Two-time Lagrangian velocity correlation function for particle pairs in two-dimensional inverse energy-cascade turbulence

Abstract

We numerically investigate a two-time Lagrangian velocity correlation function (TTLVCF) for particle pairs in two-dimensional energy inverse-cascade turbulence. We consider self similarity of the correlation function by means of incomplete similarity. In this framework, we propose a self-similar form of the correlation function, whose scaling exponents cannot be determined by only using the dimensional analysis based on the Kolmogorov's phenomenology. As a result, the scaling laws of the correlation function can depend on the initial separation. This initial-separation dependency is frequently observed in laboratory experiments and direct numerical simulations of the relative dispersion, which is directly related to the correlation function, at moderate Reynolds numbers. We numerically verify the self-similar form by direct numerical simulations of two-dimensional energy inverse-cascade turbulence. The involved scaling exponents and the dependencies on finite Reynolds number effects are determined empirically. Then, we consider implication of the scaling laws of the correlation function on the relative dispersion, i.e. the Richardson-Obukhov $t^3$ law. Our results suggest a possibility not to recover the Richardson-Obukhov $t^3$ law at infinite Reynolds number.

arXiv comment42 pages, 13 figures, published in Physical Review Fluids

References in corpus (10)

• Inverse cascade in two-dimensional turbulence: deviations from Gaussianity
• An update on the double cascade scenario in two-dimensional turbulence
• Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections
• Lagrangian statistics of particle pairs in homogeneous isotropic turbulence
• Space-time correlations in turbulent flow: A review
• Extreme events in the dispersions of two neighboring particles under the influence of fluid turbulence
• Geometry and violent events in turbulent pair dispersion
• Turbulent pair dispersion as a continuous-time random walk
• Intermittency in the relative separations of tracers and of heavy particles in turbulent flows
• The Diffusion Approximation in Turbulent Two-Particle Dispersion

Cited by in corpus (1)

• Universal alignment in turbulent pair dispersion