Uncertainty Analysis on a Few Fluid Models

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WangDMS-0606671 The investigator and colleagues study the impact of usingsimplified models as well as the effect of noise on uncertaintypropagation in terms of statistical solutions in several fluidsystems. The physical problems under investigation are largePrandtl number or small Ekman number regimes in Rayleigh-Benardconvection, large Prandtl-Darcy number or small Darcy numberregimes in convection in fluid saturated porous media, andstochastically forced quasi-geostrophic systems with randomnoise. Model reduction in the parameter regimes for theconvection problems leads to singular limit problems involvingmultiple time and spatial scales. One of the goals here is toinvestigate what kind of statistical properties can beapproximated using the statistical properties of the simplifiedmodels derived via singular limits. In the case of systems withrandom noise, which are modeled by stochastic partialdifferential equations, the investigator and his colleaguesinvestigate possible noise-induced statistical stabilities, i.e.,stability of statistical properties with respect to initialcondition and parameters. There are abundant uncertainties in nature. For instance,prediction of the path of a hurricane is influenced by(imperfect) information about the initial distribution ofatmospheric and sea surface temperatures, wind, and theatmospheric jet stream, as well as by the imperfect model itself. The climate (long-time behavior) of the earth may be influencedby the ozone layer, concentrations of carbon dioxide, and otherfactors. Transport of contaminants in ground water is influencedby porosity and permeability of the media, which are random. Studying the influence of various uncertainties on thegeophysical flows considered here helps us better understand thebehavior of the flows.