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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.
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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.
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 ...
The Batchelor–Chandrasekhar equation is the evolution equation for the scalar functions, defining the two-point velocity correlation tensor of a homogeneous axisymmetric turbulence, named after George Batchelor and Subrahmanyan Chandrasekhar.