Don L. Boyer

EFFECTS OF ROTATION ON CONVECTIVE TURBULENCE

Laboratory experiments were carried out to investigate the effects of rotation on turbulent convection. The experimental facility was a bottom-heated, water-filled, cubical tank mounted on a turntable. The investigations were performed over a wide range of bottom buoyancy fluxes q 0 and rotation rates Ω, including Ω = 0; q 0 and Ω were held constant during each experiment. The depth of the water column H was fixed for the entire experimental programme. For the non-rotating experiments, the r.m.s. velocity fluctuations were found to scale well with the convective velocity

Flow Past a Circular Cylinder on a

w_* = (q_0 H)^{\frac{1}{3}}

\beta

, while the mean and r.m.s. fluctuations of buoyancy were found to scale with q 0 / w * . The spectra of temperature fluctuations were measured and were used to assess the applicability of two types of scaling, one of which is advanced in the present study. For the rotating experiments, the convective-layer growth is affected by the rotation at a height h c ≈ 4.5( q 0 Ω −3 ) ½ . The r.m.s. horizontal velocity of the rotationally affected mixed layer is uniform throughout the mixed layer and is given by

-Plane

(\overline{u^{\prime 2}})^{\frac{1}{2}}_{\rm r}\approx 1.7(q_0\Omega^{-1})^{\frac{1}{2}}

Linearly stratified flow past a horizontal circular cylinder

. The time growth law of the mixed-layer thickness h r , when h r > h c , is given by h r ≈ 0.7( q 0 Ω −3 ) ½ Ω t , where t is the time. The rotational effects become important when the Rossby number is given by

Stratified Rotating Flow over and around Isolated Three-Dimensional Topography

Ro = (\overline{u^{\prime 2}})^{\frac{1}{2}}_{\rm r}/\omega l_{\rm r}\approx 1.5

Vortex shedding in rotating flows

, where the integral lengthscale is estimated as l r ≈ 0.25 h c . The mean buoyancy gradient in the mixed layer was found to be much higher than in the corresponding non-rotating case, and the r.m.s. fluctuations and mean buoyancies were found to scale satisfactorily with ( q 0 Ω) ½ . A spectral form for the temperature fluctuations in rotating convection is also proposed and is compared to the experimental results.

Laboratory Study of Rotating, Stratified, Oscillatory Flow over a Seamount

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.

Laboratory–Numerical Model Comparisons of Canyon Flows: A Parameter Study

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.

Synoptic classification and physical model experiments to guide field studies in complex terrain

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.