Top-hat Distribution Research Articles

A First-Order Closure for Covariances and Fluxes of Reactive Species in the Convective Boundary Layer

Abstract Covariances and fluxes of reactive species in the clear convective atmospheric boundary layer (CABL) are studied and parameterized. The covariances result from correlations between reactive species. These covariances may have a considerable influence on the modeled reaction rates in atmospheric chemistry models, but usually are neglected. To facilitate the representation of covariance effects in large-scale atmospheric chemistry models, the authors have developed a new first-order closure for covariances. The closure is based on top-hat distributions, as is common in mass-flux schemes. In addition, the authors utilize an existing nonlocal first-order closure expression for the flux, which represents the combined effects of gradient mixing and nonlocal convective mixing. The authors show how the latter also includes the impact of chemistry on the nonlocal flux contribution. The impact of the closures is illustrated first for artificial, simple chemistry cases. The results are evaluated using large...

Two-dimensional Z scan for arbitrary beam shape and sample thickness

A two-dimensional Z-scan technique has been developed using a two-dimensional charge-coupled device (CCD) detector to study the nonlinear optical properties and beam profile evolution within optical limiting devices. Using the split step beam propagation method, the far field pattern at each Z position can be calculated precisely for any arbitrary beam shape and sample thickness. A two-dimensional far field pattern is recorded by the CCD detector, and the evolution of the beam distribution inside the nonlinear optical medium can be obtained directly. This technique has been applied to study the nonlinear optical parameters and laser beam profiles in nonlinear liquids. We have used thin and thick samples and Gaussian, top-hat and split Gaussian beam distributions, and the experimental results agreed very well with the calculation. This technique also offers a simple and accurate means for optimizing the design of optical limiting devices.

A first order mixing–condensation scheme for nocturnal stratocumulus

A simple closure scheme for nocturnal stratocumulus is proposed. The scheme is formulated in conserved variables. Cloud fraction and cloud water amount are diagnosed assuming a top-hat distribution for total water. Conversion of cloud water into rain water is parameterized in terms of cloud water and the incoming rain flux. Turbulence transport in the cloud layer is accounted for by a first-order vertical diffusion scheme with a profile-type diffusivity. The length scale corresponds to the thickness of the cloud layer. The turbulent velocity scale is directly related to the long wave radiative flux divergence in the cloud. Entrainment at cloud top is implicitly treated by extending the in-cloud mixing profile slightly beyond cloud top. The excess height is derived from the buoyancy frequency at cloud top and a radiative–convective velocity scale. The scheme is capable of simulating realistic profiles of the conserved variables and cloud parameters for a case of nocturnal stratocumulus prepared on the basis of ASTEX data.

A study of the effect of multiple reflections on the shape of the keyhole in the laser processing of materials

In the deep penetration laser welding of materials as well as in other laser material processing it is usual for the laser to generate a keyhole in the material. One of the principal mechanisms of energy absorption in the keyhole is the Fresnel absorption process on the keyhole wall. In order to take account of the Fresnel absorption process properly it is necessary to include the effect of multiple reflections in the keyhole. With this end in view an axisymmetrical numerical model is presented in which the keyhole geometry is not fixed at the outset, but instead the keyhole wall is considered to be a free boundary whose shape changes after each iteration in the numerical process. In this connection each complete set of reflections constitutes a step in the iteration process. Convergence is reached for a reasonably wide set of initial geometries and discretization steps. The model is used to analyse keyhole profiles and intensity distributions with depth for the cases of a Gaussian and of a uniform top-hat distribution in the laser beam. The model allows the effect of inverse bremsstrahlung absorption in the keyhole to be taken into account, this being the other principal mechanism for the absorption of laser light in the keyhole.

Fluid modeling of dense gas dispersion over a ramp

The basic nature of the transport and dispersion of a dense gas plume in the simulated neutral atmospheric boundary layer of a wind tunnel was investigated, both in flat terrain and over a ramp. Measurements were made of the concentration fields downstream of a ground-level, circular source; these measurements consisted of longitudinal ground-level, vertical, and crosswind profiles at various distances downwind. Both neutrally buoyant (air) and negatively buoyant (CO 2) source gases were used so that the specific effects of the density difference could be observed. Similarly, measurements were made in both flat terrain and over the ramp (14° slope followed by an elevated plateau) so that specific effects of the terrain could be observed. Flow visualization was done to ascertain that the dense plume was turbulent, hence, that the effects of molecular properties were insignificant. For the particular value of the buoyancy parameter used in these experiments, the plume buoyancy was significant; the resulting dense plume was significantly wider in the lateral direction and much narrower in the vertical direction, yet the longitudinal ground-level concentration profile downwind was essentially identical to that from the neutral plume. The lateral concentration profiles of the neutral plumes were essentially Gaussian in character, whereas the dense gas plumes exhibited top-hat distributions for considerable distances from the source. The vertical concentration profiles of the neutral plumes were not Gaussian, but displayed variations of the form C/ C mx = exp (− Az n ) with n ⋍ 1.5. On the other hand, the dense gas plumes displayed vertical variations of the form C/ C mx = exp [− z/ z ], where z is the centroid of the distribution. The net effect of the ramp on the dense gas plume was a small reduction in ground-level concentration (less than a factor of two, even for a source relatively close to the base of the ramp). This reduction was quite similar to that observed for the neutral plume.

An evaluation of several numerical advection schemes

Three categories of numerical advection techniques are tested: SHASTA, a flux-corrected onedimensional algorithm; FCT, a multi-dimensional flux-corrected technique; and the BIQUINTIC method, a polynomial approximation algorithm. The tests include the transport of a finite amount of material through a 25 × 25 cell grid driven by three different flow fields: one-dimensional linear flow, two-dimensional linear flow, and rotational flow. For each of these tests, two initial distributions of material are used: a rectangular blockshape and an ellipse-shape. In addition, a test with a non-divergent flow field with a homogeneous material field was performed to check for inherent divergence in a particular method. Results show that the FCT and BIQUINTIC methods maintain the integrity of an initial distribution of material better than SHASTA through a simulation. While SHASTA is the fastest of the methods tested computationally it also produces the greatest amount of spurious numerical diffusion. The FCT method has a tendency to flatten the top of a peaked distribution, and the BIQUINTIC method tends to produce a peak in a top-hat distribution during numerical transport. The BIQUINTIC scheme requires more computer time to execute than the other methods tested.