KINEMATICS OF HOMOGENEOUS AXISYMMETRICAL TURBULENCE

It is shown that the expressions for the correlation tensors of homoge neous axisymmetric turbulence can be considerably simplified compared to previous analyses of Batchelor (1946) and Chandrasekhar (1950). Rep resentations of the axisymmetric two-point correlations tensors are fo und, such that each measurable correlation corresponds to a single sca lar function, and moreover such that the equations of continuity relat ing different tensor components to each other take the most simple for m. Reflectional symmetry in planes normal to but not in planes through the axis of symmetry is demanded, which allows a full description of states with rotation about the axis of symmetry. The second and third- order velocity correlation tensors and the first-order pressure-veloci ty correlation tensor are analysed with the new method. Small separati on expansions of the correlation functions yield the quantities which have to be measured to determine various terms in the governing equati ons for the Reynolds stresses and the dissipation tenser. A scalar Poi sson equation for the pressure-strain is derived, and the single-point solution is written as a sum of integrals over measurable correlation functions. The simplified analysis can be of great experimental impor tance. It reveals in a simple way how a full experimental picture of h omogeneous axisymmetric turbulence can be obtained by measuring compon ents of the velocity at two points at variable distance from each othe r on a line perpendicular to the mean flow in a wind tunnel. By using the Fourier-Bessel transform it is also shown that the three-dimension al energy, transfer, and pressure-strain spectra can be extracted from such measurements.