Finite-time localized singularities as a mechanism for turbulent dissipation

TL;DR

This paper explores how finite-time singularities in a nonlinear Schrödinger model can explain turbulent dissipation, showing that dissipation occurs near singularities and exhibits chaotic, intermittent behavior similar to fluid turbulence.

Contribution

It introduces a singularity-based turbulence mechanism using the nonlinear Schrödinger equation, linking singularities to dissipation and turbulence spectra.

Findings

Dissipation occurs near singularities only.

Strong events are random in space and time.

The mean dissipation rate remains nearly constant with varying viscosity.

Abstract

We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these singularities are regularized, and the inclusion of an external forcing results in a chaotic fluctuating state. The strong events appear randomly in space and time, making the dissipation rate highly fluctuating. The model shows that: i) dissipation takes place near the singularities only, ii) such intense events are random in space and time, iii) the mean dissipation rate is almost constant as the viscosity varies, and iv) the observation of an Obukhov-Kolmogorov spectrum with a power law dependence together with an intermittent behavior using structure functions correlations, in close correspondence with fluid turbulence.