Search Results

You are looking at 1 - 7 of 7 items for

  • Author or Editor: Timothy W. Kao x
  • Refine by Access: All Content x
Clear All Modify Search
Timothy W. Kao

Abstract

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starring with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. The full time-dependent diffusion and Navier-Stokes equations with constant eddy diffusion and viscosity coefficients and for a constant Coriolis parameter are used in this study. Scaling analysis reveals three independent length scales of the problem, viz., a radius of deformation or inertial length scale L 0, a buoyancy length scale h 0 and a diffusive length scale h v. Two basic dimensionless parameters are formed from these length scales: the thermal (or more precisely, the densimetric) Rossby number, Ro=L 0/h 0 and the Ekman number E=(h v/h 0)2. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on E alone for problems of oceanic interest. Under this scaling, the solutions are similar for all Ro sufficiently large. It is also shown that 1/Ro is a measure of the frontal slope, so that Ro is large for all oceanic density fronts. The governing equations, in the form used in a previous paper by Kao el al. (1978), are solved numerically and the scaling analysis is confirmed. The solution indicates that an equilibrium state is established. The front can then be rendered stationary by a barotropic current from a larger scale alongfront pressure gradient. In that quasi-steady state and for small values of E, the main thermocline and the inclined isopycnics forming the front have evolved, together with an intense alongfront jet and a crossfront (or cross-stream) circulation with surface discharge toward the front and return flow at greater depth. Conservation of potential vorticity is also obtained in the light water pool. The surface jet exhibits anticyclonic shear in the light water pool and cyclonic shear across the front. It is also shown that horizontal diffusive effects are unimportant. Comparisons with known hydrographic features of the Gulf Stream are made, showing good agreement, especially on the major features. It is thus seen the mean Gulf Stream dynamics can indeed be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front. This mechanism is thus suggested in this paper as a mechanism for the maintenance of the Gulf Stream dynamics.

For large values of E, it will be shown that another type of scaling is required. That result will be shown in a subsequent paper as Part II of this series, and is relevant to the study of density and current structure on the East Coast continental shelf of North America from Newfoundland to Chesapeake Bay, a region subject to forcing by freshwater river discharges.

Full access
Timothy W. Kao

Abstract

In Part I of this series, a framework was introduced for the study of oceanic frontal dynamics. The dynamics was studied by posing an initial value problem, starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. An essential aspect of the framework was the identification of the proper length scales: an inertial length scale L 0, a buoyancy length scale h 0 and a diffusive length scale hv. In Part I, the horizontal and vertical dimensions were scaled by L 0 and h 0, respectively; and two dimensionless parameters were formed, viz., Ro = L0/h0 and E = (hv/h0)2. It was shown in Part I that under this scaling, the normalized equations depended on E only for Ro sufficiently large. The solution for E small, i.e., for the almost inviscid case, was given in Part I; and the equilibrium state was discussed in a frame of reference in which the front was stationary.

In this paper, we present the solution for large E. It will be shown that a universal similarity (in the sense of a fully scaled set of governing equations without any parameter) is obtained, when the horizontal and vertical dimensions are now scaled by L 0 and hv, respectively, for a given dimensionless depth ; constitutes the only parameter of the problem and enters it through the location of the bottom. The solution for ≈ 10 is relevant to the study of the establishment of current and density structure of the shelf water subject to forcing by freshwater discharge along the coast, such as the mid-shelf region of the east coast continental shelf of North America. It is shown that when equilibrium is reached, a frontal region can be identified, which propagates steadily but slowly across the shelf. Behind the frontal region the horizontal flow field is steady. The nature of the force balance in the cross-shelf and along-shelf directions is clarified.

This paper is totally self–contained and can be read without reference to Part I.

Full access
Timothy W. Kao

Abstract

The nature of the balance of forces in the downstream direction is discussed. It is shown that the ageostrophic cross-stream flow is in adjective equilibrium in which the Coriolis force is balanced by the nonlinear inertia force.

Full access
Timothy W. Kao

Abstract

The structure of the Gulf Stream Current is associated with the quasi-permanent density front in the western North Atlantic. The lighter mass of warmer but saltier water of the Sargasso Sea is separated from the slope water by inclined isopycnals that form the front. Recent satellite altimeter measurements have also revealed a well-defined sea-surface height change across the front. In this paper, a model of the Gulf Stream cross-sectional density and current structure is presented, using the complete dynamical and mass-conservation equations. The model postulates a forcing, at the interior ocean boundary, by a cross-stream ageostrophic circulation with inflow of light water in the upper ocean and a return flow at greater depths. The model Gulf Stream is found to develop after initial geostrophic adjustment of several inertial periods.

In the quasi-steady state, the normalized structural results constitute a single representation of the structure of all Gulf Stream sections; i.e., all sections are similar. The normalization requires only two observational inputs; (i) either a suitably defined depth of a representative isopycnal in the main pycnocline beneath the Sargasso Sea or the total sea-surface height change across the front, and (ii) the maximum downstream surface velocity of the Stream. The model can therefore be used to produce the entire cross-sectional structure of the Gulf Stream and its front from simple and limited observational inputs.

The results are compared with representative field data from (i) the Gulf Stream ’60 experiment, (ii) the Seasat altimeter experiment, and (iii) the recent Gulf Stream Current measurements by the University of Rhode Island group using the Pegasus current profiler. Quantitative agreement between the model results and the field data is found.

Full access
K. K. Wong and Timothy W. Kao

Abstract

No abstract available.

Full access
Shenn-Yu Chao and Timothy W. Kao

Abstract

The frontal instability of major baroclinic ocean currents such as the Gulf Stream is numerically studied here, using a three-dimensional, primitive-equation model. The model current is driven by a buoyant discharge near the surface from the light water side of the front. Subsequent geostrophic adjustment produces a baroclinic analysis in which a prescribed mean current is subject to eddy dissipation with no provision for its maintenance. At low latitudes small-amplitude unstable waves are generated. The eddy fluxes are shown to be largely upgradient and responsible for the maintenance of the front. At higher latitudes the model produces anticyclonic barotropic instability. The triggering mechanism for instability is related to the outward surge of the front during the initial stage of geostrophic adjustment, which in turn is related to the inertial oscillations of surface isopycnals. The outward surge is surface-trapped. To trigger instability, the surge must be shallow and intense in lower latitudes, and becomes deeper and weaker in higher latitudes. The Richardson number decreases below 0.25 shortly before and after onset of instability, and increases again after unstable waves have fully developed. The instability is initially of grid scale, and subsequently evolves into larger scales through nonlinear cascading processes, rendering themselves to baroclinic instability.

Full access
K. K. Wong and Timothy W. Kao

Abstract

An investigation is made of the two-dimensional flow of a stratified fluid over an extended obstacle, characterized by a source disturbance, for an infinite medium and for a layer of finite depth. The problems are posed as initial-boundary value problems, and steady-state solutions for the flow field are obtained in the limit of large time. The results show an unattenuated system of jets or shear layers extending far upstream from the obstacle, which occurs whenever a system of lee waves is present. For the finite depth case detailed calculations are made, starting with realistic mean values for the atmosphere. The final established profile indicates a variable shear and density profile far upstream, characterized by variable local Richardson numbers. The wind shears induced are also of the order of shears due to thermal wind effects, though quite apart from these effects. The study therefore points to the importance of topographical features on vertical wind shear in the troposphere.

Full access