Related papers: A harmonic maps approach to fluid flows
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that…
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs)…
For a moving hypersurface in the flow of a nonautonomous ordinary differential equation in $n$-dimensional Euclidean spaces, the fluxing index of a passively-advected Lagrangian particle is the total number of times it crosses the moving…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…
We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a…
We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…
The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…
We present an Eulerian vortex method based on the theory of flow maps to simulate the complex vortical motions of incompressible fluids. Central to our method is the novel incorporation of the flow-map transport equations for line elements,…
In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing…
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the…
We consider the functional of total variation of maps from an interval into a Riemannian submanifold of $\mathbb R^N$. We define a notion of strong solution to the system of equations corresponding to the $L^2$-gradient flow of this…
We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions.…
By means of the Hamiltonian approach to two-dimensional wave motions in heterogeneous fluids proposed by Benjamin, we derive a natural Hamiltonian structure for ideal fluids, density stratified in four homogenous layers, constrained in a…
We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector rather than the velocity. It enables a feasible Lagrangian study of fluid dynamics, as the isosurface of…
We prove local well-posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose…