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107
Fast singular oscillating limits of
the three-dimensional "primitive" equations of
geophysical fluid flows are analyzed.
We prove existence on infinite time intervals
of regular solutions to the
3D "primitive" Navier-Stokes equations for strong
stratification (large stratification parameter N).
This uniform existence is proven for
periodic or stress-free boundary conditions
for all domain aspect ratios,
including the case of three wave resonances
which yield nonlinear " dimensional"
limit equations...
Motivé par l'étude des fluides tournants entre deux plaques, nous considérons l'équation tridimensionnelle de Navier-Stokes incompressible avec viscosité verticale nulle. Nous démontrons l'existence locale et l'unicité de la solution dans un espace critique (invariant par le changement d'échelle de l'équation). La solution est globale en temps si la donnée initiale est petite par rapport à la viscosité horizontale. Nous obtenons l'unicité de la solution dans un espace plus grand que l'espace des...
Durations of rain events and drought events over a given region provide important information about the water resources of the region. Of particular interest is the shape of upper tails of the probability distributions of such durations. Recent research suggests that the underlying probability distributions of such durations have heavy tails of hyperbolic type, across a wide range of spatial scales from 2 km to 120 km. These findings are based on radar measurements of spatially averaged rain rate...
2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations
that involve fractional derivatives in space and time. They are useful to
model anomalous diffusion, where a plume of particles spreads in a different
manner than the classical diffusion equation predicts. An initial value problem
involving a space-fractional diffusion equation is an abstract Cauchy
problem, whose analytic solution can be written...
The free oscillations of the gate system proposed [1,2] to defend the Venice Lagoon from the phenomenon of high water are analyzed. Free transverse modes of oscillations exist which may be either subharmonic or synchronous with respect to typical waves in the Adriatic sea. This result points out the need to examine whether such modes may be excited as a result of a Mathieu type resonance occurring when the gate system is forced by incident waves. The latter investigation is performed in part 2 of...
We show that the transverse subharmonic modes characterizing the free oscillations of the gate system proposed to defend the Venice Lagoon from the phenomenon of high water (see Note I[1]) can be excited when the gate system is forced by plane monochromatic waves orthogonal to the gates with the typical characteristics of large amplitude waves in the Adriatic sea close to the lagoon inlets. A linear stability analysis of the coupled motion of the system sea-gates-lagoon reveals that for typical...
This contribution reviews the nonlinear
stochastic properties of turbulent velocity and passive scalar
intermittent fluctuations in Eulerian and Lagrangian turbulence.
These properties are illustrated with original data sets of (i)
velocity fluctuations collected in the field and in the
laboratory, and (ii) temperature, salinity and in vivo
fluorescence (a proxy of phytoplankton biomass, i.e. unicelled
vegetals passively advected by turbulence) sampled from highly
turbulent coastal waters. The strength...
We present here a series of works which aims at describing geophysical flows in the equatorial zone, taking into account the dominating influence of the earth rotation. We actually proceed by successive approximations computing for each model the response of the fluid to the strong Coriolis penalisation. The main difficulty is due to the spatial variations of the Coriolis acceleration : in particular, as it vanishes at the equator, fast oscillations are trapped in a thin strip of latitudes.
As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments...
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