Scaling of acceleration in locally isotropic turbulence

where Dui/Dt denotes the time derivative following the motion of the fluid particle, and ui is velocity. Here, ν is the kinematic viscosity, ∇x ≡ ∂xn∂xn is the Laplacian operator, ∂ denotes differentiation with respect to the subscript variable, summation is implied by repeated indices, p is pressure divided by fluid density; density is constant. ε is energy dissipation rate per unit mass of fluid. Kolmogorov’s (1941) scaling (K41 scaling) uses ε and ν as parameters, and is based on the assumption that local isotropy is accurate for a given distance r between two points of measurements, x and x′ ≡ x + r, r ≡ |r|. Refinement of K41 to include the effects of turbulence intermittency (Kolmogorov, 1962) leads to quantification of the Reynolds number dependence of the deviation from K41 scaling. The choice of Reynolds number has been