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

  • Debarghya BanerjeeEmail author
Open Access
Regular Article
  • 35 Downloads

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 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.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

Notes

Acknowledgments

Open access funding provided by Max Planck Society.

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Copyright information

© The Author(s) 2019

Open Access 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.

Authors and Affiliations

  1. 1.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany

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