Mixing in thermal convection

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Phenomenology of RT turbulenceEnergy balance:turbulent kinetic energy E=(1/2) produced frompotential energy P=-βg dEdt = β g wT− ε = − dPdt − εε = ν (∇u) 2Dimensional balance:2durmsdt β gθ0urmsthereforeLarge scale velocity fluctuations grow as u rms (t)≈AgtTurbulent mizing layer of width h(t) grows as h(t) ≈ Agt 2Kinetic energy in pumped in the system at a rateε u2τ u3h (Ag)2 t-> time evolving turbulence
Fermi’s model (Fermi and von Neumann, ‘50)Potential U and kinetic K energy variationfor generating two rectangular plumesU = ρ 2 − ρ 12L 2 ga 2K = ρ 2 + ρ 12L 2 a 2 aLagrange equationsddt∂K∂ a − ∂K∂a= −r∂U∂a(r=fraction of potentialenergy converted intolarge scale energy)gives aa + 1 a 2 = 12 4 rAgaand therefore, for the width of themixing layer h(t)=2a(t)h(t) = h 0+ (r / 2)Agh 0t + (r / 8)Agt 2 asquare plume
Page 2: Rayleigh-Taylor turbulence: a toy m
Page 9: Equation of motion and setupSingle
Page 14: Numerical simulationsNumerical inte
Page 19 and 20: Evolution of the mixing layert=1.4t
Page 22 and 23: From geometrical to dynamical quant
Page 24 and 25: Effects of polymers onthermal conve
Page 26 and 27: Viscoelastic RT turbulenceFluid mod
Page 28 and 29: Acceleration of the growthof mixing
Page 30 and 31: Heat transfer enhancementNu is larg
Page 32: ConclusionsRayleigh-Taylor turbulen

Mixing in thermal convection

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