Statistical physics-informed turbulence:
Navier-Stokes equations have been long used to theorise turbulence; most likely because of the pedestal these equations have got. However, at sub-Kolmogorov scales, the intrinsic effects due to molecules can also get important; which transforms the deterministic nature of fluids to fluctuating, stochastic nature. The additional term in NS is the fluctuating stress, which is prescribed by a Gaussian random field and its variance given by a fluctuating-dissipation relation. While the precise mathematical meaning of equations upon inclusion of fluctuating stress is not clear, one trick, used by statistical physicists, to use an effective, low-wavenumber field theory and truncate terms at certain wavenumber cutoff Λ is often used. Such cutoff converts fluctating NS equations into well-defined stochastic ODEs for finite Fourier modes. Now, traditional turbulence theory (K41) needs to be updated. Apart from viscosity and mean dissipation rate, thermal energy kT and length-scale of flow L becomes important. The relation
describes the choice of cutoff Λ that exists between gradient length of fluid l_Δ (below which velocity field is smooth) and mean-free-path λ_micr. A recent paper [1] has used this effective field theory to argue that thermal fluctuations are relevant at Kolmogorov scales and hydrodynamic equations are not valid at such scales; fluctuating NS equations need to be envisaged. However, current experimental techniques are not enough to venture into sub-Kolmogorov scales; new techniques need to be envisaged.
For the von-Karman turbulent flow, Kolmogorov scale η varies as [2]
which is 0.4 mm for 10 cm of the length of setup at Re=6000. The best PIV setup can not go below 0.5 mm in resolution; hence, a new imaging system for below-millimetre resolution is required to compare experiment results of dissipation range with the fluctuating NS theory.
SMCL 