Hamiltonian Fluid Mechanics

On the Hamiltonian Description of Fluid Mechanics

We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light on the origin of Clebsh variabes, introduced in the previous century. The develoted formalism permitts to relate the circulation conservation (Tompson theorem) with the invariance of the theory with res...

Hamiltonian structure of a drift-kinetic model and Hamiltonian closures for its two-moment fluid reductions

Automatic Extraction and Characterization of Structures in Area-preserving Maps

Many natural phenomena found in various areas, such as orbital mechanics, fluid dynamics or quantum mechanics, can be described in terms of Hamiltonian dynamics. Multi-dimensional Hamiltonian systems often exhibit chaotic behaviour, which makes their analysis difficult. The use of surfaces of sections, such as a Poincaré return map, is commonly employed to get insight into the phase space of dy...

Energy-conserving and Hamiltonian low-order models in geophysical fluid dynamics

Arbitrary truncations in the Galerkin method commonly used to derive low-order models (LOMs) may violate fundamental conservation properties of the original equations, causing unphysical behaviors in LOMs such as unbounded solutions. To avoid these, energy-conserving LOMs are developed in the form of coupled Volterra gyrostats, based on analogies between fluid dynamics and rigid body mechanics....

Statistical mechanics of vortex lines

Statistical mechanics of three-dimensional flows of an ideal incompressible fluid is considered. An ideal fluid differs from the usual Hamiltonian systems of statistical mechanics by possessing an infinite number of integrals of motion that are circulations of velocity over closed fluid contours. To reduce the problem to a standard one, the governing equations should be written in a Hamiltonian...

Hamiltonian closures for fluid models with four moments by dimensional analysis

Fluid reductions of the Vlasov–Ampère equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are found. Two Hamiltonian models emerge, for which the explicit closures a...