The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a
vast range of spatial and temporal scales. The understanding of the climate's structural and …

This paper presents a few of the research tools of modern physics that can successfully be
used to achieve a better understanding of the temporal and spatial variability of the multi …

Point-vortex models are presented for the generalized Euler equations, which are
characterized by a fractional Laplacian relation between the active scalar and the stream …

Nambu field theory, originated by Névir and Blender for incompressible flows, is generalized
to establish a unified energy–vorticity theory of ideal fluid mechanics. Using this approach …

A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D)
hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals …

We consider the Nambu and Hamiltonian representations of Rayleigh–Bénard convection
with a nonlinear thermal heating effect proportional to the Eckert number (Ec). The model …

Concrete examples of the construction of Nambu brackets for equations of motion (both 3D
and 2D) of Boussinesq stratified fluids and also for magnetohydrodynamical equations are …

The paper focuses on two interrelated problems: developing physically sound low-order
models (LOMs) for atmospheric dynamics and employing them as novel time-series models …

Wide ranges of symmetry methods are applied to several differential equations arising in the
atmospheric sciences. Lie point symmetries of the barotropic vorticity equation, the …

A typical problem with the conventional Galerkin approach for the construction of finite-mode
models is to keep structural properties unaffected in the process of discretization. We …