Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow

Can geostrophic adjustment of baroclinic disturbances in tropical atmosphere explain MJO events?

International audienceUsing the two-layer moist-convective rotating shallow water model, we study the process of relaxation (adjustment) of localized large-scale pressure anomalies in the lower equatorial troposphere, and show that it engenders coherent structures strongly resembling the Madden Julian Oscillation (MJO) events, as seen in vorticity, pressure, and moisture fields. We demonstrate that baroclinicity and moist convection substantially change the scenario of the quasi-barotropic "dry" adjustment, which was established in the framework of one-layer shallow water model and consists, in the long-wave sector, in the emission of equatorial Rossby waves, with dipolar meridional structure, to the West, and of equatorial Kelvin waves, to the East. If moist convection is strong enough, a dipolar cyclonic structure, which appears in the process of adjustment as a Rossby-wave response to the perturbation, transforms into a coherent modon-like structure in the lower layer, which couples with a baroclinic Kelvin wave through a zone of enhanced convection and produces, at initial stages of the process, a self-sustained slowly eastward-propagating zonally-dissymmetrical quadrupolar vorticity pattern. At the same time, a weaker quadrupolar structure of opposite sign arises in the upper layer, the whole picture similar to the active phase of the MJO events. The baroclinic Kelvin wave then detaches from the dipole, which keeps slow eastward motion, and circumnavigates the Equator, catching up and interacting with the dipole

Rhines scale and spectra of the beta-plane turbulence with bottom drag

We study two-dimensional incompressible turbulence on the beta planeand propose a modification to the Rhines scale that takes into accountthe bottom friction

Propagation of barotropic modons over topography

Submitted to: Geophys. Astrophysics Fluid DynamicsSIGLEITItal

Modon stability to topographic perturbation

SIGLEITItal

Influence of topography on modon propagation and survival

To be published in: Mesoscale/synoptic Coherent Structure in Geophysical Turbulence. Ed.: J.C. Nihoul. Amsterdam, Elsevier, 1989SIGLEITItal