Inter-scale Energy Transfer in a Multi-scale Flow

Multi-scale generated turbulent flows are observed to possess some remarkable features, such as the rapid spreading of forest fires. Here, for simplicity, we consider the flow past a two-dimensional multi-scale arrangement of bars of various thicknesses in which wakes of different characteristic sizes and frequencies interact. We apply a novel multi-scale triple decomposition on the velocity field in order to distinguish between the mean flow, coherent fluctuations of various characteristic frequencies (associated with the various length scales present in the multi-scale array) and the residual/stochastic fluctuations. In this chapter we report on the observation of secondary coherent modes at the various wake intersection points, appearing at frequencies f(l) +/- f(m), where f(l) and f(m) are the fundamental shedding frequencies associated with the bars producing the intersecting wakes. We subsequently derive the multi-scale triple-decomposed energy budgets to reveal the source term for these secondary coherent modes. Consideration of these energy budgets reveals an inverse cascade mechanism by which energy is transferred from the higher frequency of the two interacting fundamental coherent motions to the lower frequency secondary coherent mode under the catalytic action of the lower frequency fundamental mode.