Nonlinear Evolution of Hydrodynamical Shear Flows in Two Dimensions | Zendy

Yoram Lithwick | Zendy

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Nonlinear Evolution of Hydrodynamical Shear Flows in Two Dimensions

Author(s) -

Yoram Lithwick

Publication year - 2007

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.376

H-Index - 489

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/522074

Subject(s) - physics , instability , wavenumber , vorticity , inviscid flow , classical mechanics , mechanics , rotational symmetry , turbulence , angular momentum , shear flow , perturbation (astronomy) , shear (geology) , nonlinear system , vortex , optics , quantum mechanics , petrology , geology

We examine how perturbed shear flows evolve in two-dimensional,incompressible, inviscid hydrodynamical fluids, with the ultimate goal ofunderstanding the dynamics of accretion disks. To linear order, vorticity wavesare swung around by the background shear, and their velocities are amplifiedtransiently before decaying. It has been speculated that sufficiently amplifiedmodes might couple nonlinearly, leading to turbulence. Here we show hownonlinear coupling occurs in two dimensions. This coupling is remarkably simplebecause it only lasts for a short time interval, when one of the coupled modesis in mid-swing. We focus on the interaction between a swinging and anaxisymmetric mode. There is instability provided that k_{y,swing}/k_{x,axi}

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