Related papers: Lagrangian fluid mechanics
The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The functional…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…
We present a new approach, based on Noether's energy-momentum tensor, to construct the lagrangian for nonrelativistic nonisentropic Euler fluids. An advantage of this approach is that it naturally provides a generalised Clebsh decomposition…
The auto-parallel equation over spaces with affine connections and metrics is considered as a result of the application of the method of Lagrangians with covariant derivatives (MLCD) on a given Lagrangian density.
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the…
Equations of motions and energy-momentum density tensors are obtained for a dispersive and dissipative medium sustaining electric and magnetic polarizations, using Lagrangian formalisms. A previous work on the subject by the authors has…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
The invariant projections of the energy-momentum tensors of Lagrangian densities for tensor fields over differentiable manifolds with contravariant and covariant affine connections and metrics [$(\bar{L}_n,g)$-spaces] are found by the use…
The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic…
Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle…
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field…
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid…
We obtain a covariant decomposition of the motion of a relativistic charged particle into parallel motion and perpendicular gyration, and transform to guiding-center coordinates using Lie transforms. The natural guiding-center Poisson…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. Stress (tension) tensors are considered, obtained by the use of the method of Lagrangians with covariant derivatives (MLCD). On the…
Lagrange scalar densities which are concomitants of two scalar fields, a pseudo-Riemannian metric tensor, and their derivatives of arbitrary differential order are investigated in a space of four-dimensions. I construct the most general…
Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress…