Measured scaling properties of inhomogeneous turbulent flows

A turbulent flow lacking homogeneity and isotropy has been studied using the technique of photon-correlation homodyne spectroscopy to measure velocity differences in different directions and at various length scales. The measured intensity correlation function G(qt,L) is found to be of the scaling form G(qtu(L)) with u(L){~}L^ξ, where u(L) is the characteristic turbulent velocity at the length scale L and q is the scattering vector. The exponent {ξ} varies with scattering geometries and with flow cells. The scaling behavior of G(qt,L) is found to be independent of spatial positions and orientations. A scaling G(qtu(L)) indicates that the velocity-density function P(V,R) has a scaling form Q(V/u(R))/u(R). The experiment suggests that the scaling argument can still be used to describe anisotropic and inhomogeneous turbulent flows, and that the exact functional form of P(V,R) (which is of scaling form) may vary with spatial positions and orientations in turbulent flows, reflecting the inhomogeneity and anisotropy of the turbulence.