Integrated analysis of energy transfers in elastic-wave turbulence

TL;DR

This paper investigates energy transfer mechanisms in elastic-wave turbulence, revealing nonlocal and intermittent energy exchanges between weak and strong turbulence regimes through numerical analysis and analytical expressions.

Contribution

It provides a detailed analysis of energy transfers in elastic-wave turbulence, combining numerical simulations with analytical expressions to characterize nonlocal and intermittent interactions.

Findings

Nonlocal energy transfer from stretching energy to large wave numbers.

Resonant interactions produce cascading energy transfer in weak turbulence.

Energy transfers are intermittent and vary with active and moderate phases.

Abstract

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both of the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produces cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.