Weak finite-time Melnikov theory and three-dimensional viscous perturbations of Euler flows
From MaRDI portal
Publication:1852652
DOI10.1016/S0167-2789(02)00742-XzbMath1006.76020OpenAlexW2028615390MaRDI QIDQ1852652
Sanjeeva Balasuriya, Christopher K. R. T. Jones, Igor Mezić
Publication date: 7 January 2003
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0167-2789(02)00742-x
perturbationordinary differential equationsvanishing viscosityMelnikov theoryfluid particle trajectoriesEuler flowtwo-dimensional heteroclinic manifold destruction
Navier-Stokes equations for incompressible viscous fluids (76D05) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45)
Related Items
Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows, Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux, Leaving flatland: diagnostics for Lagrangian coherent structures in three-dimensional flows, Stochastic Sensitivity: A Computable Lagrangian Uncertainty Measure for Unsteady Flows, Optimal perturbation for enhanced chaotic transport, Explicit invariant manifolds and specialised trajectories in a class of unsteady flows
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exponential dichotomies, heteroclinic orbits, and Melnikov functions
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- An example of bifurcation to homoclinic orbits
- Global bifurcations and chaos. Analytical methods
- Chaotic transport in dynamical systems
- Dichotomies in stability theory
- Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II: Construction of the Navier-Stokes solution
- On the integrability and perturbation of three-dimensional fluid flows with symmetry
- Transport in 3D volume-preserving flows
- Vanishing viscosity in the barotropic \(\beta\)-plane
- On steady flows with Lamb surfaces
- Well-posedness of the Euler and Navier-Stokes equations in the Lebesgue spaces \(L^ p_ s({\mathbb{R}}^ 2)\)
- Exponential dichotomies and transversal homoclinic points
- Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
- Nonstationary plane flow of viscous and ideal fluids
- Groups of diffeomorphisms and the motion of an incompressible fluid
- Nonstationary flows of viscous and ideal fluids in \(R^3\)
- Chaotic advection in bounded Navier–Stokes flows
- An analytical study of transport, mixing and chaos in an unsteady vortical flow
- Predicting chaotic dispersion with Eulerian symmetry measures: Wavy Taylor-vortex flow
- Some remarks on chaotic particle paths in time-periodic, three-dimensional swirling flows
- The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
- The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems
- Viscous perturbations of vorticity-conserving flows and separatrix splitting
- Reduction of three-dimensional, volume-preserving flows with symmetry
- Melnikov theory for finite-time vector fields
- The Convergence with Vanishing Viscosity of Nonstationary Navier-Stokes Flow to Ideal Flow in R 3
- Invariant manifolds