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G. T. Csanady

Abstract

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G. T. Csanady

Abstract

In a two-layer model of stratified fluid flow, motions in the internal mode are governed by the distribution of an equivalent depth he. For a typical continental shelf, the distribution of he with distance from shore may be closely approximated by two straight-line distributions patched at the shelf break, one of constant slope and one of constant (equivalent) depth. For such a simple model the forced response to a suddenly imposed wind stress (in the internal mode) is easily calculated. The component of the wind stress perpendicular to shore produces a step-like feature of the thermocline at the shelf, and a longshore Ekman drift gradually reducing to zero at the coast from the infinite ocean value far offshore. Wind stress parallel to the shore produces a thermocline step and a longshore jet at the shelf break, both of linearly increasing amplitude (in time), and an onshore or offshore Ekman drift, again reducing to zero at the coast but having the infinite-ocean magnitude far offshore.

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G. T. Csanady

Abstract

When a relatively large diffusing cloud is transported by the flow in an Ekman layer, the trajectory and the rate of spread of the cloud are affected by the velocity variations both along and across the geostrophic wind. In a first approximation, these effects may be calculated with the aid of the classical diffusion equation using a constant eddy diffusivity and the classical Ekman layer velocity profile, also derived on the basis of a constant eddy viscosity.

Analytical solutions (obtained by the “concentration-moment” method) show that the ground level trajectory of an instantaneously released cloud departs significantly from the surface wind track at distances from the source beyond a few kilometers, and that while this trajectory remains in the sector between surface and geostrophic winds, it does not follow asymptotically either wind direction. The spread of the cloud, as observed at ground level, is dominated, beyond the first few kilometers of travel by the “wind-shear effect” on diffusion, the mean-square dispersion increasing rather more rapidly than it would due to atmospheric turbulence alone. Asymptotically (and this means at very large distances, in practice on a global scale), the mean-square dispersion at ground level becomes proportional to an “effective” shear diffusivity several orders of magnitude greater than the eddy diffusivity.

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G. T. Csanady

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The generation by unsteady winds of standing oscillations on the pycnocline of lakes and enclosed seas, which are much longer than they are wide, is studied on the assumption that end effects are negligible. The approach is valid for a limited period only, and then only to the exclusion of end zones. Regardless of wind direction, only odd modes are excited by a suddenly imposed, horizontally uniform wind stress. If the lake is no wider than a few times the radius of deformation in the internal mode, the excitation is heavily concentrated on the uninodal transverse seiche. In much wider lakes the excitation is evenly spread out over the first few modes having 1, 3, 5, … nodes across the basin. Observations on Lakes Michigan and Ontario (which are “wide” in the above sense) indeed show such multinodal internal seiches to be prominently present, in contrast with smaller lakes in which uninodal internal seiches are usually dominant. Also the amplitudes of observed internal seiches in the Great Lakes are in qualitative accord with the simple theory of their generation.

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G. T. Csanady

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The dynamic interaction of a sloping seafloor with along-isobath density variation is calculated for cases involving a sharp pycnocline and a surface-to-bottom front. Pycnocline depth is supposed to vary in the alongshore direction only, over a sloping plane seafloor; the bottom trace of the surface-to-bottom front is supposed to cut across isobaths. The calculations are diagnostic and make use of linearized equations with a linear bottom friction term.

The results illustrate the manner in which cross-isobath baroclinic flow is converted at the slope into a barotropic flow field, with velocities nearly parallel to the isobaths. The “forward” portion of the slope (that which lies in the direction of Kelvin wave propagation) only is affected, if there is only one inflow or outflow region. However, for equal and opposite inflow and outflow, a closed circulation pattern arises connecting these two regions, accompanied by a secondary closed circulation cell forward of both the inflow and outflow legs. The pressure distribution at the coast is a strongly filtered and phase-shifted version of the off-shore steric-height variation.

In the example of a surface to-bottom front, the divergence of the intensifying baroclinic flow over increasing depth is again drawn from the forward sector, or discharged into that sector when the baroclinic flow is convergent, i.e., passes from deep into shallow water.

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G. T. Csanady

Abstract

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G. T. Csanady

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G. T. Csanady

Abstract

Field observations on coastal currents near Oshawa on the north shore of Lake Ontario during summer and fall are described. The technique of observations (flag-station chain) has been given in Part I, together with a description of the dynamic regime during the spring period. Observations during summer and fall show that the kinetic energy level of water movements increases considerably from spring to summer and again from summer to fall. Much as in the spring, a nearshore band (some 10 km wide) becomes a unique kind of “boundary layer” in which mid-lake motions adjust to the presence of the shares. In this shore zone, currents are shore-parallel and relatively persistent. During summer and fall, mid-lake motions are wave-like, consisting mainly of near-inertial oscillations. Within the shore zone, the current-like motions are associated with thermocline displacements, upward if the current flows to the east, downward if it flows to the west, so that the pressure gradients caused by the non-uniform density distribution are at least partly balanced by the Coriolis force. The lakewide flow pattern is mainly determined by a few periods of relatively strong winds, which can reverse an opposing current and lead to a complete man exchange between the shore zone and mid-lake as a consequence of large thermocline movements. Advection of momentum from the outer zone into the coastal zone also plays a significant role in maintaining coastal currents.

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G. T. Csanady

Abstract

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G. T. Csanady

Abstract

Nearshore transcends, following the development of transient coastal upwelling, characteristically show “intermediate” density fluid occupying the immediate nearshore band. Large cross-shore particle excursions during the development of upwelling may be inferred from be-fore and after transects, and the movement of surface layers seaward, intermediate density fluid shoreward through a distance of the order of kilometers, and the bottom layers also shoreward by a 1esser amount. Some inevitable vertical Mixing together with the large cross-shore displacements results in efficient cross-shore mass exchange.

The main dynamical features of similar events may be investigated by means of three-layer models. Linear theory is conveniently discussed first, the conclusions of which are easily generalized to multilayer models, Finite-amplitude (i.e., “full”) upwelling is then considered using a potential-vorticity conserving impulsive model. The results show that the wind “peels” off the surface layer over which the wind stress is effectively distributed. Thus the next lightest layer becomes exposed to the atmosphere. The lower layers generally respond in the barotropic mode, becoming “equally stretched” on the removal of the surface layer, except within a distance of the order of the baroclinic radius of deformation from the pycnocline outcropping. The maximum velocity of the jet associated with the pycnocline outcropping is limited to an effective densimetric velocity. Cross-shore displacements behave similarly in the model and the observed cases.

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