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B. L. Sawford

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B. L. Sawford

Abstract

Lagrangian statistical (Monte Carlo) simulations of the mean and fluctuating concentration fields due to turbulent dispersion are critically reviewed. Attention has been restricted to work in which particle trajectories are modeled directly, which in effect means simulations based on the Langevin equation (or in finite difference form, Markov-chains) and its generalization. The material covered has been selected and presented so as to achieve an orderly progression from simple to more complex turbulent flows. At present this field involves many heuristic modeling assumptions and an attempt is made to justify some of these by appeal to special and limiting cases.

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B. L. Sawford and F. M. Guest

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A generalized Langevin model is used to conduct Lagrangian statistical simulations of turbulent dispersion in a shear-free convective boundary layer. This model more nearly realizes a well-mixed steady state than previous models. It is, therefore, less influenced by spurious concentration gradients and so is more appropriate for the analysis of flux-gradient relationships.

For instantaneous area sources mean concentration predictions compare very favorably with convection tank data and with other modeling attempts. Diffusivities calculated for a near-surface source also agree very well with convection tank data and show substantial regions of countergradient flux. Calculations for other source heights also show regions of countergradient flux and confirm that the diffusivity is a strong function of source height.

For continuous area sources model predictions are in excellent agreement with the results of large-eddy simulations. They show that there is a strong asymmetry between “top-down” and “bottom-up” dispersion processes and that the bottom-up process has a substantial region of countergradient flux in the upper half of the boundary layer.

Calculations of the third-order moment w2c throw doubt on the validity of the flux-gradient relation used to parameterize this quantity in second-order modeling.

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P. C. Manins and B. L. Sawford

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A new model of katabatic winds is presented. A hydraulic approach is employed in which the detailed vertical structure of the flow is replaced by a quiescent stably stratified environment and an equivalent flowing layer which is subject to sustained layer cooling, surface stress and interfacial entrainment. A scaling which contains most of the parametric behavior is found. It shows that interfacial entrainment is the dominating retardation mechanism of the flow and that surface stress may be relatively unimportant.

Steady solutions are presented to show that katabatic winds are essentially supercritical on all practical slopes (slope angles >0.1°), and are affected by ambient stratification only at large distances. The model is in satisfactory quantitative agreement with the limited field data available.

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J. S. Frederiksen and B. L. Sawford

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The effects of topography in forcing the stationary eddy flow field of the atmosphere have been examined using the spherical equivalent barotropic model. Fully nonlinear solutions obtained using the methods of equilibrium statistical mechanics have been compared and contrasted with linearized steady-state solutions, and both of these have been compared with observed flows.

Incorporation of nonlinear effects eliminates the resonant behavior characteristic of the linear solutions and thus leads to wide differences between the two types of solutions. Whereas the linear solutions are strongly dependent on the strength of the zonal flow, the qualitative appearance of the nonlinear eddy fields is remarkably constant over a wide variation of the relevant parameters and is essentially a filtered version of the topographic field. The nonlinear fields also show no evidence of the wavetrains which are such a striking feature of the linear fields.

Comparison with observed fields shows nonlinear effects to be most important at low altitudes. The nonlinear stationary flow field at 850 mb gives as realistic a representation of the qualitative observed features as can be produced by much more complicated models, whereas the linear field shows far too much structure. At high levels, where the zonal flow is stronger, the linear approximation (including drag) is better than at low levels.

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J. S. Frederiksen and B. L. Sawford

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We derive the statistical mechanical equilibrium properties of two-dimensional flow on a sphere, described by the truncated inviscid nondivergent barotrapic model. It is found that probability distribution functions and expectation values are considerably different from those on a rotating beta-plane. The approach of numerical simulations to equilibrium is established by integrations for 208 days starting with observed meteorological global fields. It is found that the smaller scales of the observed initial field with a rhomboidal truncation wavenumber of 15 are indistinguishable from those of a realization of the equilibrium ensemble, while by days 70–80 this applies to all scales including the slowly changing zonal flow contributions. The effects of changing the resolution in the numerical simulations are examined and it is shown that the growth of differences between high-and low-resolution integrations may also be explained in terms of the nonuniforin relaxation of different scales to equilibrium. We find that differences between such simulations started with identical fields are under-estimated for the first few days, compared with using increased initial resolution in the high-resolution integration, while subsequently differences at the larger scales tend to be overestimated as the smaller scales equilibrate. For a given number of degrees of freedom, the equilibrium spectra are found to be relatively insensitive to the truncation scheme used and we propose the use of a more efficient parauelogrammic truncation scheme for numerical spectral models.

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