On the elimination of the sweeping interactions from theories of hydrodynamic turbulence

In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather than one-time but still weaker than many-time global homogeneity. We argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi-Lagrangian transformation.Comment: v1: submitted to Physica D. v2: major revisions; resubmitted to Physica D. v3: minor revisions requested by referee

Scattering effects on ocean acoustics coherence for low-frequency long-range propagation

The mutual coherence function (MCF) of the received acoustic field is derived using an analysis based upon coupled mode theory. Separations in transverse horizontal position, time and frequency are treated. The mean horizontal array response and the shape of an ensemble-averaged pulse are evaluated from the MCF. The application is illustrated by computation of the considered effects for rough ocean surface scattering in an upper-sound channel