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SUMMARY:Plenary Lecture 3: Free Boundaries and Fluid Mixing at the Micro L
 evel - Glimm\, J (Stony Brook University)
DTSTART:20140623T123000Z
DTEND:20140623T131500Z
UID:TALK53080@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Turbulent mixing often occurs with immiscible fluids or with m
 iscible fluids over rapid time scales\, so that the flow is locally inhomo
 geneous at a micro level for periods of interest. We start with a review o
 f problems in which such flows arise.\n\nThe flow regions in which the mix
 ing occurs can generally be identified reliably\; examples will be given. 
 The challenge for current research is to describe the microscopic and inho
 mogeneous mixture in a statistical sense.\n\nFull resolution of the flows 
 is generally out of the question and will remain so for decades. Thus we a
 re interested in statistical properties of the flow that are stable and ap
 pear to converge under mesh refinement\, with sufficient detail in the sta
 tistical description (for example a pdf or cdf (cumulative distribution fu
 nction) to support reaction processes in flows of engineering interest. A 
 first step\, generally insufficient\, is to compute means and variances of
  fluctuating processes.\n\nThis goal is still in the future. Partial resul
 ts leading in this direction will be presented. We formulate a notion of s
 tochastic convergence and present numerical algorithms which appear to be 
 convergent in this metric. We introduce theoretical ideas related to conve
 rgence based on the renormalization group\, including the important notion
  that the solution\, at the LES level of resolution of necessity considere
 d here\, is not unique. In other words\, the usual standard of convergence
  under mesh refinement is not sufficient to guarantee a simulation in agre
 ement with experimental data. We discuss methods to mitigate this serious 
 obstacle to scientific progress. Basically\, experiments are essential to 
 select the correct non-unique solution and the algorithm and its adjustabl
 e parameters to reach this goal. While flows of interest are commonly at h
 igh Reynolds numbers outside the regime of relevant experiments\, the expa
 nsion parameter is 1/Reynolds number. In terms of this parameter\, the per
 turbation from experiment to applications is small\, within normally accep
 ted ranges for perturbative extensions of validation regimes. "cambridge.1
 4.abs" 37L\, 2201C\n
LOCATION:Seminar Room 1\, Newton Institute
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