Related papers: Action Principles for Extended MHD Models
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which is described by a kinetic equation. When the Vlasov description is adopted for the energetic particles, different Vlasov-MHD…
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling…
In an attempt to generalize the Hamilton's principle, an action functional is proposed which, unlike the standard version of the principle, accounts properly for all initial data and the possible presence of dissipation. To this end, the…
Nonlinear energy-conserving drift-fluid equations that are suitable to describe self-consistent finite-beta low-frequency electromagnetic (drift-Alfven) turbulent fluctuations in a nonuniform, anisotropic, magnetized plasma are derived from…
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how…
We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the…
A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on a Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by…
By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is…
We consider the Vlasov-Maxwell equations with one spatial direction and two momenta, one in the longitudinal direction and one in the transverse direction. By solving the Jacobi identity, we derive reduced Hamiltonian fluid models for the…
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets…
The Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry is proposed. For an arbitrary half-integer value of the parameter l, the Hamilton and non-canonical Poisson brackets are found, in terms of which…
We derive the conditions under which the fluid models obtained from the first two moments of Hamiltonian drift-kinetic systems of interest to plasma physics, preserve a Hamiltonian structure. The adopted procedure consists of determining…
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling…
We provide a novel action principle for nonrelativistic ideal magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type parametrisation. Both Lagrangian and Hamiltonian formulations have been considered. Within the Hamiltonian…
A nonlinear unified fluid model that describes the Equatorial Electrojet, including the Farley-Buneman and gradient-drift plasma instabilities, is defined and shown to be a noncanonical Hamiltonian system. Two geometric constants of motion…
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…
This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on the product of an arbitrary number of two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations are developed in a…
Variational principles for magnetohydrodynamics (MHD) were in\-troduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…