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  • Author or Editor: Branko Grisogono x
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Branko Grisogono

Abstract

A simple parameterization of turbulence in an analytical study of wave drag (WD) is used upon governing equations for linearized, parallel, adiabatic, dry Boussinesq flow. Besides the known dependencies of WD on vertical profiles of the mean wind and temperature and the shape of orographic disturbance, WD also depends on eddy diffusivity, which parameterizes turbulence. Since eddy diffusivity is present, WD is not constant with height but is continuously dissipated in the atmospheric boundary layer (ABL). This dissipation is sometimes not negligible because characteristic wavelengths associated with an ABL over small ridges are short enough (λ x ∼ 1 km) to experience overall turbulence. Under certain conditions and when no critical level is encountered (although critical level might be approached asymptotically here), WD can be reduced for roughly 15%–20% of its surface value. Hence, it is revealed that dissipation of WD can support turbulence in the stable ABL.

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Michael Tjernström
and
Branko Grisogono

Abstract

Fully 3D nonlinear model simulations for supercritical flow along locations at the California coast, at Cape Mendocino, and Point Sur, are presented. The model results are objectively and subjectively verified against measurements from the Coastal Waves 1996 experiment with good results. They are then analyzed in terms of the flow structure, the impact of the local terrain, the atmospheric forcing on the ocean surface, and the momentum budgets. It is verified that the flow is supercritical (Fr > 1) within a Rossby radius of deformation from the coast and that it can be treated as a reduced-gravity, shallow water flow bounded by a sidewall—the coastal mountain barrier. As the supercritical flow impinges on irregularities in the coastline orientation, expansion fans and hydraulic jumps appear. The modeled Froude number summarizes well the current understanding of the dynamics of these events. In contrast to inviscid, irrotational hydraulic flow, the expansion fans appear as curved lines of equal PBL depth and “lens-shaped” maxima in wind speed residing at the PBL slope. This is a consequence of the realistic treatment of turbulent friction. Modeled mean PBL vertical winds in the hydraulic features range ±∼1–2 cm s−1, while larger vertical winds (±∼5–10 cm s−1) are due to the flow impinging directly on the mountain barrier. Local terrain features at points or capes perturb the local flow significantly from the idealized case by emitting buoyancy waves. The momentum budget along straight portions of the coast reveals a semigeostrophic balance modified by surface friction. While being geostrophic in the across-coast direction, the along-coast momentum shows a balance between the pressure gradient force and the turbulent friction. In the expansion fans, the flow is ageostrophic, and the imbalance is distributed between turbulent friction and ageostrophic acceleration according to the magnitude of the former. There is also a good correspondence between the magnitude of the local curl of the surface stress vector and the measured depression in sea surface temperature (SST) in areas where the latter is large and the along-coast flow is relatively weak, implying that a substantial portion of the upwelling is driven locally. Supplying the measured SST in the numerical simulations, with a considerable depression along the coast, had only marginal feedback effects on the character of the flow.

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Branko Grisogono
and
Johannes Oerlemans

Abstract

A simple form of the Prandtl model addressing pure katabatic flows is solved. The new analytic solution is valid for almost any assigned eddy diffusivity K(z) and constant Prandtl number. This model assumes a one-dimensional steady state for momentum and heat balance. Its approximate solution, obtained using the WKB method, appears as a generalization and improvement of the classic analytic solution for the constant-K case. It is compared favorably against a numerical solution. A comparison with observations from PASTEX, Austria 1994, shows that the new solution is much closer to the data than the constant-K solution. The dynamics revealed with this new solution is discussed (relatively sharper near-surface profiles, their gradients, and the low-level jet), and a suggestion toward improving boundary layer parameterizations is offered.

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Thorsten Mauritsen
,
Gunilla Svensson
,
Sergej S. Zilitinkevich
,
Igor Esau
,
Leif Enger
, and
Branko Grisogono

Abstract

This paper presents a turbulence closure for neutral and stratified atmospheric conditions. The closure is based on the concept of the total turbulent energy. The total turbulent energy is the sum of the turbulent kinetic energy and turbulent potential energy, which is proportional to the potential temperature variance. The closure uses recent observational findings to take into account the mean flow stability. These observations indicate that turbulent transfer of heat and momentum behaves differently under very stable stratification. Whereas the turbulent heat flux tends toward zero beyond a certain stability limit, the turbulent stress stays finite. The suggested scheme avoids the problem of self-correlation. The latter is an improvement over the widely used Monin–Obukhov-based closures. Numerous large-eddy simulations, including a wide range of neutral and stably stratified cases, are used to estimate likely values of two free constants. In a benchmark case the new turbulence closure performs indistinguishably from independent large-eddy simulations.

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