Real-space Manifestations of Bottlenecks in Turbulence Spectra
arXiv:1206.0948 · doi:10.1103/PhysRevLett.110.064501
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.
arXiv comment5 pages, 2 figures
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- 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
- Revisiting the SABRA Model: Statics and Dynamics
- Adaptive solution of initial value problems by a dynamical Galerkin scheme
- Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales
- Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions
- How to extract a spectrum from hydrodynamic equations
- Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation