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Inner-outer interaction in turbulent wall layers

Thursday 11th September 2008 - 17:10 to 17:30
INI Seminar Room 1
Session Chair: 
B Sawford
A physical, but non-taxonomical, description of wall turbulence is presented. The requirements of self-similarity are discussed and, in particular, the effects of inner-outer interaction are explored. This interaction may be described as "bottom-up" (e.g. surface roughness) or "top-down" (e.g. high Reynolds number) and the consequences of each are discussed. It is shown that, while a weak interaction is, in fact, a statement of Townsend's ideas of ‘inactive’ motion, it is only a linear first approximation of a nonlinear process, which occurs primarily through the wall-normal component of velocity and the static pressure. It is shown that the interaction leads to a lack of similarity in terms of the structure and the second-order statistics. Using observations from a discrete wavelet analysis, a heuristic model of wall turbulence is described in which it is shown that the motion is driven by pressure-gradient fluctuations arising from the dominance of quasi-streamwise vortices. For linear control, the need for model reduction therefore suggests transient growth. Early results from measurements of roughness-induced transient growth in a Blasius base flow are described: issues concerning receptivity (to the initial disturbance) and observability are discussed. Some results from associated control experiments and simulations involving surface deformation are also presented.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons