Real-space Manifestations of Bottlenecks in Turbulence Spectra

Abstract

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.

5 pages, 2 figures

References in corpus (3)

• Burgers Turbulence
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws

Cited by in corpus (8)

• Transition from dissipative to conservative dynamics in equations of hydrodynamics
• Turbulent cascade, bottleneck and thermalized spectrum in hyperviscous flows
• The Onset of Thermalisation in Finite-Dimensional Equations of Hydrodynamics: Insights from the Burgers Equation
• Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Adaptive solution of initial value problems by a dynamical Galerkin scheme
• Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales
• How to extract a spectrum from hydrodynamic equations