Ideal Fluid Dynamics Research Articles

Mixed state quantum mechanics in hydrodynamical form

A newly derive set of quantum fluid dynamical equations appropriate for the description of mixed state dynamics is presented. Based essentially on moments of the Wigner function, the theory presented here uses an expansion of the pseudodistribution function in conjunction with a renormalization technique to obtain a semiclassical approximation for the dynamics of the probability, probability current, and energy densities. Particularly simple equations, ideal fluid dynamics with a nonlocal potential, result from using a local Maxwellian ansatz for the Wigner function. Further, the transformed potential may be easily computed from the fields being convected. Analogies with classical kinetic theory and fluid dynamics are exploited whenever possible.

Sui principi variazionali di Lagrange-D'Alembert e di Hamilton nella dinamica dei fluidi ideali classici

We show that the Euler equation of classical ideal fluid dynamics can be deduced either from the Lagrange-D' Alembert principle or from the Hamilton principle by means of only one method, which is valid both to ideal compressible and to incompressible fluids. Futhermore, making use of some thermodynamical relations we determine the conditions under which the motion of the medium must occur in order to be possible to introduce the Hamilton's action A and the Lagrangian L of the motion.

Cylindrically invariant flows in relativistic fluid dynamics

We show that partially cylindrically symmetric solutions of the motion equations of special relativistic, adiabatic, ideal fluid dynamics, have the same noncanonical Hamiltonian structure as the original motion equations.

A multipressure regularization for multiphase flow

The standard theory of ideal single-pressure multiphase fluid dynamics is known to be ill posed. To regularize this theory we dispense with the constraint of equal pressures for the different phases by introducing multiple pressures and quantities associated with interface dynamics and inertia. Via the Hamiltonian formalism, we extend the noncanonical Poisson brackets for the standard single-pressure equations to the case of multiple pressures. This formalism is used to find Lyapunov stability conditions for the regularized system. The regularized system is shown to be hyperbolic.

Foundations of Radiation Hydrodynamics

Exposes the great foundation-stones of research on radiating flows in astrophysics. Upon them are built the walls of methodology (some understandably incomplete). Concentration is on fundamentals but with only few applications. Coverage broadly involves non-radiating fluids, physics of radiation, radiation transport, and dynamics of radiating fluids, and finally the elements of sensor calculus as used in this volume. Contents, abridged: Microphysics of gases. Dynamics of ideal fluids. Relativistic fluid flow. Radiation and radiative transfer. Radiating flows. Glossary of physical symbols. Index.

Discretization of ideal fluid dynamics in the Eulerian representation

A Hamiltonian discretization of one-dimensional compressible fluid dynamics is made possible by analyzing the properties of semidirect product Lie algebras associated to representations of the Lie algebra of vector fields in R″.

Multipressure regularization for multiphase flow

The standard theory of ideal single-pressure multiphase fluid dynamics, which is known to be ill-posed, is regularized via the hamiltonian formalism by extending the noncanonical Poisson brackets for the standard single-pressure equations to the case of multiple pressures. This formalism is used to find Lyapunov stability conditions for the regularized system.

Relativistic fluid dynamics as a Hamiltonian system

The equations of ideal relativistic fluid dynamics in the laboratory frame form a noncanonical hamiltonian system with the same Poisson bracket as for nonrelativistic fluids, but with dynamical variables and hamiltonian obtained via a regular deformation of their nonrelativistic counterparts.

Calculation of the pressure in stationary problems of ideal fluid dynamics

Calculation of the pressure in stationary problems of ideal fluid dynamics

Canonical maps between poisson brackets in eulerian and Lagrangian descriptions of continuum mechanics

Noncanonical, Lie algebraic, hamiltonian structures in the eulerian description of ideal continuum mechanics are shown to be compatible with nearly canonical structures in the lagrangrian description. Examples are given for compressible ideal fluid dynamics, magnetohydrodynamics, nonlinear elasticity, multifluid plasmas, superfluids 4He and 3He-A, and chromohydrodynamics.

Rayleigh-Taylor instability and the use of conformal maps for ideal fluid flow

Potential theory permits ideal fluid dynamics to be formulated in terms of boundary motion. In two dimension, the flow can then be found using conformal mapping. The evolution of some Rayleigh-Taylor instabilities is calculated well into the large amplitude nonlinear regime. The Rayleigh-Taylor calculation for Atwood ratio unity is used as a prototype for a system of theoretical and numerical techniques exploiting complex variable theory and high-order quadrature methods.

A variational principle in relativistic magnetofluid dynamics

The definition of the generalized antipotential four-vector makes it possible to give a relativistically covariant variational formulation in the dynamics of ideal charged fluids. A special relativistically covariant form of Maxwell's equation is given. The antipotential four-vector does not explicitly appear in the Lagrangian density. The derivation of the equation of motion of a single charged particle is given, to illustrate the theory.