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J. E. Hart

Abstract

The Eady problem concerning the stability of quasi-geostrophic baroclinic flows which have uniform vertical shear is generalized to include time-dependent basic flows. By means of a simple transformation an exact solution can be obtained. The instability of the flow, in the sense of boundedness as t → ∞, is determined by the usual Eady criterion derived for steady basic flows, but the growth rates can be significantly enhanced or diminished. In the special case of purely periodic time dependence, the flow is always stable in the above sense.

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J. E. Hart

Abstract

A simple parallel flow model is derived for a thin (depth to length ratio ≪1) Hadley circulation in a two-dimensional box with rigid horizontal boundaries maintained at a temperature which increases linearly with the horizontal coordinate x. Vertical velocities are assumed to he confined to narrow regions near the ends. The stability of this solution is discussed. Several modes of energy transfer to and from the mean kinetic and potential energies exist. As opposed to the case of thermal convection between isothermal plates in a constant shear, transverse disturbances with symmetry normal to the shear vector are always more unstable than longitudinal disturbances with symmetry parallel to the shear vector. Implications of these results for recent theoretical ideas on the Venusian circulation are discussed.

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J. E. Hart

Abstract

Several aspects of thermal convection in the presence of a lateral shear associated with either a shear line [with velocity V(x)] or a circular vortex [with azimuthal velocity V(r)] are considered. Parameter settings that favor suppression of convection near the axis of the shear flow or near the center of a cyclonic vortex are determined by looking at the structure of the linear neutral modes at the onset of convection, or at the modes that have the largest growth rates at highly supercritical Rayleigh numbers where the motions are nearly inviscid. Both parallel [or axisymmetric (2D longitudinal)] and wavy [or nonaxisymmetric (3D)] disturbances are considered, although the analysis focuses on the former. A weakly nonlinear amplitude equation shows that the bifurcation is supercritical, but even in the presence of vertical asymmetry in the applied thermal mean gradient, there is not a significant preference for upwelling or downwelling at the axis. Within the context of the linear model of convection in lateral shear, it is suggested that strong atmospheric vortices may suppress thermal convection in their cores, a mechanism possibly associated with vortex “eyes.” A simple laboratory demonstration of the main result is included.

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J. E. Hart

Abstract

A plate tilted at 42° from the horizontal is oscillated along its length with frequency ω and amplitude a in a linearly stratified fluid (salt water) of kinematic viscosity ν. If the Reynolds number Rc = a(ω/ν)½ is small, a parallel oscillating boundary layer is set up. As Re is increased from zero the parallel flow becomes unstable. If ω2≲N̂2 (where N̂ is a transverse Brunt-Väisälä frequency), the motion appears to be a convective overturning associated with periodic reversals of the density gradient. If ω2≪N̂2, these plumes just mix up the fluid next to the plate. If, however, ω2≈N̂2 and Re is not too large, then the plumes interact with the oscillating shear flow and mix in such a way as to set up layers which extend into the interior of the fluid. It is suggested that these effects might also be present when internal waves propagate over a slope.

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J. E. Hart

Abstract

A two-layer model is constructed for wind-driven flow over topography in a closed polar basin where thevariation of Coriolis force with latitude is negligible. The model equations are reduced using scales appropriate for the Arctic Ocean. The nonlinear equations governing the geostrophic flow in the two layers can, fora basin with strong topography, be reduced to a linear differential equation. This is solved for a "model"topography which mimics the bathymetry of the Canadian Basin. The asymmetry or intensification inthe surface water is described as a function of the non-dimensional parameters which contain informationon the basic stratification, rotation and vertical mixing.

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J. E. Hart

Abstract

We consider the instability properties of a circular current in the upper layer of a two-layer quasi-geostrophic ocean over a unidirectional slope. This particular flow-topography geometry is intended as a crudemodel of geophysical gyres where the variation of the Coriolis force is negligible. Such currents occur in theArctic and in Gulf Stream rings. The slope destabilizes the flow; the critical Froude number is lowered as theslope increases. Baroclinic instabilities tend to generate time-independent or mean currents in the upperand lower layers which, because of the slope, are markedly asymmetric across the gyre.

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J. E. Hart

Abstract

Baroclinic instability of a circular current is modified by the presence of a unidirectional bottom slope.An analytical theory is developed for the slightly unstable flow regime over a weak slope. The presence of theslope creates azimuthal sidebands n∓ to the basic azimuthal wavenumber n, of the instability. The interaction of the sidebands with the slope causes a decrease in the stability of the flow compared with that inthe case with a flat bottom. The interaction of the sidebands with the primary baroclinic wave produces atime-independent asymmetric current. In addition, the basic wave self-interaction produces a time-independent current which flows up the slope and generates asymmetric vorticity. This latter effect is predominant when the Rossby radius of deformation is much smaller than the radius of the basic current.

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J. E. Hart

Abstract

A simple, two-layer, quasi-geostrophic model is used to investigate the stability of baroclinic currents confined to a finite length scale L in a basin of considerably larger dimension (4L). The current distributions studied are typical of oceanic boundary currents and of certain oceanic and atmospheric eddies. The sharp shear zone which couples the relativity broad interior portion of the current to the resting ocean makes it possible for instabilities to arise which can get their energy either from the available potential energy of the tilted interface or from the basic zonal kinetic energy of the current. In a two-layer inviscid ocean of density contrast Δρ on an f-plane, and with a flat bottom, the two parameters governing the stability of a given current are the internal Froude number F=ρf 2 L 2(gΔρH)−1 and the layer depth ratio δ=H top/H bottom. The stability calculations show that these finite-width currents can be stable for intermediate values of F if δ is small enough. For moderate δ (0.2 to 1.0) the current distributions studied are unstable for all values F. The growth rates for the instabilities are given.

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Daniel J. Halperin
,
Andrew B. Penny
, and
Robert E. Hart

Abstract

Operational forecasting of tropical cyclone (TC) genesis has improved in recent years but still can be a challenge. Output from global numerical models continues to serve as a primary source of forecast guidance. Bulk verification statistics (e.g., critical success index) of TC genesis forecasts indicate that, overall, global models are increasingly able to predict TC genesis. However, as global model configurations are updated, TC genesis verification statistics will change. This study compares operational and retrospective forecasts from three configurations of NCEP’s Global Forecast System (GFS) to quantify the impact of model upgrades on TC genesis forecasts. First, bulk verification statistics from a homogeneous sample of model initialization cycles during the period 2013–14 are compared. Then, composites of select output fields are analyzed in an attempt to identify any key differences between hit and false alarm events. Bulk statistics indicate that TC genesis forecast performance decreased with the implementation of the 2015 version of the GFS, but then modestly recovered with the 2016 version of the model. In addition, the composite analysis suggests that false alarm forecasts in the 2015 version of the GFS may have been the result of inaccurately forecasting the location and/or strength of upper-level troughs poleward of the TC. There is also evidence of convective feedbacks occurring, such as ridging above the low-level circulation and upper-level convective outflow that were too strong, in this same set of false alarm forecasts. Overall, analyzing retrospective forecasts can assist forecasters in determining the strengths and weaknesses associated with a new configuration of a global model with respect to TC genesis.

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Daniel J. Halperin
,
Robert E. Hart
,
Henry E. Fuelberg
, and
Joshua H. Cossuth

Abstract

The National Hurricane Center (NHC) has stated that guidance on tropical cyclone (TC) genesis is an operational forecast improvement need, particularly since numerical weather prediction models produce TC-like features and operationally required forecast lead times recently have increased. Using previously defined criteria for TC genesis in global models, this study bias corrects TC genesis forecasts from global models using multiple logistic regression. The derived regression equations provide 48- and 120-h probabilistic genesis forecasts for each TC genesis event that occurs in the Environment Canada Global Environmental Multiscale Model (CMC), the NCEP Global Forecast System (GFS), and the Met Office's global model (UKMET). Results show select global model output variables are good discriminators between successful and unsuccessful TC genesis forecasts. Independent verification of the regression-based probabilistic genesis forecasts during 2014 and 2015 are presented. Brier scores and reliability diagrams indicate that the forecasts generally are well calibrated and can be used as guidance for NHC’s Tropical Weather Outlook product. The regression-based TC genesis forecasts are available in real time online.

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