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Douglas B. Boudra

Abstract

Development of a framework for study of the Great Lakes' effects on late fall-early winter cyclones andArctic air masses has been initiated. The central theoretical component is a three-dimensional numericalprimitive equations model. The 40-45 km horizontal grid point spacing provides for resolution of the shapeand dimension of each lake, and 15 levels in the vertical resolve interaction of boundary layer and midtropospheric processes. Over land, locally computed vertical diffusion coefficients depending on static stabilityand Richardson number are used to parameterize subgrid-scale turbulent processes throughout the depthof the atmosphere. At over-lake grid points, the Businger et al. (1971) formulation of the Monin-Obukhov(1954) similarity equations is used in the constant flux layer, and the combined O'Brien (1971) K profileand Deardorff (1974) boundary layer depth prediction equation are used for turbulence parameterizationin the rest of the boundary layer. The prognostic variables, pressure, u, v, and water vapor mixing ratio,are unstaggered on the Cartesian finite difference grid. Horizontal differencing operators are fourth-orderaccurate and the vertical operators are of second-order accuracy formulated for an uneven grid. The equationsare cast over a limited area 50 x 40 x 15 grid points, and the Perkey-Kreitzberg (1976) method isincorporated for the variable tendencies near the lateral boundaries. A real data case exhibiting vigorouscyclone development and subsequent strong cold air advection over the lake region is chosen for simulation.The dynamic variables are analyzed with the optimum iaterpolation scheme on isentropic surfaces developedby Bleck (1975) and are interpolated to the model grid matrix. Likewise, the moisture field is analyzedusing a scheme described by Perkey (1976). The model is initialized with the first of four analyses atconsecutive radiosonde observation times. The remaining three analyses are used in the lateral boundaryregions for the eternally specified tendencies during a 36 h simulation.

The remaining components of the study consist of several forms of observation taken during the periodof the simulation: 1) the objective analyses of radiosonde data at 12 h intervals, 2) surface analysis on theNorth American synoptic chart, 3) the hourly precipitation data network in the United States, 4) radarsummaries and 5) satellite imagery. The operational forecast generated on the LFM2 model by the NationalMeteorological Center is used as an additional point of reference. It is found that the LFM2 forecast, whichignores the Great Lakes, predicts the cyclone motion realistically, but makes considerable error otherwise.Agreement between the very fine scale simulations and observation is generally much better and encouragesdevelopment of diagnostic methods for a rigorous comparison of the observed and simulated lake effects.

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Rainer Bleck
and
Douglas B. Boudra

Abstract

An ocean circulation model, developed for the study of mesoscale to gyre-scale circulation and heat transport, is described and tested. The model employs density as vertical coordinate except in the immediate vicinity of possible coordinate surface intersections with the ocean surface. Test simulations are carried out for a double-gyre ocean basin of the type used by Holland (1978), but with better resolution in the upper 1000 m of the model ocean. The final state of a 5-year coarse-mesh (50 km resolution on a 2400 km × 1200 km domain) spin-up is used as the initial state for mesoscale experimentation on a 25 km mesh. Basin energetics, as well as mean mass transport streamfunction and mean potential vorticity fields are given for three mesoscale experiments, in which the magnitude and formulation of lateral dissipation are varied. Each of these experiments, run for approximately five years, exhibits vigorous mesoscale activity associated with western boundary current separation and the free jet. The mean gyre patterns and exchange of potential vorticity between the northern and southern gyres are considerably less symmetric with respect to the wind forcing pattern than those shown in Holland and Lin (1975b, case 10) and Holland (1978). The asymmetry results from a pronounced southward shift of the separation point of the free jet relative to the position of maximum wind stress, and from the tendency of the jet to form strong quasi-steady meanders in the western part of the basin. A reason for the difference between these results and those mentioned above is suggested, and the proposed experimentation to determine its validity is outlined.

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Douglas B. Boudra
and
Eric P. Chassignet

Abstract

The Agulhas retroflection region of the wind-driven idealized South Atlantic–Indian Ocean model described by DeRuijter and Boudra is analyzed in detail. Here, in Part I, the physical mechanisms of the model retroflection are elucidated through illustration of Agulhas' vorticity balance among various experiments. In Part II, the ring formation process is described in terms of its vertical structure and the associated energy conversions.

A one-layer model demonstration shows that both inertia and internal friction may account for a partial retroflection where a linear, weakly viscous system has none. In the nonlinear, weakly viscous one-layer model, the retroflection is accomplished through a free inertial boundary layer, as suggested originally by De Ruijter. When stratification is introduced and baroclinicity increased, using the Bleck and Boudra quasi-isopycnic coordinate model with 2 or 3 layers, the stretching term exerts an increasing influence. With 40-km resolution, terms included so that the numerical model conserves potential vorticity become important as well. Both encourage retroflection of the fluid separating from Africa's trip. When grid spacing is halved, the importance of the extra conserving terms diminishes and the stretching term exerts an even greater influence. The importance of a substantial viscous stress curl along the coast of Africa, as provided by the no-slip condition, is illustrated through comparison with a slippery Africa experiment.

Finally, an experiment with a more realistic South Africa coastal geometry, giving a more realistic order of importance to βv in the separating Agulhas, is described. It is shown that the retroflection is still strong but that the associated recirculation is less intense. An interesting new aspect of the retroflection is the separation of the mean current core from the coast a few hundred kilometers upstream from the tip. The planetary vorticity advection term plays a smaller role along the coast. Viscous effects on the coastal side of the current are still strong, however, and are balanced primarily by stretching and relative vorticity advection. As the mean current passes Africa's tip, the sink of positive vorticity produced in the stretching and planetary vorticity advection terms is left behind, and the Agulhas turns eastward. These results support the notion, advanced by De Ruijter and Boudra, that the change in the vorticity balance at separation leads to the model retroflection, and they point to the increasing importance of the divergent component of flow in the vorticity balance as more realism is introduced.

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Eric P. Chassignet
and
Douglas B. Boudra

Abstract

An energetics analysis of several numerical experiments on an idealized South Atlantic-Indian Ocean basin is presented. The model used in the experiments is the quasi-isopycnic coordinate model of Bleck and Boundra forced by wind and configured with two or three layers. The region of focus is the most dynamically active one, the Agulhas Current retroflection south of Africa, and the dynamical mechanisms associated with formation of Agulhas rings are given special attention.

Whether rings form in the model and their frequency depend on two primary factors: the shape of Africa and southward inertia/baroclinicity in the overshooting Agulhas. The boundary condition on Africa (no-slip/free-slip) and horizontal resolution are also important. Experiments in which rings form exhibit considerably larger values of K M to K E transfer than those in which no rings form. In three of the experiments, ring formation is studied in detail with the help of instantaneous top and bottom layer flow patterns and time series energetics. In a low Rossby number experiment with a rectangular Africa, rings are formed almost continuously, and basin mode resonance plays a significant role in ring formation. Whether a form of instability (barotropic or baroclinic) play an important role as well is unclear. In two high Rossby number experiments, one with rectangular and the other with triangular African geometry, basin mode resonance is not a factor, and, it is suggested that ring formation is associated with release of mixed barotropic-baroclinic instability.

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