Non-local dispersion and the reassessment of Richardson's <i>t</i>³-scaling law

The Richardson scaling law states that the mean square separation of a fluid particle pair grows according to t3 within inertial range and at intermediate times. theories predicting this regime assume is dispersion local, meaning only eddies scale contribute. These assumptions ignore structural organization turbulent flow into large-scale shear layers, where intense small-scale motions are bounded by energetic motions. Therefore, large scales contribute velocity difference across structures. It shown that, indeed, inside these layers highly non-local approaches Taylor in way fundamentally different from law. Also, layer's contribution overall remains significant as Reynolds number increases. This calls question validity theoretical assumptions. Moreover, literature survey reveals so far, not observed for initial separations range. We propose transition region connects Batchelor- with final Taylor-dispersion regime. Such simple interpretation be consistent observations, able explain why found one specific outside model incorporates dispersion, because it requires small-time-scale properties properties.