4,529 research outputs found
Energy Spectrum of Quasi-Geostrophic Turbulence
We consider the energy spectrum of a quasi-geostrophic model of forced,
rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2}
valid for wave numbers that are smaller than a wave number associated to the
forcing injection scale. This upper bound separates this spectrum from the
Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a
two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical
support for the k^{-2} spectrum observed in recent experiments
Particle trajectories in linearized irrotational shallow water flows
We investigate the particle trajectories in an irrotational shallow water
flow over a flat bed as periodic waves propagate on the water's free surface.
Within the linear water wave theory, we show that there are no closed orbits
for the water particles beneath the irrotational shallow water waves. Depending
on the strength of underlying uniform current, we obtain that some particle
trajectories are undulating path to the right or to the left, some are looping
curves with a drift to the right and others are parabolic curves or curves
which have only one loop
Steady water waves with multiple critical layers: interior dynamics
We study small-amplitude steady water waves with multiple critical layers.
Those are rotational two-dimensional gravity-waves propagating over a perfect
fluid of finite depth. It is found that arbitrarily many critical layers with
cat's-eye vortices are possible, with different structure at different levels
within the fluid. The corresponding vorticity depends linearly on the stream
function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid
Mec
On the particle paths and the stagnation points in small-amplitude deep-water waves
In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
arXiv:1106.382
Kinetic and Exchange Energy Densities near the Nucleus
We investigate the behavior of the kinetic and the exchange energy densities
near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we
derive analytical expressions near the nucleus, for single shells, as well as
in the semiclassical limit of large non-relativistic neutral atoms. We show
that a model based on the helium iso-electronic series is very accurate, as
also confirmed by numerical calculations on real atoms up to two thousands
electrons. Based on this model, we propose non-local density-dependent
ingredients that are suitable for the description of the kinetic and exchange
energy densities in the region close to the nucleus. These non-local
ingredients are invariant under the uniform scaling of the density, and they
can be used in the construction of non-local exchange-correlation and kinetic
functionals.Comment: 11 pages, 7 figure
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