It is well-known that laminar and turbulent flows are governed by mass, momentum, and energy equations along with considering species in case of combustion. The governing equations (also called Navier-Stokes equations) can be solved analytically for only a few cases for laminar flow at certain conditions.
However, turbulent flow and combustion are difficult to handle using analytical techniques. Therefore, numerical procedures are adopted to approximate the governing equations solution, some cases however, (e.g., turbulent combustion, three-dimensional, curvature, rotation, separation, and swirl flows) remain complex and give a serious challenge to the numerical modeling.
The main numerical modeling approaches used to model the governing equations are; direct numerical simulations (DNS), large eddy simulations (LES), and Reynolds-average Navier-Stokes equations (RANS).
DNS technique solves the full instantaneous Navier-Stokes equations without any model of turbulent motions; clearly, this approach is computationally expensive and still limited to simple academic flows. LES solves the turbulent large scale eddies explicitly whereas the effect of smaller eddies is modeled by sub-grid closure rules.
Finally, RANS approach is used to solve Navier-Stokes equations for time-mean quantities only. Therefore, the averaged equations require closure modeling to fully approximate the governing equations. Eddy-viscosity turbulence models (EVMs) are widely used in engineering applications for averaged-equations closure which include zero-equation, one-equation, and two-equations models (e.g., k ε− and k − ω models). Reynolds-stress models (RSMs) takes advantage over EVMs in terms of predicting accurately the complex flow, however, they include more equations (up to seven) and then computationally expensive.
So, dear experts, how quantum mechanics helps us understand turbulence and then SOLVE or PREDICT NS equations.?
And, Is it possible to replace NS equations by equations driven through quantum mechanics?
If you are looking for any properties in the atomic and subatomic level for turbulence, or effect of nanomaterials in it, then it should help. You can look at quantum mechanics as an equivalent equations to newtonian equations (entropy driven equations).
See please the papers by Kondaurova and Nemirovski and the literature cited therein. They use super-fluid Helium as an proxy for an almost infinitely high Reynolds number. Here is an example:
Article Numerical Study of Stochastic Vortex Tangle Dynamics in Superfluid He
The only point which needs to be added for a full picture is - due to the fundamental conservation laws of vorticity (Helmholtz; see Kundu pages 128 - 140 - that the "elementary particles of turbulence" (in analogy to Brownian motion of molecules in fluids or gases) are represented not by single vortices, but by counter-rotating VORTEX COUPLES. Only these couples move forward, like in real life where in a marriage the individuals counter each other, but move forward .... Their interaction and its consequences are described in my papers (att.) which give the three major FUNDAMENTAL NUMBERS of turbulence: Karman, Kolmogorov spectral constants in wavenumber and frequency space, and which are the final cornerstone for the picture sketched initially by Kolmogorov 1942 in form of the so-called k-Omega model.
Now I decided not to call it a MODEL, but I prefer to call it the (closed!) "theory of asymptotic turbulence (Re=>\infty)". Regards, and, dear Oma Musa, compliments for your question because it forces all of us to move - forward to a still better and better understanding of mother nature.
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