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We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the…
Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study…
The vortex dynamics of Euler's equations for a constant density fluid flow in $R^4$ is studied. Most of the paper focuses on singular Dirac delta distributions of the vorticity two-form $\omega$ in $R^4$. These distributions are supported…
For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the…
Ocean submesoscales, flows with characteristic size around 10 m - 10 km, are transitional between the larger, rotationally-constrained mesoscale and three-dimensional turbulence. In this paper we present simulations of a submesoscale ocean…
At high Reynolds number, the interaction between two vortex tubes leads to intense velocity gradients, which are at the heart of fluid turbulence. This vorticity amplification comes about through two different instability mechanisms of the…
The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlators and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes…
The complex flow features resulting from the laminar-turbulent transition (LTT) in a sudden expansion pipe flow, with expansion ratio of 1:2 subjected to an inlet vortex perturbation is investigated by means of direct numerical simulations…
We investigate the 2D instability recently discussed by Gallet et al. (2010) and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed on a centrifugally-stable swirling flow. By finding a simpler rectilinear example of…
Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent…
In particle-laden turbulent flows the turbulence in carrier fluid phase gets affected by the dispersed particle phase for volume fraction above $10^{-4}$ and hence reverse coupling or two-way coupling becomes relevant in that volume…
Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability…
This paper develops a simple model of the inertial range of turbulent flow, based on a cascade of vortical filaments. A binary branching structure is proposed, involving the splitting of filaments at each step into pairs of daughter…
We investigate the dynamic behavior of optical vortices, or phase singularities, in random wavefields and demonstrate the direct experimental observation of the anomalous diffusion of optical vortices. The observed subdiffusion of optical…
In this paper, we find a new large scale instability displayed by a rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic…
In this work, we study numerically the temporal evolution of an initially random large-scale velocity field under governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution.…
We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…
In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and…
In a recent article (Forterre, PRL, 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we…
We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDL) is accompanied by an intrinsic drift of the pattern. Single…