shown that the effect of the porous boundary can be incorporated by means of a parameter λ which represents the ratio of the characteristic time of porous drainage, τ, to that of horizontal spread, x0 =(g′h0)1/2, where x0 and h0 are the length and height of the fluid initially behind the lock and g′ is the reduced gravity. The value of τ is assumed to be known for the fluid–boundary combination under simulation. The interesting cases correspond to small values of λ; otherwise the current has drained before any significant propagation can occur. Typical solutions are presented for various values of the parameters, and differences to the classical current (over a non-porous boundary) are pointed out. The results are consistent with the experiments in a rectangular tank reported by Thomas, Marino & Linden (1998), but a detailed verification, in particular for the axisymmetric geometry case, requires additional experimental data.

Velocity and surface measurements in three turbulent hydraulic jumps are analysed in detail. The velocity measurements were obtained in a hydraulic ume using laser- Doppler velocimetry and the surface measurements were obtained using capacitance wave gauges. The purpose is to extract information about the flow field and the stresses in the jumps and the geometrical extension of the recirculating region called the roller. To achieve this we first ensure that the overall continuity and momentum conservation for the flow is satisfied. This includes comparison with the classical results for hydraulic jumps. It is found that deviations from uniform-depth Reynolds- averaged velocities and hydrostatic pressure give small but important corrections to the conservation equations. Careful evaluation of the velocity measurements in conjunction with the continuity equation makes it possible to determine the lower limit of the recirculating roller region. Measurements of the Reynolds stresses are analysed, in particular in the roller region, and a simple model established that illustrates the mechanisms of the flow in the roller and predicts well the stresses along the lower limits of the roller. In combination with the analysis of the vorticity distribution, this leads to a qualitative description of the processes for the generation of vorticity. It suggests both similarities and differences from the hypothesis of the existence of a shear layer inside the jump. Similarity profiles are developed for the variation of stresses, vorticity, and eddy viscosity along the lower limit of the roller. Finally, the total angular momentum for the jumps is examined and compared to the analysis of Hornung, Willert & Turner (1995).

A laboratory study was carried out to directly measure the turbulence properties in a benthic boundary layer (BBL) above a uniformly sloping bottom where the BBL is energized by internal waves. The ambient fluid was continuously stratified and the steadily forced incoming wave field consisted of a confined beam, restricting the turbulent activity to a finite region along the bottom slope. Measurements of dissipation showed some variation over the wave phase, but cycle-averaged values indicated that the dissipation was nearly constant with height within the BBL. Dissipation levels were up to three orders of magnitude larger than background laminar values and the thickness of the BBL could be defined in terms of the observed dissipation variation with height. Assuming that most of the incoming wave energy was dissipated within the BBL, predicted levels of dissipation were in good agreement with the observations.

Measurements were also made of density and two orthogonal components of the velocity fluctuations at discrete heights above the bottom. Cospectral estimates of density and velocity fluctuations showed that the major contributions to both the vertical density flux and the momentum flux resulted from frequencies near the wave forcing frequency, rather than super-buoyancy frequencies, suggesting a strong nonlinear interaction between the incident and reflected waves close to the bottom. Within the turbulent BBL, time-averaged density fluxes were significant and negative near the wave frequencies but negligible at frequencies greater than the buoyancy frequency N. While dissipation rates were high compared to background laminar values, they were low compared to the value of εtr ≈ 15vN2, the transition value often used to assess the capacity of a stratified flow to produce mixing. Existing models relating mixing to dissipation rate rely on the existence of a positive-definite density flux at frequencies greater than N as a signature of fluid mixing and therefore cannot apply to these experiments. We therefore introduce a simple model, based on the concept of diascalar fluxes, to interpret the mixing in the stratified fluid in the BBL and suggest that this may have wider application than to the particular configuration studied here.

It has long been known from linear stability theory that heating a surface immersed in water flow tends to stabilize the boundary layer on the surface, suggesting that there may be a corresponding delay in transition. Experiments confirm the suggestion, but based on intermittency data on a heated body of revolution (Lauchle & Gurney 1984) it has been inferred that incremental changes in transition Reynolds number diminish as the overheat increases. The parameter chosen to locate transition in the analysis leading to this conclusion corresponds to the point where the intermittency is 0.5. However, intermittency distributions in the transition zone on an axisymmetric body may contain what have been called ‘subtransitions’ (Narasimha 1984). Taking this possibility into account, we formulate here a model for the variation of intermittency with flow Reynolds number at a fixed station on the body, as in the experiments. The rate at which turbulent spots merge with each other is shown to determine the location of subtransition. The transition onset Reynolds number (corresponding to the location where intermittency begins to depart from zero), inferred from the data on the basis of this model, shows a continuing increase with the temperature overheat, a trend in closer agreement with stability theory; but the axisymmetric body geometry results in a very short transition zone, countering in part the benefits of transition delay.

The present work constitutes a reassessment of the role of potential-flow analyses in describing alluvial-bed instability. To facilitate the analyses, a new potential-flow description of unsteady alluvial flow is presented, with arbitrary phase lags between local flow conditions and sediment transport permitted implicitly in the flow model. Based on the present model, the explicit phase lag between local sediment transport rate and local flow conditions adopted for previous potential-flow models is shown to be an artificial measure that results in model predictions that are not consistent with observed flow system behaviour. Previous potential-flow models thus do not provide correct descriptions of alluvial flows, and the understanding of bed-wave mechanics inferred based upon these models needs to be reassessed. In contrast to previous potential-flow models, the present one, without the use of an explicit phase lag, predicts instability of flow systems of rippled or dune-covered equilibrium beds. Instability is shown to occur at finite growth rates for a range of wavelengths via a resonance mechanism occurring for surface waves and bed waves travelling at the same celerity. In addition, bed-wave speeds are predicted to decrease with increasing wavelength, and bed waves are predicted to grow and move at faster rates for flows of larger Froude numbers. All predictions of the present potential-flow model are consistent with observations of physical flow systems. Based on the predicted unstable wavelengths for a given alluvial flow, it is concluded that bed waves are not generated from plane bed conditions by any potential-flow instability mechanism. The predictions of instability are nevertheless consistent with instances of accelerated wave growth occurring for flow systems of larger finite developing waves. Potential-flow description of alluvial flows should, however, no longer form the basis of instability analyses describing bed-form (sand-wavelet) generation from flat bed conditions.

The three-dimensional flow in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the ‘Taylor’ streamlines of the well-known ‘paint-scraper’ problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honed by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows.

Experimental data are presented from 138 synchronized channels of hot-wire anemometry in an investigation of the large-scale, or coherent, structures in a high Reynolds number fully developed, turbulent axisymmetric shear layer. The dynamics of the structures are obtained from instantaneous realizations of the streamwise velocity field in a single plane, x/D = 3, downstream of a round jet nozzle. The Proper Orthogonal Decomposition (POD) technique is applied to an ensemble of these realizations to determine optimal representations of the velocity field, in a mean-square sense, in terms of an orthogonal basis. The coefficients of the orthogonal functions, which describe the temporal evolution of the POD eigenfunctions, are determined by projecting instantaneous realizations of the velocity field onto the basis.

Evidence is presented to show that with a partial reconstruction of the velocity field, using only the first radial POD mode, the large-scale structure is objectively educed from the turbulent field. Further, it is shown that only five azimuthal Fourier modes (0,3,4,5,6) are necessary to represent the evolution of the large-scale structure. The results of the velocity reconstruction using the POD provide evidence for azimuthally coherent structures that exist near the potential core. In addition to the azimuthal structures near the potential core, evidence is also found for the presence of counter-rotating, streamwise vortex pairs (or ribs) in the region between successive azimuthally coherent structures as well as coexisting for short periods with them. The large-scale structure cycle, which includes the appearance of the ring structure, the advection of fluid by the ribs in the braid region and their advection toward the outside of the layer by a following ring structure, repeats approximately every one integral time scale. One surprising result was that the most spatially correlated structure in the flow, the coherent ring near the potential core which ejects fluid in the streamwise direction in a volcano-like eruption, is also the one with the shortest time scale.

This paper shows that a long vertical columnar vortex pair created by a double flap apparatus in a strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known to occur in homogeneous fluid. This new instability, which we name zigzag instability, is antisymmetric with respect to the plane separating the vortices. It is characterized by a vertically modulated twisting and bending of the whole vortex pair with almost no change of the dipole's cross- sectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest Brunt–Väisälä frequency N = 1.75 rad s−1 that may be achieved in the experiments, the zigzag instability is observed only in the range of Froude numbers: 0.13 < Fh0 < 0.21 (Fh0 = U0/NR, where U0 and R are the initial dipole travelling velocity and radius). When Fh0 > 0.21, the elliptic instability develops resulting in three-dimensional motions which eventually collapse into a relaminarized vortex pair. Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability Fh0 = 0.2±0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for Fh0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re0 < 260. In geophysical flows characterized by low Froude numbers and large Reynolds numbers, we conjecture that this viscous stabilization will occur at much lower Froude number.

It is tentatively argued that this new type of instability may explain the layering widely observed in stratified turbulent flows.

Direct numerical simulations are performed of gravity-current fronts in the lock-exchange configuration. The case of small density differences is considered, where the Boussinesq approximations can be adopted. The key objective of the investigation is a detailed analysis of the flow structure at the foremost part of the front, where no previous high-resolution data were available. For the simulations, high-order numerical methods are used, based on spectral and spectral-element discretizations and compact finite differences. A three-dimensional simulation is conducted of a front spreading along a no-slip boundary at a Reynolds number of about 750. The simulation exhibits all features typically observed in experimental flows near the gravity-current head, including the lobe-and-cleft structure at the leading edge. The results reveal that the flow topology at the head differs from what has been assumed previously, in that the foremost point is not a stagnation point in a translating system. Rather, the stagnation point is located below and slightly behind the foremost point in the vicinity of the wall. The relevance of this finding for the mechanism behind the lobe-and-cleft instability is discussed. In order to explore the high-Reynolds-number regime, and to assess potential Reynolds-number effects, two-dimensional simulations are conducted for Reynolds numbers up to about 30 000, for both no-slip and slip (i.e. shear-stress free) boundaries. It is shown that although quantitative Reynolds-number effects persist over the whole range examined, no qualitative changes in the flow structure at the head can be observed. A comparison of the two-dimensional results with laboratory data and the three-dimensional simulation provides evidence that a two-dimensional model is able to capture essential features of the flow at the head. The simulations also show that for the free-slip case the shape of the head agrees closely with the classical inviscid theory of Benjamin.

Results are presented from a linear-stability analysis of the flow at the head of two-dimensional gravity-current fronts. The analysis was undertaken in order to clarify the instability mechanism that leads to the formation of the complex lobe-and-cleft pattern which is commonly observed at the leading edge of gravity currents propagating along solid boundaries. The stability analysis concentrates on the foremost part of the front, and is based on direct numerical simulation data of two-dimensional lock-exchange flows which are described in the companion paper, Härtel et al. (2000). High-order compact finite differences are employed to discretize the stability equations which results in an algebraic eigenvalue problem for the amplification rate, that is solved in an iterative fashion. The analysis reveals the existence of a vigorous linear instability that acts in a localized way at the leading edge of the front and originates in an unstable stratification in the flow region between the nose and stagnation point. It is shown that the amplification rate of this instability as well as its spanwise length scale depend strongly on Reynolds number. For validation, three-dimensional direct numerical simulations of the early stages of the frontal instability are performed, and close agreement with the results from the linear-stability analysis is demonstrated.

Large-eddy simulation (LES) has been used to predict the statistically three-dimensional turbulent boundary layer (3DTBL) over a rotating disk. LES predictions for six parameter cases were compared to the experimental measurements of Littell & Eaton (1994), obtained at a momentum thickness Reynolds number of 2660. A signal-decomposition scheme was developed by modifying the method of Spalart (1988) to prescribe time-dependent boundary conditions along the radial direction, entrainment towards the disk surface was prescribed by satisfying global mass conservation. Predictions of the mean velocities and r.m.s. fluctuations are in good agreement with data, with the largest discrepancy occurring in the prediction of the wall-normal intensities. The primary and two secondary shear stresses are also in good agreement with the measurements and one-dimensional energy spectra of the velocity fluctuations agree well with established laws, i.e. a −1 slope in the buffer region and −5/3 slope near the edge of the boundary layer.

Conditionally averaged velocities provide new evidence in support of the structural model of Littell & Eaton (1994) concerning the interaction of mean-flow three-dimensionality and shear-stress producing structures. Inside the buffer region under strong ejections, the conditionally averaged crossflow (radial) velocity is larger than the unconditioned mean, and the profile conditioned on strong sweeps is smaller than the mean. This is consistent with the notion that streamwise vortices having the same sign as the mean streamwise vorticity, and beneath the peak crossflow location, are mostly responsible for strong sweep events; streamwise vortices with opposite sign as the mean streamwise vorticity promote strong ejections. Comparison of two-point spatial correlations with previous measurements in two-dimensional turbulent boundary layers (2DTBLs) indicates interesting structural similarities, e.g. the correlation of wall pressure and surface-normal velocity fluctuations is an odd function of streamwise separation, being positive downstream and negative upstream. These similarities offer quantitative indirect support to the hypothesis advanced by Littell & Eaton (1994) and Johnston & Flack (1996) that structural models describing 2DTBLs may be employed as a baseline in (equilibrium) 3DTBL structural studies.

This paper presents a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Kármán vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0 [les ] M [les ] 85 and the interaction parameter N in the range 0 [les ] N [les ] 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed. The spanwise wavelength of the rib vortices was found to be about 2–3 cylinder side lengths in the near wake. At Re = 250 the flow appears more organized showing a regular B mode pattern and a spanwise wavelength of about 1 cylinder side length. With an applied magnetic field a quasi-two-dimensional flow can be obtained at low N ≈ 1 due to the strong non-isotropic character of the electromagnetic forces. The remaining vortices have their axes aligned with the magnetic field. With increasing magnetic fields these vortices are further damped due to Hartmann braking. The result that the ‘quasi-two-dimensional’ vortices have a curvature in the direction of the magnetic field can be explained by means of an asymptotic analysis of the governing equations. With very high magnetic fields the time-dependent vortex shedding can be almost completely suppressed. By three-dimensional visualization it was possible to show characteristic paths of the electric current for this kind of flow, explaining the action of the Lorentz forces.

A stratified body of fluid with compensating horizontal temperature and salinity gradients can undergo an interleaving instability which takes the form of almost horizontal intrusions. As the amplitude of these intrusions grows they can undergo secondary instabilities which eventually leads to the mixing of the fluid in the interior of the intrusions. A previous study of the secondary instabilities focused on two-dimensional disturbances. These corresponded to experimental observations of that time which all seemed to indicate that flows were indeed two-dimensional. Some more recent experiments have shown that the initial secondary instability can make the flow three-dimensional, with the secondary instabilities taking the form of rolls with their axes aligned with the direction of the flow in the intrusions. Here we present a three dimensional stability analysis of steady finite-amplitude intrusions and look at the circumstances which can lead to the three-dimensional instabilities being more likely to be observed.

Laboratory experiments are used to investigate the processes governing steady convectively driven circulation in a basin that communicates with a large external reservoir over a shallow sill. The motion is maintained by a steady loss of buoyancy distributed over the surface of the basin. Turbulent convection associated with the forcing produces a horizontal buoyancy gradient across the sill and the resulting mean flow consists of a layer directed into the basin near the surface with a dense counter flow below.

To first order, the magnitude of the exchange flow over the sill is determined by the horizontal momentum balance within the basin. Measurements of the mean and turbulent flow fields are used to show that inertia, buoyancy and friction may each contribute significantly to the balance. The interior flow produces a horizontal pressure gradient near the surface which must also contribute to the momentum balance. The density of the lower layer at the sill reflects the cumulative effect of interior processes, such as mixing, and these in turn influence the hydraulically controlled exchange flow over the sill. The basin dynamics are therefore coupled in a nonlinear fashion with the submaximal sill exchange. This coupling is investigated first by showing how interior processes are affected by changes in the magnitude of the forcing, and then by observing the associated variation of the flow state at the sill. The flow state is defined in terms of its relative proximity to the theoretical maximal exchange limit. Results show that the exchange flows are submaximal with flow rate approximately 85% of the maximal limit. This state appears to change very little in response to increasing forcing.

For a stratified basin, which exhibits a deep stagnant layer under the convectively driven near-surface exchange flow, the possibility of basin ventilation or erosion of deep fluid exists in the long term. This process and its dependence on external parameters is also explored.

The steady translational motion of a sphere in a Boussinesq stratified fluid, where the motion is parallel to the stratification surfaces, is studied. A model based on existing linear gravity wave theory for large Froude numbers and on new theory for small Froude numbers is presented. The small-Froude-number theory describes wave generation and the presence of a rectangular-section attached wake whose size and shape is controlled by the size and shape of the wave generation regions. Existing laboratory data are used to evaluate the model's prediction for the drag coefficient of the sphere as a function of Froude number.

A method for the theoretical determination of the wall shear stress under impinging jets of various configurations is presented. Axisymmetric and two-dimensional incompressible jets of a wide range of Reynolds numbers and jet heights are considered. Theoretical predictions from this approach are compared with available wall shear stress measurements. These data are critically evaluated based on the method of measurement and its applicability to the boundary layer under consideration. It was found that impingement-region wall shear stress measurements using the electrochemical method in submerged impinging liquid jets provide the greatest accuracy of any indirect method. A unique wall shear stress measurement technique, based on observing the removal of monosized spheres from well-characterized surfaces, was used to confirm the impinging jet analysis presented for gas jets. The technique was also used to determine an empirical relation describing the rise in wall shear stress due to compressibility effects in impinging high-velocity jets.