The Howarth . Kirwan relation ( see Bonin - Saglom , vol -2 ; Pope ) ° fundamental statistical quantity of interest : velocity correlation tensor Rijlx , , x.at )= ( hill , ,t ) ujlxut ) > . evolution equation from Nse , = ( uiuj ' > of ( uiujstdkcuiuauj ) tai ( uiujui > = . 2 ; ( pujs - a :( pin ; > + r Qiluiujltudjicuiuj > Gi closure problem ! Go Statistical symmetries for homogeneous isotropic turbulence : homogeneity : ( uiuj ' )= Rijlr ) with 1=1 ' - I ↳ d×i= - On . %=2r ; isotropy : 1) pressure - velocity correlations : ( nip 's = ago ) : scalar function only isotropic depending our only tensor of rank I ↳ dri ( hip 's = air )r÷r÷ tar ) ( { . rig ) = a 'lr ) +2g acr ) t 0 ( incompressibility ) G is solved by alr ) = 0 ✓ acr ) = r - 2 ^ can be excluded on physical grounds because of divergence at origin
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The Howarth Kirwan Pope -2 - Max Planck Society · The Howarth Kirwan relation (see Bonin-Saglomvol-2 Pope) ° fundamental statistical quantity of interest velocity correlation tensor
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The Howarth . Kirwan relation ( see Bonin - Saglom ,vol -2 ; Pope )