Laboratory experiments on the flow of negatively buoyant two-dimensional plumes adjacent to a wall in a density-stratified environment are described. The flow passes through several stages, from an inertial jet to a buoyant plume, to a neutrally buoyant jet, and then a negatively buoyant plume when it overshoots its equilibrium density. This fluid then ‘springs back’ and eventually occupies an intermediate range of heights. The flow is primarily characterized by the initial value of the buoyancy number, B 0 = Q 0 N 3 / g ′ 0 2 , where Q 0 is the initial volume flux per unit width, g ′ 0 is the initial buoyancy and N is the buoyancy frequency of the environment. Scaled with the initial equilibrium depth D of the in flowing fluid, the maximum depth of penetration increases with B 0 , as does the width of the initial down flow, which is observed to increase very slowly with distance downward. Observations are made of the profiles of flow into and away from the plume as a function of height. Various properties of the flow are compared with predictions from the ‘standard’ two-dimensional entraining plume model, and this shows generally consistent agreement, although there are differences in magnitudes and in details. This flow constrasts with flows down gentle slopes into stratified environments, where two-way exchange of fluid occurs.
Topographic features on the earth's surface with length scales of 5–100 km have a significant effect on the general circulation of the atmosphere. This is accomplished by the drag that they exert on the atmosphere through the generation of internal gravity waves that may propagate to great heights, through hydraulic transitions in low level air-streams across mountain ranges, and through the formation of wakes. The satisfactory representation of these processes in general circulation models is important for both weather and climate forecasting. This may be accomplished by characterising the small-scale topography by suitable statistical parameters, and (conceptually) replacing it by simpler topography that has the same values of these parameters, and for which the dynamics have been studied and are reasonably well known. The drag of this topography on the atmospheric flow may then be estimated for modelling purposes. The extension of these concepts to flow past topography in lakes is discussed. As a beginning, this is done by examining the properties of stratified flow past obstacles on an inclined plane surface, simulating part of the bottom of a typical lake. The three dynamical processes listed above for the atmosphere are again relevant, with conspicuous asymmetries present because of the sloping terrain.
Variability in the southern atmospheric circulation at mid- to high latitudes with a dominant quasi-stationary wavenumber-3 pattern has been reported in many observational studies. The variability is barotropic in nature with signals in the middle troposphere as well as at the atmosphere–ocean interface. Moreover, there are preferred fixed centers for the strongest anomalies. These features are well reproduced by the Commonwealth Scientific and Industrial Research Organisation coupled model on various timescales. On the interannual timescale, an index of the modeled wavenumber-3 pattern shows little correlation with the modeled Southern Oscillation index, suggesting that the variability associated with wavenumber-3 anomalies is separate to modeled ENSO-like events. However, the variation of the pattern index is strikingly similar to, and highly correlated with, the modeled oceanic variability. The associated oceanic anomalies move eastward and are similar to those of the observed Antarctic circumpolar wave (ACW). The modeled ACW-like anomalies exist not only at the surface but also through middle ocean depths, with a similar barotropic nature to those of the atmospheric anomalies. The oceanic anomalies also display a wavenumber-3 pattern. The essential elements of the dynamics of the modeled ACW are the advection of SST anomalies by the surface Antarctic Circumpolar Current (ACC), and the interactions between anomalies of SST and mean sea level pressure (MSLP). Associated with the standing wavenumber-3 pattern, there are fixed centers for the strongest MSLP anomalies. As a positive SST anomaly advected by surface ACC approaches a center of a positive MSLP anomaly, the MSLP decreases. The positive (negative) SST anomalies are generated by anomalous latent and heat fluxes, which are in turn induced by southward (northward) meridional wind stress anomalies resulting from geostrophic balance. These MSLP anomalies change sign when the positive (negative) SST anomalies move to a location near the centers. Once MSLP anomalies change sign, positive (negative) SST anomalies are generated again reinforcing the anomalies entering from the west. The time for the surface ACC to advect one-sixth of the circuit around the pole corresponds to the time of a half-cycle of the standing MSLP oscillations. Thus the surface ACC determines the frequency of the standing oscillation. In the present model, the speed of the surface ACC is such that the period of the standing oscillation is 4–5 yr, and it would take 12–16 yr for an anomaly to encircle the pole. These and other features of the modeled ACW, together with associated dynamic processes, are analyzed and discussed.
A simple explanation is given for the result of Fels (1977) that a reflected internal wave field may have a larger associated momentum flux than the incident wave field. The reflected momentum flux may also be less than the incident, and this property is related to the shape of the reflecting surface and the forces on it.
Abstract Observations of dense downslope flows into a density-stratified environment are described, and these observations are interpreted quantitatively in terms of dynamical processes. The system is two-dimensional (x -z), the slope is at 6° to the horizontal, and the dense fluid is released at a uniform rate at the top of the slope for a finite period of time. The main down flow has the form of a gravity current with a distinct upper interface, with some similarities to the flow into a homogeneous environment described by Ellison and Turner (1959), but with major differences.
The initial value problem related to axisymmetric forced oscillations of a rigidly rotating inviscid fluid enclosed in a finite circular cylinder is examined in linear approximation with the aid of the Laplace transform technique. An impulsive starting motion is considered. The solution consists of a ‘periodic’ motion which oscillates with the forcing frequency, together with a doubly infinite set of inertial modes whose presence is determined by the initial conditions and whose frequencies form a dense set in the range (−2ω, 2ω), where ω is the angular velocity. The nature of the periodic or ‘steady-state’ part of the solution is strongly dependent on the precise value of the forcing frequency α (α > 0) when α ≤ 2ω. In particular the system will resonate if α equals any one value of the dense set of resonant frequencies. It is shown that no internal sets of discontinuities in velocity or velocity gradient are present in the inviscid flow for finite times. Effects of viscosity on the inviscid solution are also discussed, and it is argued that when the inertial modes decay the steady-state flow will contain pseudo-random patterns of internal shear layers for some values of α < 3ω. It seems possible that these shear layers may be interpreted as owing their existence indirectly to viscosity.
Laboratory experiments were conducted on spin-up of a linearly stratified fluid in a rotating axisymmetric annular channel formed by two cylindrical coaxial walls and a flat bottom. Secular as well as instantaneous variation in rotation speeds was investigated for a range of Rossby numbers ε=ΔΩ∕Ω⩽1, where ΔΩ is the change in the rotation rate and Ω is the final rotation rate of the annulus. The experimental studies reported by Smirnov et al. [S. A. Smirnov, P. G. Baines, D. L. Boyer, S. I. Voropayev, and A. N. Srdic-Mitrovic, “Long-time evolution of linearly stratified spin-up flows in axisymmetric geometries,” Phys. Fluids 17, 016601 (2005)] were extended to (i) explore the density structure of the corner regions formed adjacent to the inner and outer sidewalls of the annular channel during spin-up, and to (ii) investigate the role of the boundary conditions at the vertical sidewalls in the development of nonaxisymmetric disturbances and formation of large columnar eddies at late spin-up times. The latter was achieved by introducing roughness elements in the form of vertical prisms at the inner sidewall. Observations demonstrated that isopycnals (surfaces of constant density) experience large vertical displacements near the lateral boundaries during spin-up. The density gradient reduces to near zero in the corner regions, where the fluid is stirred, and increases above/below them near the outer/inner sidewalls, respectively. The relative height of the corner regions h∕H (H is the depth of the fluid layer) was found to be determined only by the relative values of the Rossby (ε) and Burger (Bu) numbers and follows the experimental dependence h∕H=0.54ε1∕2∕Bu. A flow stability regime diagram is presented as a function of the Rossby and Burger numbers. Introduction of roughness elements at the inner sidewall did not alter significantly the process and time scales of stratified spin-up, large eddy formation, and subsequent relaxation to the initial state obtained with smooth sidewalls. This finding confirms that the growth of instability in the sidewall shear layers studied by Smirnov et al. does not depend on viscosity.
Topographically induced flows around Antarctica in a rotating tank experiment with both homogeneous and stratified fluid are analyzed and compared with the mean tropospheric circulation. A circular tank of fluid was brought to a state of near-rigid clockwise rotation, and a topographic model of the Antarctic continent was then rotated counterclockwise to simulate a mean westerly zonal wind. Stratification was chosen to give the same ratios of topographic and dynamical length scales as in the atmosphere, as was the Rossby number based on the ratio of rotation rates. After the onset of the relative rotation of the Antarctic model, cyclonic eddies evolved in the coastal areas with, in the homogeneous case, anticyclonic eddies over the Antarctic dome. After about ten tank rotation periods, a dominant wavenumber 3 structure with cyclonic eddies in the Ross and Weddell seas and Prydz Bay is observed as an approximately steady state. Flow over the topography is relatively stagnant, with weak anticyclonic circulation. Variation of the Rossby number by a factor of 4 about the mean atmospheric value showed that the same general behavior was obtained, although there were differences in detail. These flows show remarkable similarity to the observed mean 700 mb height and 850 rob wind fields around Antarctica. This strongly suggests that the same dynamical factors are operating, namely conservation of potential vorticity and strong coupling in the vertical, so that these motions are virtually baratropic. The large cyclonic eddies am then forced by flow separation around prominent coastal irregularities such as the Antarctic Peninsula.
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