Variational Methods in the pursuit of an Action Principle in Fluid
Malkus (1954a,b). ``Of all the possible solutions, the one which is selected is that which has the largest heat transport''. Malkus & Veronis (1958) ...
Variational Methods in the pursuit of an Action Principle in Fluid Turbulence Rich Kerswell Mathematics Bristol University
• Malkus’ original idea – Maximum Entropy Production • Variational Techniques a) Euler-Lagrange (Howard-Busse) b) Background approach (Doering-Constantin) • “Efficiency” functional
Rayleigh-Benard convection
Malkus (1954a,b) ``Of all the possible solutions, the one which is selected is that which has the largest heat transport’’
Malkus & Veronis (1958)
Extend competition to non-solutions - Howard (1963)
Busse 1970
Plasting & K 2003
Summary Variational methods are a valuable tool
• Extract (inequality) scaling laws e.g. wall-bounded shear flows e ~ O(1) as n Boussinesq convection
0
1/2
Nu ~ Ra
• Test hypotheses (a) effect of extra constraints… (b) look for an Action functional - Efficiency is promising but unsubstantiated Key omissions are Stability constraints…
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