Dr. Evelyn Lunasin, US Naval Academy
Location
Mathematics/Psychology : 401
Date & Time
March 7, 2014, 12:00 pm – 1:00 pm
Description
Title: Optimal mixing and optimal stirring for fixed energy, fixed power, and fixed palenstrophy flows
We focus on the optimal stirring strategy recently proposed by Lin,Thiffeault and Doering (2011). We then show an explicit example demonstrating finite-time perfect mixing with a finite energy constraint on the stirring flow. On the other hand, if the two-dimensional incompressible flow is constrained to have a particular smoothness property finite-time perfect mixing is ruled out. We discuss some recent results for the case of finite power constraints and discuss related problems from other areas of analysis.
Abstract: The advection of a substance by an incompressible flow is important in many physical settings. This process often involves complex evolving structures of wide range of space and time scales. We concentrate on the case of scalar advection where the transported quantity is passive, so has negligible feedback on the flow. We address the following question: Given an initial tracer distribution what incompressible flow field, satisfying certain reasonable amplitude constraints, should be imposed that will stir the scalar quantity in an optimal manner.
We will discuss how one can quantify the degree of “mixedness” of the passive scalar field, what we mean by optimal stirring and what is the quantity that needs to be optimized in the stirring process. We will also discuss the relevant constraints on the flows.We focus on the optimal stirring strategy recently proposed by Lin,Thiffeault and Doering (2011). We then show an explicit example demonstrating finite-time perfect mixing with a finite energy constraint on the stirring flow. On the other hand, if the two-dimensional incompressible flow is constrained to have a particular smoothness property finite-time perfect mixing is ruled out. We discuss some recent results for the case of finite power constraints and discuss related problems from other areas of analysis.
Room: MP 401
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