Hamiltonian fluid dynamics and distributed chaos

TL;DR

This paper demonstrates that distributed chaos in Hamiltonian fluid dynamics exhibits a specific stretched exponential frequency spectrum, with experimental and geophysical applications confirming the theoretical predictions.

Contribution

It introduces a new understanding of distributed chaos with broken time symmetry and connects it to observable phenomena in laboratory and geophysical fluid systems.

Findings

Experimental data at high Rayleigh number matches the theoretical spectrum.

The spectrum follows a stretched exponential form with exponent 1/2.

Applications include temperature dynamics in large cities and climate oscillation indices.

Abstract

It is shown that distributed chaos with spontaneously broken time translational symmetry (homogeneity) has a stretched exponential frequency spectrum $E(f) \propto \exp-(f/f_0)^{1/2}$. Good agreement has been established with a laboratory experimental data obtained at large values of Rayleigh number $Ra \sim 3\cdot 10^{14}$ in thermal convection. Applications to geophysical fluid dynamics (temperature dynamics for large cities, the North Atlantic Oscillation index and the Pacific/North American pattern) have been considered.