Eye of the tyger: Early-time resonances and singularities in the inviscid Burgers equation
Cornelius Rampf, U. Frisch, Oliver Hahn
Abstract
We detect so far unknown complex singularities in the temporal domain of the inviscid Burgers equation in one space dimension. The (early!) loss of time-analyticity of the velocity is accompanied by the appearance of initially localized resonant behavior which, as we claim, is a temporal manifestation of the so-called tyger phenomenon, reported in Galerkin-truncated implementations of inviscid fluids. We test two methods that reduce the amplitude of these tygers significantly. Our techniques are straightforwardly adapted to higher dimensions and/or applied to other equations of hydrodynamics.
Topics & Concepts
Inviscid flowGravitational singularityBurgers' equationSpacetimeMathematical analysisDimension (graph theory)Classical mechanicsPhysicsGalerkin methodSpace (punctuation)AmplitudeMathematicsPartial differential equationComputer sciencePure mathematicsQuantum mechanicsNonlinear systemOperating systemQuantum chaos and dynamical systemsNonlinear Waves and SolitonsFluid Dynamics and Turbulent Flows