3,838 research outputs found
Enstrophy dissipation in freely evolving two-dimensional turbulence
Freely decaying two-dimensional Navier--Stokes turbulence is studied. The
conservation of vorticity by advective nonlinearities renders a class of
Casimirs that decays under viscous effects. A rigorous constraint on the
palinstrophy production by nonlinear transfer is derived, and an upper bound
for the enstrophy dissipation is obtained. This bound depends only on the
decaying Casimirs, thus allowing the enstrophy dissipation to be bounded from
above in terms of initial data of the flows. An upper bound for the enstrophy
dissipation wavenumber is derived and the new result is compared with the
classical dissipation wavenumber.Comment: No figures, Letter to appear in Phys. Fluid
Local transfer and spectra of a diffusive field advected by large-scale incompressible flows
This study revisits the problem of advective transfer and spectra of a
diffusive scalar field in large-scale incompressible flows in the presence of a
(large-scale) source. By ``large-scale'' it is meant that the spectral support
of the flows is confined to the wave-number region , where is
relatively small compared with the diffusion wave number . Such flows
mediate couplings between neighbouring wave numbers within of each other
only. It is found that the spectral rate of transport (flux) of scalar variance
across a high wave number is bounded from above by ,
where denotes the maximum fluid velocity and is the spectrum
of the scalar variance, defined as its average over the shell .
For a given flux, say , across , this bound requires
This is consistent with recent
numerical studies and with Batchelor's theory that predicts a spectrum
(with a slightly different proportionality constant) for the viscous-convective
range, which could be identified with . Thus, Batchelor's
formula for the variance spectrum is recovered by the present method in the
form of a critical lower bound. The present result applies to a broad range of
large-scale advection problems in space dimensions , including some
filter models of turbulence, for which the turbulent velocity field is advected
by a smoothed version of itself. For this case, and
are the kinetic energy spectrum and flux, respectively.Comment: 6 journal pages, 1 "cartoon" figure, to appear in PR
Impeded inverse energy transfer in the Charney--Hasegawa--Mima model of quasi-geostrophic flows
The behaviour of turbulent flows within the single-layer quasi-geostrophic (Charney-Hasegawa-Mima) model is shown to be strongly dependent on the Rossby deformation wavenumber lambda (or free-surface elasticity). Herein, we derive a bound oil the inverse energy transfer, specifically on the growth rate dl/dt of the characteristic length scale e representing the energy centroid. It is found that dl/dt = l(s) >> lambda(-1)) the inverse energy transfer is strongly impeded, in the sense that under the usual time scale no significant transfer of energy to larger scales occurs. The physical implication is that the elasticity of the free surface impedes turbulent energy transfer in wavenumber space, effectively rendering large-scale vortices long-lived and inactive. Results from numerical simulations of forced-dissipative turbulence confirm this prediction.Publisher PDFPeer reviewe
Large-scale energy spectra in surface quasi-geostrophic turbulence
The large-scale energy spectrum in two-dimensional turbulence governed by the
surface quasi-geostrophic (SQG) equation
is studied. The nonlinear transfer of this system conserves the two quadratic
quantities and
(kinetic energy), where denotes
a spatial average. The energy density is bounded and its spectrum
is shallower than in the inverse-transfer range. For
bounded turbulence, in the low-wavenumber region can be bounded by
where is a constant independent of but dependent on the domain
size. Results from numerical simulations confirming the theoretical predictions
are presented.Comment: 11 pages, 4 figures, to appear in JF
Impeded inverse energy transfer in the Charney--Hasegawa--Mima model of quasi-geostrophic flows
The behaviour of turbulent flows within the single-layer quasi-geostrophic
(Charney--Hasegawa--Mima) model is shown to be strongly dependent on the Rossby
deformation wavenumber (or free-surface elasticity). Herein, we
derive a bound on the inverse energy transfer, specifically on the growth rate
\d\ell/\dt of the characteristic length scale representing the energy
centroid. It is found that \d\ell/\dt\le2\norm q_\infty/(\ell_s\lambda^2),
where \norm q_\infty is the supremum of the potential vorticity and
represents the potential enstrophy centroid of the reservoir, both invariant.
This result implies that in the potential energy dominated regime
(), the inverse energy transfer is strongly
impeded, in the sense that under the usual time scale no significant transfer
of energy to larger scales occurs. The physical implication is that the
elasticity of the free surface impedes turbulent energy transfer in wavenumber
space, effectively rendering large-scale vortices long-lived and inactive.
Results from numerical simulations of forced-dissipative turbulence confirm
this prediction.Comment: 8 pages, 2 figures, accepted for publication in JF
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