28 research outputs found
Thermal convection in a cylindrical annulus heated laterally
In this paper we study thermoconvective instabilities appearing in a fluid
within a cylindrical annulus heated laterally. As soon as a horizontal
temperature gradient is applied a convective state appears. As the temperature
gradient reaches a critical value a stationary or oscillatory bifurcation may
take place. The problem is modelled with a novel method which extends the one
described in (numerico). The Navier Stokes equations are solved in the
primitive variable formulation, with appropriate boundary conditions for
pressure. This is a low order formulation which in cylindrical coordinates
introduces lower order singularities. The problem is discretized with a
Chebyshev collocation method easily implemented and its convergence has been
checked. The results obtained are not only in very good agreement with those
obtained in experiments, but also provide a deeper insight into important
physical parameters developing the instability, which has not been reported
before.Comment: 17 pages, Latex, 13 figures. Version improved in the physical
results. To appear in Journal of Physics A: Mathematical and genera
Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets
International audienceIn this paper, we describe a unified algorithm for locating and computing hyperbolic trajectories, and then computing their stable and unstable manifolds, for finite time velocity fields in the form of a data set defined on a space-time grid. The algorithm is applied to a turbulent regime of a quasigeostrophic wind-driven double gyre in a rectangular domain