The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Vortex merger near a topographic slope in a homogeneous rotating fluid

This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.PostprintPeer reviewe

Analysis of viscous fluid flow in a pressure-swirl atomizer using large-eddy simulation

A computational fluid dynamics study is carried out on the inner nozzle flow and onset of liquid sheet instability in a large-scale pressure-swirl atomizer with asymmetric inflow configuration for high viscosity fluids. Large-eddy simulations (LES) of the two-phase flow indicate the unsteady flow character inside the nozzle and its influence on liquid sheet formation. A novel geometric volume-of-fluid (VOF) method by Roenby et al. (2016), termed isoAdvector, is applied for sharp interface capturing. We carry out a Reynolds number sweep (420 ≤ Re ≤ 5300) in order to investigate the link between the asymmetric inner nozzle flow and liquid sheet characteristics in laminar, transitional and fully turbulent conditions. Inside the nozzle, the numerical simulations reveal counter-rotating Dean vortices, flow impingement locations, and strong asymmetric flow features at all investigated Reynolds numbers. A helical, rotating gaseous core is observed when Re ≥ 1660. For laminar flow (Re=420), an S-shaped liquid film isobserved, while the gas core presence at Re ≥ 1660 results in a hollow cone liquid sheet. For the intermediate value Re=830, the numerical simulations indicate a liquid sheet of mixed type. Consequences of the inflow asymmetry and Reynolds number to the uniformity of the injected liquid mass distribution and liquid sheet instability are pointed out.Peer reviewe

Comparison of collective Thomson scattering signals due to fast ions in ITER scenarios with fusion and auxiliary heating. Plasma Physics and Controlled Fusion, 51(3):035006

Abstract. Auxiliary heating such as neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH) will accelerate ions in ITER up to energies in the MeV range, i.e. energies which are also typical for alpha particles. Fast ions of any of these populations will elevate the collective Thomson scattering (CTS) signal for the proposed CTS diagnostic in ITER. It is of interest to determine the contributions of these fast ion populations to the CTS signal for large Doppler shifts of the scattered radiation since conclusions can mostly be drawn for the dominant contributor. In this study, fast ion distribution functions are calculated for beam ions with the ASCOT code or for fast ions generated by ICRH with the PION code for a steady-state ITER burning plasma equilibrium. The parameters for the auxiliary heating systems correspond to the design currently foreseen for ITER. The geometry of the CTS system for ITER is chosen such that near perpendicular and near parallel velocity components are resolved. In the investigated ICRH scenario, waves at 50 MHz resonate with tritium at the second harmonic off-axis on the low field side. Effects of a minority heating scheme with 3 He are also considered. CTS scattering functions for fast deuterons, fast tritons, fast 3 He, and the fusion born alphas are presented, revealing that fusion alphas dominate the measurable signal by an order of magnitude or more in the Doppler shift frequency ranges typical for fast ions. Hence the observable CTS signal can mostly be attributed to the alpha population in these frequency ranges. The exceptions are limited regions in space with some non-negligible signal due to beam ions or fast 3 He which give rise to about 30% and 10-20% of the CTS signal, respectively. In turn, the dominance of the alpha contribution implies that the effects of other fast ion contributions will be difficult to observe by CTS