https://doi.org/10.1140/epjb/e2019-90751-4
Regular Article
Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions
Max Planck Institute for Dynamics and Self-Organization,
Am Faßberg 17,
Göttingen
37077, Germany
a e-mail: debarghya.banerjee@ds.mpg.de
Received:
22
December
2018
Received in final form:
19
May
2019
Published online: 16 September 2019
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 α ∈ [1, 2] where α = 1 corresponds to normal viscosity and α = 2 corresponds to hyperviscosity of order 2. We show that even for the slightest fractional increment in the order of hyperviscosity (α) bottlenecks show up in the energy spectrum.
Key words: Statistical and Nonlinear Physics
© The Author(s) 2019. This article is published with open access at Springerlink.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Open access funding provided by Max Planck Society.
