Simone Zuccher

Quantum vortex reconnections

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnections are time symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium and discuss the different length scales probed by the two models and by experiments.

Algebraic growth in a Blasius boundary layer: optimal and robust control by mean suction in the nonlinear regime

Optimal and robust control for the three-dimensional algebraically growing instability of a Blasius boundary layer is studied in the nonlinear regime. First, adjoint-based optimization is used to determine an optimal control in the form of a spanwise-uniform wall suction that attenuates the transient growth of a given initial disturbance, chosen to be the optimal perturbation of the uncontrolled flow. Secondly, a robust control is sought and computed simultaneously with the most disrupting initial perturbation for the controlled flow itself. Results for both optimal and robust control show that the optimal suction velocity peaks near the leading edge. In the robust-control case, however, the peak value is smaller, located farther downstream from the leading edge, and the suction profile is much less dependent on the control energy than in the optimal-control case.

Parabolic approach to optimal perturbations in compressible boundary layers

Optimal perturbations in compressible, non-parallel boundary layers are considered here. The flows past a flat plate and past a sphere are analysed. The governing equations are derived from the linearized Navier–Stokes equations by employing a scaling that relies on the presence of streamwise vortices, which are well-known for being responsible for the ‘lift-up’ effect. Consequently, the energy norm of the inlet perturbation encompasses the wall-normal and spanwise velocity components only. The effect of different choices of the energy norm at the outlet is studied, testing full (all velocity components and temperature) and partial (streamwise velocity and temperature only) norms. Optimal perturbations are computed via an iterative algorithm completely derived in the discrete framework. The latter simplifies the derivation of the adjoint equations and the coupling conditions at the inlet and outlet. Results for the flat plate show that when the Reynolds number is of the order of 10 3 , a significant difference in the energy growth is found between the cases of full and partial energy norms at the outlet. The effect of the wall temperature is in agreement with previous parallel-flow results, with cooling being a destabilizing factor for both flat plate and sphere. Flow divergence, which characterizes the boundary layer past the sphere, has significant effects on the transient growth phenomenon. In particular, an increase of the sphere radius leads to a larger transient growth, with stronger effects in the vicinity of the stagnation point. In the range of interesting values of the Reynolds number that are typical of wind tunnel tests and flight conditions for a sphere, no significant role is played by the wall-normal and streamwise velocity components at the outlet.

Helicity conservation under quantum reconnection of vortex rings.

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross-Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that the total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion, and intrinsic twist of the reconnecting vortex rings.

Optimal Disturbances in the Supersonic Boundary Layer Past a Sharp Cone

Optimal disturbances for the supersonic ∞ow past a sharp cone are computed in order to assess the efiects due to ∞ow divergence. This geometry is chosen because previously published studies on compressible optimal perturbations for ∞at plate and sphere did not allow to discriminate the in∞uence of divergence alone, as many factors characterized the growth of disturbances on the sphere (∞ow divergence, centrifugal forces and dependence of the edge parameters on the local Mach number). Flow-divergence efiects result in the presence of an optimal distance from the cone tip for which the optimal gain is the largest possible, showing that divergence efiects are stronger in the proximity of the cone tip. By properly rescaling the gain, wavenumber and streamwise coordinate due to the fact that the boundary layer on the sharp cone is p 3 thinner than the one over the ∞at plate, it is found that both the gain and the wavenumber compare fairly well. Moreover, results for the sharp cone collapse into those for the ∞at plate when the initial location for the computation tends to the flnal one and when the azimuthal wavenumber is very large. Results show also that a cold wall enhances transient growth.

Optimal disturbances in compressible boundary layers - Complete energy norm analysis

In the present work we revise results of transient growth in compressible boundary layers (∞at plate and sphere) to consider the complete Mack energy norm at the outlet, without the assumption that the out∞ow perturbation is comprised solely of streaky structures. Optimal perturbations are still in the form of counter-rotating streamwise vortices and this justifles the choice of the scaling in the governing equations. A strong efiect of the complete (full) energy norm at the outlet is found for the ∞at plate in supersonic regimes. No signiflcant efiects of the choice of the outlet norm can be appreciated for the sphere, in the range of parameters that are relevant to wind tunnel testing or ∞ight conditions.

The phase-locked mean impulse response of a turbulent channel flow

We describe the first DNS-based measurement of the complete mean response of a turbulent channel flow to small external disturbances. Space-time impulsive perturbations are applied at one channel wall, and the linear response describes their mean effect on the flow field as a function of spatial and temporal separations. The turbulent response is shown to differ from the response of a laminar flow with the turbulent mean velocity profile as the base flow.

Relaxation of twist helicity in the cascade process of linked quantum vortices

By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged throughout the process. The gradual transfer from writhe (due to initial linking) to twist helicity, followed by a continuous relaxation of twist across scales during the evolution is shown to be a generic mechanism that consistently takes place on each individual component.

Cubic nonlinear Schrödinger equation with vorticity

In this paper, we introduce a new class of nonlinear Schrodinger equations (NLSEs), with an electromagnetic potential(A,8), both depending on the wavefunction9. The scalar potential8 depends on |9| 2 , whereas the vector potential A satisfies the equation of magnetohydrodynamics with coefficient depending on9. In Madelung variables, the velocity field comes to be not irrotational in general and we prove that the vorticity induces dissipation, until the dynamical equilibrium is reached. The expression of the rate of dissipation is common to all NLSEs in the class. We show that they are a particular case of the one-particle dynamics out of dynamical equilibrium for a system of N identical interacting Bose particles, as recently described within stochastic quantization by Lagrangian variational principle. The cubic case is discussed in particular. Results of numerical experiments for rotational excitations of the ground state in a finite two-dimensional trap with harmonic potential are reported.

The Inverse Power Method for the

We present an inverse power method for the computation of the first homogeneous eigenpair of the