Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

TL;DR

This paper investigates how fractional hyperviscosity influences the development of bottlenecks in the energy spectrum of Burgers equation solutions, revealing that even slight increases in hyperviscosity order induce spectral bottlenecks.

Contribution

It provides numerical and analytical insights into the growth of bottlenecks and oscillations as the hyperviscosity order is varied between 1 and 2.

Findings

Bottlenecks appear even with minimal fractional hyperviscosity increase.

Oscillations in velocity fields correlate with spectral bottlenecks.

Bottleneck growth is analytically characterized as hyperviscosity order increases.

Abstract

Energy spectrum of turbulent fluids exhibit a bump at an intermediate wavenumber, between the inertial and the dissipation range. This bump is called bottleneck. Such bottlenecks are also seen in the energy spectrum of the solutions of hyperviscous Burgers equation. Previous work, have shown that this bump corresponds to oscillations in real space velocity field. In this paper we present numerical and analytical results of how the bottleneck and its' real space signature, the oscillations, grow as we tune the order of hyperviscosity. We look at a parameter regime $\alpha \in [1,2]$ where $\alpha = 1$ corresponds to normal viscosity and $\alpha = 2$ corresponds to hyperviscosity of order 2. We show that even for the slightest fractional increment in the order of hyperviscosity ($\alpha$) bottlenecks show up in the energy spectrum.