Peter A. Davies

Flow Past a Circular Cylinder on a

With a view to obtaining a fuller understanding of the interactions between topography and large-scale geophysical flows, a series of laboratory investigations have been performed on the flow past a right circular cylinder in a rotating water channel. For large-scale flows on a spherical Earth the variation of the Coriolis parameter, F = 2Ωsinϕ , with latitude, ϕ, is commonly written (Pedlosky 1979) as F = f + β0y where f = 2Ωsinϕo, βo = 2Ωcosϕo/RE, y is the distance to the north from the reference latitude ϕo, and RE and Ω( = 7.29 x 10-5 s-1) are the radius and rotation rate of the Earth respectively. In this paper we shall discuss laboratory experiments in which the variation of F can be simulated. We shall refer to those studies in which β = 0 (i.e. the Coriolis parameter is uniform over the latitudinal extent of the region under investigation) as f-plane experiments. Models for which βo is non-zero will be referred to as β-plane experiments. In the experiments the β-effect has been simulated by tilting the upper and lower surfaces of the channel so that the depth of the fluid varies in the cross-stream direction. Flow patterns have been obtained over a range of five independent non-dimensional parameters: Rossby and Ekman numbers, cylinder aspect ratio, β-parameter and flow direction (‘eastward’ or ‘westward’). A dramatic difference in downstream behaviour is found between f-plane, β-plane westward and /plane eastward flows. In particular, the β-plane eastward flows are characterized by bunching and pinching of streamlines in the wake region, the generation of damped stationary Rossby waves and downstream acceleration. Compared with f-plane flows the β-effect is shown to inhibit boundary layer separation from the cylinder for eastward flow and to enhance the separation for westward flow. Data are presented from all cases to show the asymmetry of the downstream flows and the transitions from fully attached to unsteady flows. Under otherwise identical conditions the downstream extent of the separated bubble region is much greater for β-plane westward flow than, in turn, for f-plane and β-plane eastward flows. In addition, the data indicate that the size of the bubble increases with increasing Rossby number and decreases with increasing Ekman number and cylinder aspect ratio. For eastward flow the bubble size decreases with increasing β-parameter and for westward flow it increases with increasing β-parameter. Unsteady flows are investigated and instances of asymmetrical vortex shedding are presented.

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Satellite image sequences (covering periods of a few days throughout the annual cycle) of the waters off southern Iberia have been analyzed in conjunction with concurrent surface wind speed data from coastal stations. Qualitative analysis reveals a large degree of temporal and spatial variability in the thermal signature of the sea surface over periods of both a few days and several months. During the summer, a cool seasurface temperature signature extends from the western Iberian coast around Cape St. Vincent and eastward as far as Faro. At the same time, a warm signature originating on the Iberian coast between Faro and Cadiz extends into the Strait of Gibraltar. These two features are shown to sometimes adopt more westerly positions, and the strait experiences regions of cool thermal signature originating at its southern side. During winter, the surface flow into the Mediterranean through the Strait of Gibraltar is anomalously warm and appears to come from the interior of the Gulf of Cadiz. Quantitative measurements show that temporal variability over timescales of a few days at individual sites is maximum in midsummer. Spatial thermal variability over the whole region is found to peak toward the end of the summer. Statistical analyses of the data reveal the coupling between the surface wind field in the Gulf of Cadiz and the surface thermal pattern (especially during the summer). Wind-induced, across-stream upwelling in the Strait of Gibraltar, although dynamically subordinate to tidal and density-driven processes, is shown to occasionally dominate the surface thermal signature.

-Plane

An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2– 1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0–8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Remotely sensed sea surface thermal patterns in the Gulf of Cadiz and the Strait of Gibraltar: Variability, correlations, and relationships with the surface wind field

The spin‐up from rest of (i) a homogeneous and (ii) a linearly stratified fluid in a rectangular container has been examined in the laboratory. In the spin‐up process leading to the ultimate state of rigid‐body rotation, three main stages can be discerned, these being (1) the starting flow, characterized by zero absolute vorticity, (2) flow separation due to cyclonic vorticity generation at the lateral tank walls, and (3) a subsequent organization of the flow into a regular array of alternately cyclonic and anticyclonic cells. During the final stage the flow in these cells gradually decays due to the spin‐down/spin‐up mechanism provided by the Ekman boundary layer present at the bottom of each cell. Experiments have been performed with free‐surface and rigid‐lid upper boundary conditions, and the organization of the flow in these cases was observed to be essentially different. In particular, it was noted that the central cell in the free‐surface case is always cyclonic. A model for this behavior is advanced, in terms of the tendency of cyclonic vortices to move toward the rotation axis in the free‐surface configuration.

On the breaking of internal solitary waves at a ridge

The flow of a linearly stratified fluid past a long circular cylinder in a channel is considered experimentally. The characteristics of the flow depend on the internal Froude number Fi the Reynolds number Re and the cylinder diameter to fluid depth ratio, d/H. A wide range of characteristic flow fields are observed in the parameter space investigated; i.e. 0.02⩽Fi⩽13, 5⩽Re⩽4000 and 0.03⩽d/H⩽0.20. A flow regime diagram of Fi against Re for these characteristic flows is developed. Some of the lower Fi Re experiments are compared with numerical experiments. A theory is advanced which indicates that the dimensionless length, xb∗=xb/d of the blocked region ahead of the cylinder should scale as xb∗≈(δ/d)5ReFi−2, where δ is the thickness of the shear layer between the external flow and the approximately stagnant blocked region; the results of an experimental programme that support this scaling are presented. Measurements are made which indicate that for the range of parameter space in which lee waves occur, the lee wavelengths are predicted to a good approximation by linear theory. A scaling analysis is carried out which suggests that the height of the rotors above the streamwise centreline, Zr∗=Zr/d, scales with Fi experiments aire in good agreement with this prediction. For conditions under which the wake of the cylinder is turbulent, scaling arguments suggest that the dimensionless maximum width of the wake, γm∗=γm/d, and the dimensionless streamwise distance at which this maximum occurs, βm∗=βm/d, scale as Fi12 Experiments are presented which support this scaling.

Spin‐up in a rectangular container

ABSTRACT Ecologically-appropriate management of natural and constructed surface water bodies has become increasingly important given the growing anthropogenic pressures, statutory regulations, and climate-change impacts on environmental quality. The development of management strategies requires that a number of knowledge gaps be addressed through interdisciplinary research efforts particularly focusing on the water-biota and water-sediment interfaces where most critical biophysical processes occur. This paper discusses the current state of affairs in this field and highlights potential paths to resolve critical issues, such as hydrodynamically-driven mass transport processes at interfaces and associated responses of organisms through the development of traits. The roles of experimental methods, theoretical modelling, statistical tools, and conceptual upscaling methods in future research are discussed from both engineering and ecological perspectives. The aim is to attract the attention of experienced and emerging hydraulic and environmental researchers to this research area, which is likely to bring new and exciting discoveries at the discipline borders.

Linearly stratified flow past a horizontal circular cylinder

Laboratory and numerical experiments have been conducted on the flow of a linearly stratified rotating fluid past isolated obstacles of revolution (conical and cosinesquared profiles). Laboratory experiments are considered for a range of Rossby, Ekman and Burger numbers, the pertinent dynamical parameters of the system. In these experiments, inertial, Coriolis, pressure, viscous and buoyancy forces all play a significant role. Emphasis is given to examining the nature of the time development of the flow fields as well as its long-time behaviour, including eddy shedding. It is shown, for example, that increased stratification tends to diminish the steering effect of the obstacle, other parameters being fixed, at elevation levels above the topography. At levels below the top of the obstacle, increased stratification tends to force the fluid around rather than over the body and this, in turn, tends to develop vortex shedding at smaller Reynolds numbers than would occur in corresponding lower stratification cases. Data for the cone reveal that the Strouhal number for the eddy-shedding regime is relatively insensitive to the values of Ro, Ek and S for the range of parameters investigated. Stratification tends to induce lee waves in the topography wake, and the nature of this lee-wave pattern is modified by the presence of rotation. For example, it is demonstrated that for vertically upward rotation, the lee waves on the right, facing downstream, have a larger amplitude than their counterparts at the same location on the left. The steering effects, as predicted by a three-level quasigeostrophic numerical model, are shown to be in good agreement with the laboratory results for a narrow range of parameter space. The numerical model is used to examine the effects of rotation, friction and stratification in modifying the flow. The quasigeostrophic numerical simulations do not produce eddy shedding, and it is concluded that a full, primitive equation numerical model would be needed to explore this phenomenon.

Aquatic interfaces: a hydrodynamic and ecological perspective

Large-amplitude internal solitary waves in a stratification comprising a thick, lower, homogeneous layer separated from a thin, upper, homogeneous layer by a broad gradient region are studied using simultaneous measurements of the density and velocity fields. Density field measurements are achieved through synthetic schlieren, operating in an absolute mode to allow efficient and accurate measurements of density in systems with strong curvatures and large perturbations to the density field. The images used for these density measurements are interleaved with images used for particle image velocimetry by phase locking two video cameras (one configured for the density measurements and the other for the velocity measurements) with a computer-driven LCD monitor, allowing the background texture required for synthetic schlieren to be turned off for the particle image velocimetry measurements on the mid-plane of the experimental tank. The simultaneous measurements of both density and velocity fields not only allow greater insight into the internal wave dynamics, but also allow the velocity measurements to be corrected for the normal errors associated with the refractive index variations. As an illustration of the power of this technique, we determine for the first time in an internal solitary wave the spatial structure of the local gradient Richardson number, finding regions where this falls below the limit for linear stability.

Stratified Rotating Flow over and around Isolated Three-Dimensional Topography

The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h 2 ) sandwiched between a thin upper layer (depth h 1 ) and a deep lower layer (depth h 3 ), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a 1 ) in the range a 1 > 2.24√h 1 h 2 (1 + h 2 /h 1 ), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for L x /λ < 0.86. The results show a sort of threshold-like behaviour in terms of L x /λ. The results demonstrate that the breaking threshold of L x /λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnocline.

Simultaneous synthetic schlieren and PIV measurements for internal solitary waves

The motion of a large-amplitude internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid is investigated experimentally. Measurements of the velocity fields close to the bottom boundary are presented to illustrate the generation of an unsteady boundary jet along the bed. The formation of the jet, the structural characteristics of which show striking similarities with those predicted by recent numerical model studies by Diamessis and Redekopp [J. Phys. Oceanogr. (in press)], is attributed to boundary layer separation in the adverse pressure gradient region of the wave-induced flow.