3D structures and dispersion in shallow fluid layers

Many experiments have been performed in electromagnetically driven shallow fluid layers to study two-dimensional (2D) turbulence. The shallowness of the fluid layer is commonly assumed to ensure 2D dynamics. However, contrary to the theory and numerical simulations on 2D turbulence, the experimental realisations are never purely 2D. For example, laboratory setups are bounded by a no-slip bottom and stress-free surface, which implies a vertical gradient. Surprisingly, deviations from two-dimensionality in such shallow fluid setups have hardly received any attention. The aim of this thesis was to investigate the influence of boundary and initial condition on the development of three-dimensional (3D) motion in-side shallow fluid layers. For this purpose, a dipolar vortex was considered as the canonical coherent structure in the shallow fluid layer. The dipolar vortex is one of the most elementary vortex structures in 2D turbulence. Such a vortex structure can be conveniently created by electromagnetic forcing. The first two configurations that have been investigated are the dipolar vortex in a shallow one- and two-fluid layer situation. The latter (stably stratified) two-layer setup was assumed to be an improvement with respect to the single layer configuration. Finally, the following shallow-fluid layer experiment has been considered: a periodically forced linear array of vortices near a lateral wall. All measurements have been performed with Stereoscopic Particle Image Velocimetry, providing the three-component velocity field on a horizontal plane inside the fluid layer. Furthermore, all these experiments were complemented by 3D numerical simulations of the Navier-Stokes equation. Based on the experimental and numerical results, the necessary condition for development of 3D motion in such shallow fluids was determined to be a vertical variation of the horizontal velocity field. Inside the two individual vortex cores an oscillating up- and downward motion was seen, as well as a spanwise vortex in front of the dipole. Free-surface deformations were proven to be of minor importance in generating 3D motions. Furthermore, friction exerted by the no-slip bottom and the flow initialisations were shown not to be primary actors in generating the observed complex and persistent 3D motions. Surprisingly, the 3D flow evolution of the dipole in the two-layer configuration evolved in a similar way as already seen in the single-layer setup. Contrary to statements in literature, the so-called frontal circulation was also observed in the two-layer configuration. The emergence of this structure has a different origin, however, it resulted from baroclinic vorticity production at the internal interface in stead of a propagating motion over the solid bottom of the single-layer dipole. Based on the comparison of the ratio of kinetic energy (contained in the vertical and horizontal flow components) between the single- and two-layer fluid, the two-layer fluid is not an improvement over the single-layer configuration. For the linear array of vortices, the influence of 3D motion and the presence of a lateral wall on the passive tracer transport was investigated. It was observed that particles released at the free surface form long filament-like structures related to the surface flow being convergent, in contrast with the purely 2D numerical simulations where the velocity field is by defini- tion divergence-free and a more homogeneous particle distribution remained throughout the time evolution. Particles released at mid-depth of the fluid illustrated the efficient vertical mixing: already after one forcing period the particles were almost dispersed homogeneously over the full depth of the fluid layer. With the presence of a lateral wall this rapid vertical dispersion is even further enhanced in the near-wall region. In summary, this thesis reveals the intrinsic three-dimensional flow behaviour of shallow fluid layers. Furthermore, experiments with a linear array of vortices illustrate the influence of the three-dimensional flow field and lateral walls on the dispersion of passive tracers. All the experimental and numerical results indicate that the interpretation of such experiments as two-dimensional realisations should be done with caution

On 3D structures of dipolar vortices in a shallow fluid layer

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Direct and inverse pumping in flows with homogeneous and non-homogeneous swirl

The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodew\"adt problem, where the swirl tends towards an aysmptotic value away from the wall, the well-known "tea-cup effect" drives a flow away from the plate at the centre of the vortex. Simple dimensional arguments applied to a single vortex show that if the intensity of the swirl decreases away from the wall, the sense of the recirculation can be inverted, and that the associated flow rate scales with the swirl gradient. Only if the flow is quasi-2D, does the classical tea-cup effect take place. This basic theory is confirmed by numerical simulations of a square array of steady, electrically driven vortices. Experiments in the turbulent regimes of the same configuration reveal that these mechanisms are active in the average flow and in its fluctuating part. The mechanisms singled out in this letter provide an explanation for previously observed phenomena in electrolyte flows. They also put forward a possible mechanism for the generation of helicity in flows close to two-dimensionality, which plays a key role in the transition between 2D and 3D turbulence

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $\Omega$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $\Omega=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_{\lambda}\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($\Omega\lesssim 0.2$ rad/s) to quasi-2D turbulence ($\Omega\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.Comment: 17 pages, 6 figures, 3 table

Three-dimensional structures in quasi-two-dimensional shallow flows

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Multidisciplinary Analysis of CROR Propulsion Systems: DLR Activities in the JTI SFWA Project

In the frame of the EU 7th Framework Joint Technology Initiative Smart Fixed Wing Aircraft project, the DLR Institute of Aerodynamics and Flow Technology (DLR-AS) is participating as an associated partner in the Airbus-led studies of the Contra-Rotating Open Rotor (CROR) as possible powerplant for future transport aircraft. Due to significant technical challenges in terms of noise emissions, installation effects and certification that still need to be addressed for this novel propulsion system, the numerical activities require the use of sophisticated multidisciplinary analysis tools and approaches covering aerodynamics, aeroacoustics and aeroelastics. In this paper an overview of the DLR-AS work in the project is given, which covers the numerical assessment of a novel noise reduction technology, an initial study of blade aeroelasticity as well as some in-depth studies on isolated and installed pusher-configuration CROR engine configurations. The first results of a validation of the numerical simulations using experimental test data that is being generated in Airbus-led low-speed wind tunnel tests are also presented