Ionut Danaila

Coherent structures in a round, spatially evolving, unforced, homogeneous jet at low Reynolds numbers

Three–dimensional direct numerical simulations of unforced, incompressible, free, spatially evolving round jets are used to investigate the onset of instability at low diametral Reynolds numbers (Re⩽500). Compact, coherent structures are identified by means of iso-surfaces of vorticity and pressure fields and shown to be synonymous with instability modes. Once the inflow velocity profile is fixed, as the Reynolds number increases from 200 to 500, the most amplified unstable mode switches from the helical mode to the axisymmetric one, as expected from the predictions of the viscous linear stability theory analysis and from experimental observations [J. Fluid Mech. 77, 511 (1976); Prog. Aerosp. Sci. 21, 159 (1984)] [ J. Fluid Mech. 48, 547 (1971)]. At the upper limit of the investigated range of Reynolds numbers, the present simulations are consistent with the widely accepted scenario of the space time development of the round jet instability. This scenario is analyzed in detail. The appearance of pairs of ...

Direct numerical simulation of bifurcating jets

The mechanisms leading to bifurcating jets are investigated by means of direct numerical simulation. Two distinct types of jets were obtained by applying a bi-modal perturbation at the nozzle. When forcing simultaneously the counter-rotating helical modes (flapping mode) with the same amplitude and the same frequency, the jet splits into two branches, taking a distinct Y-shape. A different evolution of the jet (Ψ-shape) is observed when superposing the axisymmetric mode at the most amplified unstable frequency on the flapping mode with the same amplitude, but subharmonic frequency. In both cases a spectacular increase of the jet spreading is observed.

A New Sobolev Gradient Method for Direct Minimization of the Gross-Pitaevskii Energy with Rotation

In this paper we improve traditional steepest descent methods for the direct minimization of the Gross-Pitaevskii (GP) energy with rotation at two levels. We first define a new inner product to equip the Sobolev space

Giant vortices in combined harmonic and quartic traps

H^1

Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement

and derive the corresponding gradient. Second, for the treatment of the mass conservation constraint, we use a projection method that avoids more complicated approaches based on modified energy functionals or traditional normalization methods. The descent method with these two new ingredients is studied theoretically in a Hilbert space setting, and we give a proof of the global existence and convergence in the asymptotic limit to a minimizer of the GP energy. The new method is implemented in both finite difference and finite element two-dimensional settings and is used to compute various complex configurations with vortices of rotating Bose-Einstein condensates. The new Sobolev gradient method shows better numerical performances compared to classical

Three-dimensional vortex configurations in a rotating Bose-Einstein condensate

L^2

Numerical simulation of the postformation evolution of a laminar vortex ring

or

A Newton method with adaptive finite elements for solving phase-change problems with natural convection

H^1

An Introduction to Scientific Computing

gradient methods, especially when high rotation rates are considered.

Vector Dark-Antidark Solitary Waves in Multi-Component Bose-Einstein condensates

We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation and analyze in detail the structure of vortices. For a quartic-plus-harmonic potential, as the angular velocity increases, the vortex lattice evolves into a vortex array with hole. The merging of vortices into the hole is highly three dimensional, starting from the top and bottom of the condensate to reach the center. We also investigate the case of a quartic-minus-harmonic potential, not covered by experiments or previous numerical works. For intermediate repulsive potentials, we show that the transition to a vortex array with hole takes place for lower angular velocities, when the lattice is made up of a small number of vortices. For the strong repulsive case, a transition from a giant vortex to a hole with a circle of vortices around is observed.