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R. K. Smith

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R. K. Smith

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This paper contains a study of the energy conversions in Pedlosky's solution for finite-amplitude baroclinic wave development for the case of small dissipation. It is shown that the solution contains an implicit, non-physical source of mean kinetic energy owing to the neglect of a certain boundary condition on the developing mean flow. Additional features of the energetics are described which do not depend explicitly on the solution with the relevant boundary condition inserted. However, the possibility of limit-cycle solutions when this boundary condition is satisfied remains an open question.

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R. K. Smith

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There is a tendency for certain flows in the atmosphere and oceans to concentrate into narrow streams or currents, which preserve their identity over very large distances. The ability of such flows to overcome the diffusive effects normally encountered in laboratory jet flows is usually explained in terms of the entrainment into the jet of relative vorticity, with a sign which helps to maintain the shear. A simple model which one would expect to exhibit this properly was described by Long who examined the flow of a two-dimensional, viscous jet on a beta-plane, and obtained the first term of an asymptotic series solution for the flow in a region far upstream from some origin. This term is essentially the solution of the linearized jet equations, which represent a balance between Coriolis and viscous forces with the pressure gradient. Unfortunately, Long did not calculate further terms in his expansion and his solution did not therefore contain the effects of advection (or entrainment) of fluid. In the present paper, the second term is calculated. This describes the largest effect of the nonlinear terms on the asymptotic flow and confirms that the entrainment of fluid into a westerly jet enhances the shear, in contrast to jet flows which have no background rotation. Further terms in Long's asymptotic series are also investigated and it is shown, in general, that these are indeterminate.

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R. K. Smith

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A new perspective of the dynamics of a tropical cyclone eye is given in which eye subsidence and the adiabatic warming accompanying it are accounted for directly from the equations of motion. Subsidence is driven by an adverse, axial gradient of perturbation pressure which is associated principally with the decay and/or radial spread of the tangential wind field with height at those levels of the cyclone where the tangential winds are approximately in gradient wind balance. However, this pressure gradient is almost exactly opposed by the buoyancy force field due to adiabatic warming. This corroborates with observational data.

The relationship between the present view of eye dynamics and those of Malkus and Kuo and a recent study by Willoughby is discussed in detail.

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R. K. Smith and Joan M. Reilly

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In an earlier paper (Smith, 1977) it is shown that when viscous effects are important only on a time scale much longer than that for incipient wave growth, the amplitude evolution of a marginally unstable baroclinic wave in a two-layer, quasi-geostrophic zonal flow is governed by an infinite system of ordinary differential equations. These equations have a steady solution which under certain conditions is unstable with respect to small perturbations in wave amplitude. In the case where viscous effects are nonzero but are exceedingly small, the asymptotic analysis in Smith (1977) shows that a stable limit cycle solution is also possible and when the steady solution is unstable, an initially incipient wave evolves toward the limit cycle, which represents an amplitude vacillation of the wave.

In this paper, some numerical integrations of the amplitude equations are presented for the case of moderate viscosity. These are compared with solutions obtained from the amplitude equations derived by Pedlosky (1971) in a theory which omits a certain boundary condition an the mean zonal flow (Smith, 1974). Although the two sets of amplitude equations differ considerably, our results confirm the important prediction of Pedlosky that for sufficiently small viscosity and/or if the steady solution is unstable, an incipient wave evolves to a state in which its amplitude undergoes regular pulsations, or vacillations, described by a stable limit cycle solution. However, the parameter range for which the steady solution is unstable is widely different in the two analyses, except for vanishingly small viscosity.

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J. V. Mansbridge and R. K. Smith

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Resonant interactions between a marginally unstable baroclinic wave and one or two pairs of neutral waves in a rotating, two-layer zonal Row model are studied. Analyses based on a multiple scaling technique are carried out for inviscid flow on a beta plane, inviscid flow on an f-plane, and slightly viscous flow on an f-plane. It is assumed that the neutral waves are of smaller order in amplitude than the unstable wave, and the flow domain is taken to be zonally periodic so that zonal wavelengths are discrete. In this and other respects, the theory differs from an earlier study by Loesch (1974a,b) and avoids a number of difficulties inherent in that work.

For an inviscid beta plane flow, the evolution of a wave triad is governed by a certain parameter N 2 N 3/U. If this is negative, the neutral waves are unable to grow substantially larger in amplitude than their respective initial amplitudes, despite which they have a disproportionately large effect on the evolution of the unstable wave. If O<N 2 N 3/U;<0.125, the neutral waves are largely unrestricted by their initial amplitudes and interact strongly with the unstable wave. Finally, if 0.125<N 2 N 3/U, all three waves grow rapidly without bound and the scaling assumption is soon violated.

For the flows on an f-plane, there exist two resonant triads with the unstable wave common to both. In this case, the neutral waves are always constrained by the size of their initial amplitudes. When the flow is inviscid, wave evolution is much the same as in the beta-plane problem with N 2 N 3/U≶0, whereas the addition of a small amount of viscosity results in the neutral waves being damped. There is no intermediate viscous regime in which the neutral waves are undamped, but “forget” their initial conditions.

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L. M. Leslie and R. K. Smith

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A recent numerical study of vortex growth in a flow configuration which models the principal characteristics of a tornado cyclone (Smith and Leslie, 1978) is extended to take account of vertical stability. It is shown that for a given strength of convection and rotation (in the model, the driving effect of a ‘supercell’ updraft is simulated by an imposed body force), the intensity of the mature vortex which forms in the presence of a typical vertical gradient of potential temperature is significantly lower than that which forms in an adiabatic atmosphere. We conclude that the effects of vertical stratification on tornadogenesis may often be important and may prevent some vortices, which might otherwise do so, from establishing ground contact.

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Mark R. Schoeberl and Anne K. Smith

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The Northern Hemisphere, quasi-geostrophic, integrated enstrophy budget for the 1978/79 winter has been analyzed from 10-0.1 mb using LIMS data. The stratospheric integrated enstrophy builds up during early winter as a result of the diabatic forcing of the polar vortex. Starting in January, an irregular and generally irreversible transfer of enstrophy from the zonal mean reservoir to planetary waves begins to reduce the total. This transfer of enstrophy to the waves produces significant imbalances in the integrated enstrophy budget at 10 mb. The imbalances appear to result from the transfer of enstrophy to smaller scales not resolved by the LIMS instrument. We believe that these imbalances are signature of Rossby wave breaking, as the imbalance episodes correspond well to the appearance of Ertel Vorticity filaments recently shown by McIntyre and Palmer.

In the mesosphere the total enstrophy shows little seasonal trend. Our analysis indicates that the mesophere may be region of continuous wave breaking during water.

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R. H. Clarke, R. K. Smith, and D. G. Reid

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This paper presents the results of a field expedition mounted in late September/early October 1979 to investigate the structure and origin of the “morning glory” of the Gulf of Carpentaria in northern Australia. The morning glory is a line wind squall, accompanied by a pressure jump, and often by a long roll-cloud or series of such clouds. It frequently occurs in the early morning, especially in October, in the Gulf area.

A light aircraft, fitted with a temperature and humidity probe, was flown in two glories to determine their thermodynamic structure, and wind fields wore obtained principally by tracking pilot balloons using the double theodolite method. Data also were obtained from a network of surface stations, recording wind velocity and pressure, installed at locations across Cape York Peninsula, which is believed to be the area of genesis.

The morning glory is identified as an internal undular bore propagating on the nocturnal and/or maritime inversion. Its origin appears to lie frequently in the interaction of a deeply penetrating sea breeze front with a developing nocturnal inversion, but there is evidence also that on occasion it may result from the effect of a katabatic flow. The factors which appear to make the Gulf region particularly favorable for the common occurrence of this phenomenon are discussed.

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Shane R. Keating, K. Shafer Smith, and Peter R. Kramer

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Several recent studies diagnose lateral stirring and mixing in the upper ocean using altimetry-derived velocity fields to advect “virtual” particles and fields offline. However, the limited spatiotemporal resolution of altimetric maps leads to errors in the inferred diagnostics, because unresolved scales are necessarily imperfectly modeled. The authors examine a range of tracer diagnostics in two models of baroclinic turbulence: the standard Phillips model, in which dispersion is controlled by large-scale eddies, and the Eady model, where dispersion is determined by local scales of motion. These models serve as a useful best- and worst-case comparison and a valuable test of the resolution sensitivity of tracer diagnostics.

The effect of unresolved scales is studied by advecting tracers using model velocity fields subsampled in space and time and comparing the derived tracer diagnostics with their “true” value obtained from the fully resolved flow. The authors find that eddy diffusivity and absolute dispersion, which are governed by large-scale dynamics, are insensitive to spatial sampling error in either flow. Measures that depend strongly on small scales, such as relative dispersion and finite-time Lyapunov exponents, are highly sensitive to spatial sampling in the Eady model. Temporal sampling error is found to have a more complicated behavior because of the onset of particle overshoot leading to scrambling of Lagrangian diagnostics. This leads to a potential restriction on the utility of raw altimetry maps for studying mixing in the upper ocean. The authors conclude that offline diagnostics of mixing in ocean flows with an energized submesoscale should be viewed with some caution.

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