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Brian H. Fiedler

Abstract

A one-dimensional numerical model KOLUM is introduced that demonstrates the use of continuous dynamic grid adaption in modeling the atmospheric boundary layer. The entrainment rates of KOLUM are compared against recent calibrations for smoke clouds and water clouds derived from large-eddy simulations. The simulations performed with KOLUM support the claim that turbulent kinetic energy–diagnostic length scale (El) models overpredict entrainment by smoke and water clouds, independent of the use of grid adaption. The benefits of grid adaption are slight. Curiously, the simulations did not confirm spurious entrainment of El models in episodes of subsidence.

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Brian H. Fiedler

Abstract

A three-dimensional, anelastic wind field on a staggered grid, with a specified normal wind component on the lateral boundaries, can be reversibly transformed into two scalar fields. In a conformal, terrain-following coordinate system these two quantities are closely related to the divergence of the horizontal wind and the vertical vorticity. The finite-difference implementation of the transform is emphasized. The exactness of the transform, and its consistency with the boundary conditions, are easily demonstrated when the transform is viewed as a problem of linear algebra in a discrete model.

The transform is shown to be useful in initializing a model wind field. A demonstration is provided with the removal of a spurious storm from the background wind field that is to be used in a forecast–analysis cycle. The divergence of the horizontal wind in the vicinity of the storm is removed. In the reconstructed wind field, the storm updraft is gone, and the adjusted horizontal velocity allows for the anelastic continuity equation to be satisfied. With integral constraints on the distribution of divergence satisfied, all boundary conditions on normal velocity are satisfied. The transform essentially provides an acoustic adjustment, preventing large-amplitude sound waves at initialization.

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Brian H. Fiedler

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No abstract available.

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Brian H. Fiedler

Abstract

An integral closure model is proposed for the vertical turbulent transport of a scalar in a mixed layer. The flux divergences at a given level is related to a vertical integral of a weighting function multiplied by the difference between the ensemble mean density of the scalar and the density at the level in question. The weighting function in the closure model is able to account for the anisotropy and inhomogeneity of mixed layer turbulence and so is able to model up-gradient diffusion of heat observed in the tank experiments of Deardorff et al. and the source-dependent flux-gradient relationship observed in numerical experiments of Wyngaard and Brost.

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Brian H. Fiedler

Abstract

No abstract available.

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Brian H. Fiedler

Abstract

The sufficient condition for inviscid, helical instability at large wavenumbers is applied to solutions for columnar vortices arising from the vortical flow of an end-wall boundary layer. The end-wall vortex arising from the laminar boundary layer under a potential vortex will be unstable at sufficiently high Reynolds number. However, if the end-wall boundary layer is turbulent, the end-wall vortex can be stable and laminar even at very high Reynolds number; therefore, stable, laminar tornadoes and waterspouts are suggested as theoretical possibilities.

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Brian H. Fiedler and Richard Rotunno

Abstract

We have developed a physical theory for the finding that the most intense laboratory vortex occurs when it is in the form of an end-wall vortex. We argue that the end-wall vortex allows no standing centrifugal waves (i.e., it is supercritical), and therefore, disturbances cannot propagate down from aloft. This allows the low central pressure of the end-wall vortex at the level of maximum azimuthal velocity to be balanced by a central axial jet which jet which accelerates from the lower end wall to this level. This supercritical, end-wall vortex undergoes a transition to a subcritical vortex aloft through a vortex breakdown. We construct a model for the maximum intensity of these vortices by developing a model for the end-wall vortex and by finding the criterion for a vortex breakdown to be in steady suspension above the lower end wall. The model agrees well with previous experimental simulations of tornado-like vortices in the Purdue tornado vortex chamber a steady end-wall vortex adjacent to the lower boundary can have a maximum azimuthal velocity approximately 1.7× the maximum azimuthal velocity in the subcritical vortex aloft.

We believe the model offers a way to reconcile the maximum observed tornado windspeeds with hydrostatic (subcritical) tornado models, which, by themselves, are inadequate to explain the highest windspeeds associated with tornadoes.

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Brian H. Fiedler and Chin-Hoh Moeng

Abstract

A closure scheme is developed for representing the mean vertical transport of a passive scalar within a convective boundary layer. The scheme predicts the evolution of the mean vertical profiles toward the form of the quasi-steady mean profiles observed in numerical large-eddy simulations of a convective boundary layer. The scheme models nonlocal transport and so is able to remedy several deficiencies of diffusive transport schemes.

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Qin Xu, Shouting Gao, and Brian H. Fiedler

Abstract

The previously developed two-layer model of cold air damming is extended to include upstream cold air inflow. The upper layer is an isentropic cross-mountain flow. The lower layer is a cold boundary layer flow partially blocked by a two-dimensional mountain with a cold dome formed on the windward side of the mountain. The interface represents a sloping inversion layer coupling the two layers. The shape of the interface can be approximated by a cubic polynomial, and the interfacial coupling condition yields a set of algebraic equations that quantify the scale and intensity of the dammed flow as functions of the external parameters characterizing the environmental conditions. It is found that the cold dome shrinks as the Froude number increases or, to a minor degree, as the Ekman number decreases or/and the upstream inflow veers from northeasterly to southeasterly (with respect to a longitudinal mountain to the west). The mountain-parallel jet speed increases as the Ekman number decreases or/and the upstream inflow veers from southeasterly to northeasterly or, to a minor degree, as the Froude number decreases. The theoretical results are qualitatively verified by numerical simulations with a full model and interpreted physically in comparison with the results of the previous two-layer model. It is also shown that our two-dimensional model may (or may not) be applied to a quasi-two-dimensional mountain ridge if the length scale of the ridge is (or is not) significantly larger than the Rossby radius of deformation multiplied by the inverse Froude number.

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Brian H. Fiedler and R. Jeffrey Trapp

Abstract

The continuous dynamic grid adaption (CDGA) technique is applied to a compressible, three-dimensional model of a rising thermal. The computational cost, per grid point per time step, of using CDGA instead of a fixed, uniform Cartesian grid is about 53% of the total cost of the model with CDGA. The use of general curvilinear coordinates contributes 11.7% to this total, calculating and moving the grid 6.1%, and continually updating the transformation relations 20.7%. Costs due to calculations that involve the gridpoint velocities (as well as some substantial unexplained costs) contribute the remaining 14.5%. A simple way to limit the cost of calculating the grid is presented. The grid is adapted by solving an elliptic equation for gridpoint coordinates on a coarse grid and then interpolating the full finite-difference grid. In our application, the additional costs per grid point of CDGA are shown to be easily offset by the savings resulting from the reduction in the required number of grid points. In the simulation of the thermal, we are able to reduce costs by a factor of 3, as compared with those of a companion model with a fixed, uniform Cartesian grid.

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