87:6145 exact analytical solutions for elliptical vortices of the shallow-water equations

2
O LR (I 987) 34 (11) A. Physical Oceanography 933 associated velocities of ~0.2 m s ~. After an inertial period, geostrophic adjustment turns the circulation into a large-scale horizontal cyclonic gyre. Boundary friction effects on advancing gravity currents are also evident. School of Earth Sci., Flinders Univ., Bedford Park, SA 5042, Australia. 87:6139 Samolyubov, B.I., 1986. Turbulent diffusion in local shear layers in a stratified near-bottom current with suspended particles. Izv. A tmos. Ocean Phys. (a translation of Fiz. Atmos. Okeana), 22(5):389- 397. The diffusion of particles in a polydispersive sus- pension and its relationship with the velocity field in turbidity clouds are studied at the levels for local shear layers in the suspension current. Analyzed are results on velocity fields and the concentration of suspension particles in the suspension current. Moscow State Univ., USSR. 87:6140 Svendsen, I.A., 1987. Analysis of surf zone turbu- lence. J. geophys. Res., 92(C5):5115-5124. Measurements of turbulent kinetic energy k under surf zone waves are analyzed to show how k varies over depth, between breaker point and shoreline, and depends on the beach slope. The variation of k over depth is remarkably weak, large values being measured a few percent of the depth above the bottom. A simple model for the dissipation mech- anism makes it possible to derive an empirical formula for the time-averaged k that accurately describes all the data considered reliable. Inst. of Hydrodynamics and Hydraulic Engng, Tech. Univ., Lyngby, Denmark. 87:6141 Treguier, A.M. and B.L. Hua, 1987. Oceanic quasi- geostrophic turbulence forced by stochastic wind fluctuations. J. phys. Oceanogr., 17(3):397-411. The quasi-geostrophic response to stochastic wind fluctuations is calculated using a doubly periodic nonlinear model, with a vertical resolution of three modes in most cases. The influence of various parameters on the response is investigated: space and time scale of the forcing, stratification, bottom friction and fl-effect. One aim of this study is to understand the influence of nonlinear transfers; therefore most simulations are situated in a param- eter range where nonlinearities are important. IFREMER, Centre de Brest, BP 337, 29273 Brest Cedex, France. 87:6142 Woods, John, Harry Leach and Peter Minnett, 1981. The GATE Lagrangian batfish experiment: sum- mary report. Ber. Inst. Meeresk. Christian- Albrechts-Univ., 88:170pp. Thirteen quasi-Lagrangian box-surveys were carried out as part of the GATE Experiment with a CTD mounted in a batfish towed body. The experiment, data acquisition and data processing are described; uncertainties in the data are estimated and a selection of standard products from the data set are presented and described. Isopycnic analysis showed that thermohaline and dynamic structures with scales comparable to those of mesoscale fronts were present. Inst. fur Meereskunde, Dusternbrooker Weg 20, D-2300 Kiel 1, FRG. A300. Fluid mechanics 87:6143 Churilov, S.M. and I.G. Shukhman, 1986. Evolution of initial perturbations in an unstably stratified shear flow. Izv. Atmos. Ocean Phys. (a translation of Fiz. Atmos. Okeana), 22(5):409-411. It is shown that an unstably stratified shear flow is actually unstable for all k; however, the asymptotic dependence of the perturbation amplitude on time in the region k2>k2(Jo) is not purely exponential. Siberian Inst. of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, USSR. 87:6144 Crisciani, Fulvio, 1986. A note about the barotropic- baroclinic energy transfer equation for oceanic flows. Boil. Oceanol. teor. appl., 4(4):211-218. Some aspects of the mechanism governing the barotropie-baroclinic instability in geophysical flows are described by the kinetic energy transfer equation. One form of this equation is sometimes deduced in the standard literature in an unconvincing way. In this paper we focus on the criticizable points of such a method and propose a revised equation for oceanic flows, lstituto Sperimentale Talassografico, C.N.R. Trieste, Italy. 87:6145 Cushman-Roisin, Benoit, 1987. Exact analytical solutions for elliptical vortices of the shallow- water equations. Tellus, 39A(3):235-244. Shallow-water equations in a rotating framework admit exact solutions for which velocity components are linear and height field is quadratic in the coordinate variables. The resulting 12 coefficients

Upload: lyhuong

Post on 03-Jan-2017

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 87:6145 Exact analytical solutions for elliptical vortices of the shallow-water equations

O LR (I 987) 34 (11) A. Physical Oceanography 933

associated velocities of ~0.2 m s ~. After an inertial period, geostrophic adjustment turns the circulation into a large-scale horizontal cyclonic gyre. Boundary friction effects on advancing gravity currents are also evident. School of Earth Sci., Flinders Univ., Bedford Park, SA 5042, Australia.

87:6139 Samolyubov, B.I., 1986. Turbulent diffusion in local

shear layers in a stratified near-bottom current with suspended particles. Izv. A tmos. Ocean Phys. (a translation of Fiz. Atmos. Okeana), 22(5):389- 397.

The diffusion of particles in a polydispersive sus- pension and its relationship with the velocity field in turbidity clouds are studied at the levels for local shear layers in the suspension current. Analyzed are results on velocity fields and the concentration of suspension particles in the suspension current. Moscow State Univ., USSR.

87:6140 Svendsen, I.A., 1987. Analysis of surf zone turbu-

lence. J. geophys. Res., 92(C5):5115-5124.

Measurements of turbulent kinetic energy k under surf zone waves are analyzed to show how k varies over depth, between breaker point and shoreline, and depends on the beach slope. The variation of k over depth is remarkably weak, large values being measured a few percent of the depth above the bottom. A simple model for the dissipation mech- anism makes it possible to derive an empirical formula for the time-averaged k that accurately describes all the data considered reliable. Inst. of Hydrodynamics and Hydraulic Engng, Tech. Univ., Lyngby, Denmark.

87:6141 Treguier, A.M. and B.L. Hua, 1987. Oceanic quasi-

geostrophic turbulence forced by stochastic wind fluctuations. J. phys. Oceanogr., 17(3):397-411.

The quasi-geostrophic response to stochastic wind fluctuations is calculated using a doubly periodic nonlinear model, with a vertical resolution of three modes in most cases. The influence of various parameters on the response is investigated: space and time scale of the forcing, stratification, bottom friction and fl-effect. One aim of this study is to understand the influence of nonlinear transfers; therefore most simulations are situated in a param- eter range where nonlinearities are important. IFREMER, Centre de Brest, BP 337, 29273 Brest Cedex, France.

87:6142 Woods, John, Harry Leach and Peter Minnett, 1981.

The GATE Lagrangian batfish experiment: sum- mary report. Ber. Inst. Meeresk. Christian- Albrechts-Univ., 88:170pp.

Thirteen quasi-Lagrangian box-surveys were carried out as part of the GATE Experiment with a CTD mounted in a batfish towed body. The experiment, data acquisition and data processing are described; uncertainties in the data are estimated and a selection of standard products from the data set are presented and described. Isopycnic analysis showed that thermohaline and dynamic structures with scales comparable to those of mesoscale fronts were present. Inst. fur Meereskunde, Dusternbrooker Weg 20, D-2300 Kiel 1, FRG.

A300. Fluid mechanics

87:6143

Churilov, S.M. and I.G. Shukhman, 1986. Evolution of initial perturbations in an unstably stratified shear flow. Izv. Atmos. Ocean Phys. (a translation of Fiz. Atmos. Okeana), 22(5):409-411.

It is shown that an unstably stratified shear flow is actually unstable for all k; however, the asymptotic dependence of the perturbation amplitude on time in the region k2>k2(Jo) is not purely exponential. Siberian Inst. of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, USSR.

87:6144 Crisciani, Fulvio, 1986. A note about the barotropic-

baroclinic energy transfer equation for oceanic flows. Boil. Oceanol. teor. appl., 4(4):211-218.

Some aspects of the mechanism governing the barotropie-baroclinic instability in geophysical flows are described by the kinetic energy transfer equation. One form of this equation is sometimes deduced in the standard literature in an unconvincing way. In this paper we focus on the criticizable points of such a method and propose a revised equation for oceanic flows, lstituto Sperimentale Talassografico, C.N.R. Trieste, Italy.

87:6145 Cushman-Roisin, Benoit, 1987. Exact analytical

solutions for elliptical vortices of the shallow- water equations. Tellus, 39A(3):235-244.

Shallow-water equations in a rotating framework admit exact solutions for which velocity components are linear and height field is quadratic in the coordinate variables. The resulting 12 coefficients

Page 2: 87:6145 Exact analytical solutions for elliptical vortices of the shallow-water equations

934 A. Physical Oceanography OLR (1987) 34 ( I 1 )

are, in general, functions of time and governed by a set of nonlinear, coupled, ordinary differential equations. The most general solution presented here contains 10 arbitrary constants of integration; these degrees of freedom are accounted for by inertial oscillations of the vortex center of mass (4), average circular structure (2), circular pulsation mode (2), and 2 by one of two possible elliptical rotation modes. The complete solution with 12 degrees of freedom would be achieved if these 2 elliptical modes could be incorporated simultaneously. This solution sheds light on the behavior of time- dependent elliptical warm-core rings as observed in the ocean. Dept. of Oceanogr., Florida State Univ., TaUahassee, FL 32306, USA.

87:6146 Goncharov, V.P., 1986. Nonlinear waves in flows that

are vorticity-homogeneous in a layerwise manner. Izv. Atmos. Ocean Phys. (a translation of Fiz. Atmos. Okeana), 22(5):355-361.

The Hamiltonian description method is extended to two-dimensional wave motions in an incompressible medium that is piecewise homogeneous in terms of density and vorticity. Long nonlinear waves are considered within the framework of the method for a plane model with a bilinear flow profile of general form and for an axisymmetrical model of a cylin- drical jet type. Inst. of Atmos. Phys., Acad. of Sci., USSR.

87:6147 Hopfinger, E.J., 1987. Turbulence in stratified fluids:

a review. J. geophys. Res., 92(C5):5287-5303.

Buoyancy length scale and internal disturbance Froude number criteria for turbulence collapse in stratified fluid are examined in the light of recent laboratory experiments, oceanographic observations, and numerical simulations. It emerges that the onset of collapse occurs when the turbulence integral length scale is of the order of the buoyancy length scale, giving a disturbance Froude number close to 1. Complete collapse of three-dimensional turbu- lence, characterized by nearly zero vertical mass flux, occurs at a value of the disturbance Froude number of 0.2-0.3. In the collapsed state, internal wave motion and quasi two-dimensional turbulence coexist on different time scales. Vertical diffusion coefficients and mixing efficiency, are also exam- ined. Inst. de Mecanique, Univ. de Grenoble, Grenoble, France.

87:6148 Kranenburg, C., 1987. Boundary-induced entrain-

merit in two-layer stratified flow. J. geophys. Res., 92(C5):5417-5425.

An integral entrainment model for two-layer strat- ified flow is based on the assumption of quasi- stationary turbulence in either layer and takes into account shear production at the boundaries and interface, buoyancy transport, and dissipation. Shear production at the interface was absent in a series of experiments with an annular duct, whereas it played a substantial part in a series with the annulus converted into a flume with a free surface. Calcu- lated results show good agreement with observations in experiments with little influence of mean-flow curvature. Dept. of Civil Engng, Delft Univ. of Tech., 2628 CN Delft, Netherlands.

87:6149 Rodi, Wolfgang, 1987. Examples of calculation

methods for flow and mixing in stratified fluids. J. geophys. Res., 92(C5):5305-5328.

Various types of prediction methods are introduced briefly, from one-dimensional integral methods to direct simulations of the Navier-Stokes equations. The paper concentrates on models for simulating the turbulent momentum, heat, and mass transport terms appearing in the statistical methods employing averaged equations. Models ranging from the simple Prandtl mixing length theory to second-order-closure schemes are discussed. Examples are presented of applications of the method covered to a variety of stratified flow situations. Inst. fur Hydromechanik, Univ. of Karlsruhe, Karlsruhe, FRG.

87:6150 Rohr, James and Charles Van Atta, 1987. Mixing

efficiency in stably stratified growing turbulence. J. geophys. Res., 92(C5):5481-5488.

Nearly steady state mixing efficiencies, as charac- terized by the flux Richardson number R~ have been measured in stably stratified, turbulent, uniform gradient shear flows. It is found that the length scale arguments successfully applied by Rohr et al. (1984) to the case of decaying, stably stratified, unsheared grid turbulence can also account for the overall behavior of the mixing efficiency (R 3 as a function of stability (Ri) in the present case of growing, stably stratified, uniform mean shear turbulence. Naval Ocean System Center, San Diego, CA, USA.

8"/:6151 Tamai, Nobuyuki and Takashi Asaeda, 1987. Con-

vection Hnes on a heated bottom plate at large Rayleigh number. J. geophys. Res., 92(C5):5489- 5495.

:-aeetlike plumes generated at the heated bottom plate are composed of several thermals generated successively. Projections of the plumes are called