Casimir cascades in two-dimensional turbulence

In addition to conserving energy and enstrophy, the nonlinear terms of the two-dimensional incompressible Navier–Stokes equation are well known to conserve the global integral of any continuously differentiable function of the scalar vorticity field. However, the phenomenological role of these addit...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 729; pp. 364 - 376
Main Author Bowman, John C.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.08.2013
Subjects
Energy conservation
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Fundamentals
Nonlinear systems
Physics
Simulation
Turbulence simulation and modeling
Turbulent flow
Turbulent flows, convection, and heat transfer
computational methods
turbulence simulation
turbulence theory
Invariant
Energy spectra
Enstrophy
Digital simulation
Vorticity
Modelling
Incompressible fluid
Turbulence structure
Navier-Stokes equations
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Summary:In addition to conserving energy and enstrophy, the nonlinear terms of the two-dimensional incompressible Navier–Stokes equation are well known to conserve the global integral of any continuously differentiable function of the scalar vorticity field. However, the phenomenological role of these additional inviscid invariants, including the issue as to whether they cascade to large or small scales, is an open question. In this work, well-resolved implicitly dealiased pseudospectral simulations suggest that the fourth power of the vorticity cascades to small scales.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2013.308