Question

If ν is the kinematic viscosity and ε is the rate of dissipation of turbulent energy, to which of these terms is the spectral energy of Kolmogorov micro-scale eddies proportional to?

(a) ν^5/3 ε^1/3

(b) ν^3/2 ε^1/2

(c) ν^1/2 ε^3/2

(d) ν^5/4 ε^1/4

This question was posed to me in an interview for job.

The origin of the question is Turbulence Modelling topic in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Right answer is (d) ν^5/4 ε^1/4

To elaborate: Kolmogorov argued that the behaviour of the smallest turbulent eddies depends on the rate of dissipation of turbulent energy. But, later studies revealed that only the spectral energy of the smallest turbulent eddies depends on the rate of dissipation of turbulent energy and the relationship is given by

spectral energy ∝ ν^5/4 ε^1/4.