Stratified rotating flow over and around isolated three-dimensional topography

Abstract

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.

Global Distribution and Characteristics of Diurnally Varying Low-Level Jets

“…A similar nocturnal vortex mechanism was discussed by Davis et al (2000) in the context of lee vortices in the bight region of California. The single cyclonic vortex is characteristic of the response to large mountains (Boyer et al 1987;Peng et al 1995) where the Rossby number (U/fL) is less than or of order unity. The term Ro in the present case, with L the cross-flow length scale of the topography, is about unity (for L 5 500 km, f 5 2.5 3 10 25 s 21 , and U 5 10 m s 21 ).…”

Rotating flow past a sliced cylinder

“…However, as is well known, such systems are unsuitable for studying flow past obstacles because of either wake interference with the incident flow ͑in cases in which the flow is azimuthal in a circular geometry͒ or the length required in a channel for the flow to become fully developed. 20 In view of these considerations, the difficulties in matching the conflicting demands of theory and experiment are clearly appreciated.…”

“…The tow tank apparatus used in the study was identical in design with that used earlier by Boyer et al 20 and Davies et al 21 It consists of a transparent acrylic ͑perspex͒ channel of dimensions 2.0ϫ0.4ϫ0.3 m, with the working fluid of depth H being bounded above by a flat horizontal perspex plate suspended from the sides of the channel with adjustable-length supports. A perspex truncated cylinder of base diameter D(ϭ2aH) and having a sloping top surface could be mounted flush on a continuous taut belt stretched over a system of rollers and running along the base of the tank.…”

A Baroclinic Laminar State for Rotating Stratified Flows

“…For a rotating homogeneous fluid with small Ro, the Taylor-Proudman theorem requires the velocity field to be vertically invariant, which gives vanishing vertical velocity under rigid boundary conditions. Laboratory experiments have demonstrated this effect (Boyer et al 1987). Meanwhile, numerical simulations also show that at the limit of small Fr vertical motions are increasingly suppressed (Waite and Bartello 2004).…”