Related papers: Initialization and the quasi-geostrophic slow mani…
The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here we introduce a new model for…
The classical Chapman-Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are…
Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record…
During this last decades, several attempts to construct slow invariant manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many…
Methods to quantify predictability properties of atmospheric flows are proposed. The ``Extended Self Similarity'' (ESS) technique, recently employed in turbulence data analysis, is used to characterize predictability properties at short and…
In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold…
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
The theory of inertial manifolds (IM) is used to develop reduced-order models of turbulent combustion. In this approach, the dynamics of the system are tracked in a low-dimensional manifold determined in-situ without invoking laminar flame…
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of…
The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
Parametrizations for internal gravity waves in atmospheric models are traditionally subject to a number of simplifications. Most notably, they rely on both neglecting wave propagation and advection in the horizontal direction (single-column…