By Victor N. Nikolaevskiy
Turbulence conception is without doubt one of the such a lot interesting elements of fluid mechanics and plenty of extraordinary scientists have attempted to use their wisdom to the advance of the speculation and to provide priceless strategies for resolution of a few functional difficulties. during this monograph the writer makes an attempt to combine many particular methods into the unified conception. the elemental premise is the easy concept that a small eddy, that's a component of turbulent meso-structure, possesses its personal dynamics as an item rotating with its personal spin speed and obeying the Newton dynamics of a finite physique. a couple of such eddies fills a coordinate mobile, and the angular momentum stability should be formulated for this spatial mobilephone. If the cellphone coincides with a finite distinction point at a numerical calculation and if the exterior size scale is big, this simple quantity may be regarded as a differential one and a continuum parameterization should be used. Nontrivial angular stability is a outcome of the asymmetrical Reynolds tension motion on the orientated facets of an basic quantity. first and foremost look, the averaged dyad of speed elements is symmetrical, == even if, if averaging is played over the aircraft with basic nj, the primary of commutation is misplaced. consequently, the strain tensor asymmetry j will depend on different components that perform the angular momentum stability. this can be the single chance to figure out a pressure in engineering.
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Extra info for Angular Momentum in Geophysical Turbulence: Continuum Spatial Averaging Method
Let us now consider the operation of spatial averaging (symbol
17) j >. 19), the value of the total momentum flux Nij includes the stress tensors, averaged over the volume AV, but as a part of true macro-stress tensor. In accordance with the Cauchy concept (see [217, 287]), the latter corresponds exactly to a force, acting at the oriented area. Therefore, a volume-average stress tensor cannot be used as a macro-stress  instead of Nij in the impulse balance (compare with ). 19) include the moments of velocity fields of higher order. They can be expressed in their turn by the balance equations for the moments of momentum of the next orders, etc.
17) J We obtain  that instantaneous change of the inertia moment is caused only by deformation that may subsequently violate initial symmetry. 10) yields ANGULAR MOMENTUM IN A VISCOUS FLUID 27 dM i = E.. aUk di jl + E.. i. 12) yields £ ijk . 21) 0ipO jl we finally obtain the following equation  for an incompressible fluid: E.. aUk di = _[CP. aU i IJk dt J ax. J ax. 22) J This means that the first right-hand side term of the Friedman vortex equation for a perfect fluid: aUk + aUp+~E.