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Asymptotics of averaged turbulent transfer in canopy flows. (English) Zbl 1398.76063

Summary: We formulate and analyse a long-time asymptotic model of dispersion in turbulent canopy flows, of an urban or industrial nature. The model is formulated in terms of the concentration averaged across the flow, for example over river depth. The general approach that laid a firm foundation for the averaging procedure was proposed by Roberts and co-authors in the late 1980s. We derive an evolution partial differential equation for the averaged concentration, involving first, second and higher derivatives with respect to spatial coordinates. The coefficients of the equation are derived and analysed against the parameters characterising the turbulent flow. In particular, we show that, in the limit of large flow depths, the values of the coefficients coincide with those obtained earlier for the flow over a smooth bottom.

MSC:

76F20 Dynamical systems approach to turbulence
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