Dynamics of partially thermalized solutions of the Burgers equation

Abstract

The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called "tygers". We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments.

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• Burgers Turbulence
• Helicity, Topology and Kelvin Waves in reconnecting quantum knots
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• Gyrokinetic statistical absolute equilibrium and turbulence
• Magnetic field reversals and long-time memory in conducting flows
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Cited by in corpus (7)

• Many-body Chaos in Thermalised Fluids
• Suppressing thermalization and constructing weak solutions in truncated inviscid equations of hydrodynamics: Lessons from the Burgers equation
• Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation
• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation
• Equilibrium states of Burgers and KdV equations
• Poles, Shocks and Tygers: The Time-reversible Burgers equation