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This is an important area of research in this field, and a major goal of the modern theory of turbulence is to understand what is universal in the inertial range, and how to deduce intermittency properties from the Navier-Stokes equations, i.e. from first principles.
In physics, the Landau–Hopf theory of turbulence, named for Lev Landau and Eberhard Hopf, was until the mid-1970s, [clarification needed] the accepted theory of how a fluid flow becomes turbulent. It states that as a fluid flows faster, it develops more Fourier modes .
Turbulence remains the major unsolved domain of fluid mechanics. Theodorsen identified the main turbulence-creating terms in the equations of motion as (q x curl q . curl curl q); he showed that two-dimensional turbulence cannot exist; that vortex lines stretching and bending is the important mechanism and ingredient of turbulence.
Lumley received the 1990 Fluid Dynamics Prize of American Physical Society, "For his outstanding contributions to the understanding of turbulent flow, in particular, the fundamental structure of turbulent shear flows, the effects of drag-reducing additives, and his widely recognized contributions to the statistical theory of turbulence, and for his personal and intellectual leadership in the ...
The statistical theory of turbulence in viscous liquids describes the fluid flow by a scale-invariant distribution of the velocity field, which means that the typical size of the velocity as a function of wavenumber is a power-law. In steady state, larger scale eddies at long wavelengths disintegrate into smaller ones, dissipating their energy ...
Consider a two-point velocity correlation tensor for homogeneous turbulence (,) = (,) (+,) ¯.For isotropic turbulence, this correlation tensor can be expressed in terms of two scalar functions, using the invariant theory of full rotation group, first derived by Howard P. Robertson in 1940, [6]
In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows.
This accounts for the transfer of kinetic energy from the mean flow to the fluctuating velocity field. It is responsible for sustaining the turbulence in the flow through this transfer of energy from the large scale mean motions to the small scale fluctuating motions. This is the only term that is closed in the Reynolds Stress Transport Equations.