Related papers: Invariant parameterization of geostrophic eddies i…
Invariant parameterization schemes for the eddy-vorticity flux in the barotropic vorticity equation on the beta-plane are constructed and then applied to turbulence modeling. This construction is realized by the exhaustive description of…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30km resolution shallow water ocean…
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equations. Conservation laws and a Hamiltonian structure for the…
Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these models. Methods for finding physical parameterization schemes…
In this paper we compare a classical finite-difference and a high order finite- volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
The global stratification and circulation of the ocean and their sensitivities to changes in forcing depend crucially on the representation of the mesoscale eddy field. Here, a geometrically informed and energetically constrained…
The long-term success of climate models that operate on multi-resolution grids will depend on access to subgrid parameterizations that act appropriately across a wide range of spatial and temporal scales. As the first step in a series of…
We present a simple parameterization for coarse-resolution ocean models. To replace computationally expensive high-resolution ocean models, we develop a computationally cheap parameterization for coarse-resolution models based solely on the…
We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…
Whenever oceanic currents flow over rough topography, there is an associated stress that acts to modify the flow. In the deep ocean, this stress is predominantly a form drag due to pressure differentials across topography, caused by the…