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High-fidelity simulations of wave breaking processesare performed with a focus on the small-scale structures of breaking waves, such as bubble/droplet size distributions. Very large grids (up to 12 billion grid points) are used in order to resolve the bubbles/droplets in breaking waves at the scale of hundreds of micrometres. Wave breaking processes and spanwise three-dimensional interface structures are identified. It is speculated that the Görtler type centrifugal instability is likely more relevant to the plunging wave breaking instabilities. Detailed air entrainment and spray formation processes are shown. The bubble size distribution shows power-law scaling with two different slopes which are separated by the Hinze scale. The droplet size distribution also shows power-law scaling. The computational results compare well with the available experimental and computational data in the literature. Computational difficulties and challenges for large grid simulations are addressed.
The presidential election of 1952 offered a unique opportunity for the study of the effect of television upon voting behavior. By happy accident—the FCC freeze on the construction of new television stations—it was possible to find areas of the United States where there were counties within television reception range and also counties otherwise similar to these with respect to their past voting behavior, but outside the reception area. In these areas the presence or absence of television can be regarded, with reasonable safety, as a genuine independent variable; and if television influenced voting behavior, there is some hope of detecting its effects.
The uniqueness of the situation and its utility for testing hypotheses about the effects of television deserve some comment. Ordinarily, one is confronted in ecological studies with an insurmountable confusion of cause and effect. For example, had there not been an “artificial” restriction on the extension of the television network in 1952, we would not be safe in regarding a county without television as comparable with a county having television. For in that case, absence of television would imply remoteness from centers of population of any size, and we could not assume that influences upon voting behavior in such remote counties would be the same as in counties closer to population centers.
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