Bifurcations of blowup in inviscid shell models of convective turbulence

TL;DR

This paper investigates finite-time singularities in inviscid shell models of convective turbulence, revealing bifurcations and universal structures in blowup behavior, with implications for turbulence theory.

Contribution

It demonstrates the existence of blowup bifurcations and characterizes various blowup structures, advancing understanding of singularities in inviscid turbulence models.

Findings

Blowup exists in inviscid shell models of convective turbulence.

Blowup structures undergo bifurcations from self-similar to chaotic regimes.

Small-scale blowup structure is universal, independent of initial conditions.

Abstract

We analyze the blowup (finite-time singularity) in inviscid shell models of convective turbulence. We show that the blowup exists and its internal structure undergoes a series of bifurcations under a change of shell model parameter. Various blowup structures are observed and explained, which vary from self-similar to periodic, quasi-periodic and chaotic regimes. Though the blowup takes sophisticated forms, its asymptotic small-scale structure is independent of initial conditions, i.e., universal. Finally, we discuss implications of the obtained results for the open problems of blowup in inviscid flows and for the theory of turbulence.