4,788 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
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
We give an elementary proof of the global well-posedness for the critical 2D
dissipative quasi-geostrophic equation. The argument is based on a non-local
maximum principle involving appropriate moduli of continuity.Comment: 7 page
An Eulerian-Lagrangian approach to the Navier-Stokes equations
This work presents an approach to the Navier-Stokes equations that is phrased
in unbiased Eulerian coordinates, yet describes objects that have Lagrangian
significance: particle paths, their dispersion and diffusion. The commutator
between Lagrangian and Eulerian derivatives plays an important role in the
Navier-Stokes equations: it contributes a singular perturbation to the Euler
equations, in addition to the Laplacian. Bounds for the Lagrangian
displacements, their first and second derivatives are obtained without
assumptions. Some of these rigorous bounds can be interpreted in terms of the
heuristic Richardson law of pair dispersion in turbulent flows
Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial
dimensions with spatial diffusion of the polymeric stresses
A Note on Ostrowski's Inequality
This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: i) the case of random variables (attached to arbitrary probability fields);
ii) the comparison is performed additively or multiplicatively; iii) the mean value is attached to a multiplicative averaging process
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