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We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection-diffusion equation to…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…
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)…
Linear global instability of the three-dimensional (3-D), spanwise-homogeneous laminar separation bubble (LSB) induced by shock-wave/boundary-layer interaction (SBLI) in a Mach 7 flow of nitrogen over a $30^{\circ}-55^{\circ}$ double wedge…
Turbulence and chaos play a fundamental role in stellar convective zones through the transportof particles, energy and momentum, and in fast dynamos, through the stretching, twisting and folding of magnetic flux tubes. A particularly…
We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular this yields the structure of stationary hydraulic jumps, both in their circular and linear versions,…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous porous media. Although it is now well recognised that novel transport phenomena can…
We introduce a time-dependent Eulerian-Lagrangian length-scale and an inverse locality hypothesis which explain scalings of second order one-particle Lagrangian structure functions observed in Kinematic Simulations (KS) of homogeneous…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…
We consider the incompressible three-dimensional Euler equations for a vortex ring with Kelvin waves undergoing radially expanding Lagrangian transport. To clarify the fundamental mechanisms underlying nonlinear scale-local deformations of…
In the preliminary design of space missions it can be useful to identify regions of dynamics that drive the system's behaviour or separate qualitatively different dynamics. The Lagrangian Coherent Structure (LCS) has been widely used in the…
Linear stability of supersonic flow over a short compression corner with ramp angles 30 and 42 is investigated using Direct Simulation Monte Carlo (DSMC) and Linear Stability Theory (LST) at Mach number 3, Reynolds number 11,200 and low…
We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…
Deterministic and probabilistic tools from nonlinear dynamics are used to assess enduring near-surface Lagrangian aspects of the Malvinas Current. The deterministic tools are applied on a multi-year record of velocities derived from…
Irreversible transport is generally attributed to vorticity, nonlinear forcing, or explicit symmetry breaking. We show that it can arise even in strictly time-periodic and locally irrotational flows through a purely geometric mechanism. By…
We introduce a new global Lagrangian descriptor that is applied to flows with general time dependence (altimetric datasets). It succeeds in detecting simultaneously, with great accuracy, invariant manifolds, hyperbolic and non-hyperbolic…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…