ETC2019 17th European Turbulence Conference Submission

16:15 Rotating Flows 3

16:15 15 mins #223	Anistropy without waves in rotating turbulence Jonathan Brons, Alban Potherat, Peter Thomas Abstract: In this study the question of how anisotropy develops in flows subject to background rotation, especially turbulent ones, is addressed. Inertial waves are generally accepted as the most efficient mechanism to transport energy anisotropically. They have been shown to transfer energy to large anisotropic, columnar structures, either through linear wave propagation or non-linear triadic interactions. Nevertheless, they cannot account for the formation of simpler steady anisotropic phenomena such as Taylor columns. Inspired by similar phenomena seen in turbulent magnetohydrodynamic flows we propose that more than one mechanism involving the Coriolis force may promote anisotropy. When the Rossby number is small, Ro<1, columnar structures of a finite length lz form as a consequence of either viscous or inertial forces opposing the Coriolis force acting on the flow field. In the inviscid limit (Re\gg1) it is shown theoretically that lz ~ Ro^-1. Equations for the average flow quantities are derived, which allow for a detailed investigation of the influence fluctuations on the mechanism driving anisotropy, with a particular focus on inertial waves. The proposed theory is tested experimentally by generating a turbulent flow field through simultaneous fluid injection and withdrawal at the bottom wall of a fluid tank situated atop a rotating turntable. From 2D-PIV measurements across a plane parallel and a number of planes perpendicular to the axis of rotation the proposed scaling for the lz is recovered experimentally. Further analysis of the average flow equations revealed that in the limit of Ro->0 the anisotropy of the average of a turbulent rotating flow develops neither as the result of inertial waves nor following the same mechanism as in Taylor columns, but from an interplay between the Coriolis force and average advection.
16:30 15 mins #431	ON THE COMPLEX BEHAVIOR OF THE LATERAL WALL BOUNDARY LAYER IN AN EXPERIMENTAL CO-ROTATING SPLIT-CYLINDER FLOW Jesús Oscar Rodríguez-García, Javier Burguete Abstract: Instabilities in rotating flows have a great interest due to their presence in many natural and industrial systems. In enclosed rotating cavities, a differential rotation creates secondary flows which can drive instabilities. And, when the background rotation is large enough, these secondary flows are restricted to the boundary layers being the internal bulk in almost solid-body rotation at the average angular velocity of the cavity. Regarding these systems, Stewartson studied the flow created in a cylindrical cavity where the lateral wall is rotating faster than the end walls finding a sandwich-like boundary layer at the cylindrical wall. An infinite cylinder split in two with one side rotating faster than the other was studied by Hocking but, for this configuration, the Ekman pumping does not appear. Then, van Heijst studied the finite case of the split cylinder using boundary layer analysis and also recovered the sandwich structure of the Stewartson boundary layer. This problem has been studied numerically focusing on the instability of the secondary flow. In this work, we study the flow in a split cylinder with one side rotating faster than the other experimentally using two PMMA co-rotating cylinders separated with a little gap to avoid friction between cylinders. The cylinders are inside a prismatic cell to avoid the fluid leaks. Each cylinder has a fixed radius, R = 5 cm, and a variable length, L, to change the aspect ratio. For the present work, the aspect ratios fixed and equal to 2. The main dimensionless parameters to characterize the flow inside the split cylinder are the Reynolds number, Re, and the Rossby number, Ro. The lateral wall boundary layer of the split cylinder is studied using a 1D LDV system for a large range of Re and Ro finding different phenomena. The azimuthal velocity of the boundary layer presents regular jumps among different values depending on the parameters which have been associated with rolls rotating near the cylindrical wall. In the azimuthal velocity the sandwich-like behavior of the Stewartson boundary layer has been found and compared with the theoretical results finding a good agreement. In the experimental case, this component of the velocity presents another behavior together with the sandwich structure that has been identified as a Kelvin mode m = 1 due to a little misalignment between cylinders intrinsic to the experimental setup. The Kelvin mode could be assimilated as the modes that appear in precessing cylinders. Finally, two columns have been observed near the axis of the cylinders but their origin is not clear yet so they could appear even in an experimental setup without misalignment.
16:45 15 mins #505	Instability of steady flow in precessing spheroids in a moderate Reynolds-number regime Yasufumi Horimoto, Atsushi Katayama, Susumu Goto Abstract: Precession of a rotating container (that is, the rotation of the spin axis of the container) filled with a viscous fluid can easily sustain a variety of fascinating flows including developed turbulence. We experimentally investigate the onset of unsteady flow, namely instability of steady flow in precessing spheroids as well as a precessing sphere by conducting particle image velocimetry (PIV). Our results mean that an instability recently found for the sphere can also occur and dominates in the spheroids for moderate Reynolds numbers. It is worth emphasizing that this cannot be found by an asymptotic analysis for the spheroid at the limit that the Reynolds number is infinitely high. At the conference, we will also discuss the relationship between this new instability and the existing ones for the spheroids.
17:00 15 mins #150	Does perforation relaminarize turbulent wakes? Vagesh Narasimhamurthy, Abhinav Singh Abstract: Despite vast literature on the bluff-body wake phenomena, the effect of perforation on wakes is not quite well understood. An early experimental investigation into turbulent wake behind perforated plates [1] reveal that the vortex-street is dominant below the critical porosity β ≈ 20% (where β is the ratio of open area to the total plate area), while it ceases to exist beyond this β. This regime shift was accompanied by abrupt changes in drag coefficient (C d ), Strouhal number (St) and peak turbulence intensity. The high porosity regime (β > 20%) was further characterized by an unusual unsteadiness in the “far” wake region. Nevertheless, no further information exists on the transitional dynamics of a wake under the influence of perforation. In the present DNS study, Reynolds number Re d , based on inflow velocity U o and plate width d, is set to 250, which is well above the critical transition Re d ≈ 105 − 110 for a non-perforated flat plate placed normal to the free-stream [2]. The perforated thin plate considered in this DNS consist of six equidistantly spaced square holes of size h = 0.4d and pitch 1d corresponding to β = 16%. Figure 1 shows λ 2 iso-contours illustrating distinct vortex topology at β = 0% and 16%. It is apparent from figure 1(b) that perforation nearly suppresses the formation of “near” wake vortex street (see the corresponding quiescent w− velocity signal in the “near” wake) and displaces it downstream as a near periodic “far” wake. Here, the terms “near” and “far” correspond to signal recording locations 1d and 15d downstream of the plate, respectively. The current DNS revealed two distinct dominant frequencies corresponding to the “near” and “far” wake, i.e. in contrast to a single dominant frequency reported by [1]. The “near” wake vortex street suppression is further accompanied by a drastic reduction in C d by about 50% when compared to non-perforated plate. It is to be noted that the high frequency irregularities in the w− velocity signal at β = 0% disappears at β = 16%. The low Re turbulent wake at β = 0% appears to be altered by perforation to a “quasi-laminar” state along with the existence of fairly regular stream-wise vortex pairs at β = 16%. These secondary vortical structures possess a symmetric pattern from one braid to the next with a span-wise wavelength of ≈ 1d, in contrast to a wavelength of ≈ 2d reported for non-perforated plates [2]. The quasi-periodicity in the wake at β = 16% is further characterized by a substantial increase in Strouhal number as a result of increased spectral energy associated with the span-wise vortex tubes. The cross-stream wake width drastically reduced to about 40% by perforation. Such a behavior could be a consequence of reduction in the flow three-dimensionality with the accompanying reduction of v rms (spanwise rms velocity). The current observations indicate that the perforation Reynolds number Re h (based on hole size) plays a major role on the relative loss of three-dimensionality in the wake. The interplay between Re h and wake further leads to the question, whether perforation can re-laminarize an already turbulent wake, and we aim to explore this further.
17:15 15 mins #308	Mean flow generation in rotating annulus with stochastic methods Wenchao Xu, Uwe Harlander Abstract: In fluid mechanics, the notation "energy cascade" refers to that the energy transfers from large scale motion to small scale motion, which is also called direct energy cascade. An inverse energy cascade also exists, where the energy transfers upscale from small scale motion to large scale motion. In a 3D rotating flow field, the entire turbulent fields can be described as a composition of interacting inertial waves. Linear inertial waves transfer injected energy and distribute the energy directly and inversely both in space and time. This theory is experimentally studied in Yarom and Sharon (2014)). Our research project focuses on investigating the influence of deep-seated stochastic shear force on Taylor-Couette flow. The laboratory experiments were carried out with an annulus that consisted of two independent rotating cylinders and partially filled with deionized water. A conic hollow cylinder is fixed at the bottom with small obstacles to generate stochastic motions and rotates simultaneously with the outer cylinder. A camera is installed over the tank and co-rotating with the outer cylinder. Illuminated by a co-rotating horizontal laser sheet, the flow velocity field in horizontal section can be quantitatively measured by using Particle Image Velocimetry (PIV). Our investigation experimentally studies the influence of a stochastically forced motion on the rotating flow. With stochastic forcing, the obstacles on the bottom excite small scale inertial waves. These waves transfer energy to wide range of length- and timescales and therefore might lead to a deep seated steady turbulent rotating flow and constraint large-scale motions.
17:30 15 mins #498	DYNAMICS OF TRANSITION TO TURBULENCE IN AXIAL VORTEX BREAKDOWN Manjul Sharma, Vishnu R, Sameen A Abstract: Flow inside a cylinder with one rotating end is a model to generate axial vortex and has been used to study vortex breakdown both experimentally as well as computationally (Escudier, 1984). This flow depends on two parameters, namely, aspect ratio, defined as Γ = H/R, and Reynolds number, defined as Re = ωR^2 /ν. Here, H and R are the height and the radius of the cylinder respectively, ω is the angular speed of the rotating top lid, and ν is the kinematic viscosity of the fluid. It exhibits bubble-type vortex breakdown beyond a certain value of Reynolds number, which affects the dynamics of the flow significantly, before leading to a turbulent state. In the present computational study, we investigate the route to turbulence through various bifurcations by varying the parameters Re and Γ. To study the dynamics of the flow, numerical probes are placed near the non-rotating bottom wall of the cylinder. Phase space of the flow is reconstructed using timeseries obtained from these probes (Abarbanel et al., 1993). For Γ = 2.5, the basic state of the flow is a steady and axisymmetric flow with two vortex breakdown bubbles. The first bifurcation of this flow is limit cycle behaviour as shown in the figure 1a leading to an axisymmetric periodic flow which occurs at Re ≈ 2600 for Γ = 2.5. The breakdown bubble oscillates along the axis periodically. The system bifurcates to period-two behaviour at Re ≈ 3400 as shown in figure 1b. This secondary bifurcation is related to the appearance of a modulated rotating azimuthal wave of wavenumber k = 5 which breaks the symmetry of the flow. This wave precesses in the same direction as the mean flow. Transition to weak turbulence is also governed by the various modes of rotating waves, in addition to k = 5, resulting from the subsequent bifurcations for Γ = 2.5. Hence, the route to turbulence for small aspect ratios (Γ ≤ 2.5) is a sequence of bifurcations first leading to axisymmetric periodic flow, subsequently, a symmetry breaking by azimuthal waves and finally a weak turbulent state supporting various modes. A specific focus of this study is to understand the route to turbulence for higher aspect ratios. Complete route from steady state to turbulence in the Γ − Re parameter space will be presented.
17:45 15 mins #500	Ekman layer resonance in an ocean-analog rotating tank experiment Miklos Vincze, Nora Fenyvesi, Marten Klein, Samuel Viboud, Joel Sommeria, Yosef Ashkenazy Abstract: One of the main open problems related to the energetics of global ocean circulation is the nature of the processes that mix the deep ocean. According to the classic theory of Ekman, constant wind stress at the water surface yields significant mixing of the seawater. This effect is confined only to an approximately 100 m thick Ekman layer at the top of the water column, as long as only stationary wind stress is considered. However, the temporal variability of wind stress}acting on the ocean surface may have a significant impact on the energy transfer between the surface ocean and the abyssal ocean. In particular, the surface ocean layer is expected to deepen when the wind's frequency matches the inertial (Coriolis) frequency, through ``Ekman layer resonance''. Here, we report on laboratory experiments conducted in the large circular rotating tank of the LEGI Coriolis platform (13 m in diameter and 0.5 m in depth) to investigate the effect of oscillating horizontal shear imposed at the water surface. The analysis of the flow structure by means of particle image velocimetry (PIV) reveals a resonant thickening of the top Ekman layer and a marked increase in the kinetic energy of the flow occurs when the forcing frequency coincides with the Coriolis frequency of the rotating tank. The findings are in agreement with the theoretical expectations and constitute evidence for the existence of the Ekman layer resonance (or near inertial resonance) phenomenon in an ocean-like configuration}. The results clearly demonstrate that a significant resonant thickening of the surface boundary layer associated with an increasing kinetic energy in the flow can be observed in an experimental setting where temporally oscillating and spatially correlated shear -- `wind stress' -- is applied at the water surface in a rotating system. In agreement with the theoretical expectations and sparse field data the resonance occurs at the Coriolis frequency. When contrasting the experimental data with solutions of the analytic approximation of the oscillating Ekman layer one finds that the weakly turbulent nature of the observed flow manifests itself mostly in the presence of non-negligible vertical velocity components. Yet, the overall character of the resonance (its frequency, the velocity profiles, the amplitude dependence) remains in fairly good agreement with the approximation.
18:00 15 mins #499	MODELING PLANETARY ATMOSPHERES AND OCEANS IN THE LABORATORY Stefania Espa, Simon Cabanes, Enrico Ferrero, Renato Forza, Boris Galperin, Federica Ive, Massimiliano Manfrin, Peter L. Read, Hélène Scolan Abstract: We present results from an experimental campaign carried out in the framework of a project funded by EuHIT [1] and aimed at the investigation of complex interactions between eddies, waves and turbulence in rotating forced flows, turbulence anisotropization, and associated transport processes [2]. The overall goal was to emulate large-scale planetary and oceanic circulations with a specific focus on replicating the regime of zonostrophic turbulence, deliniated by strongly anisotropic energy spectra and the formation of slowly evolving systems of alternating zonal jets [3]. This regime is characterized by two scales, L~(/3)1/5 and LR ~(Urms/)1/2, where  is the transfer rate of the inverse energy cascade and  is the radial gradient of the Coriolis parameter, and their ratio, known as the zonostrophy index, R = LR/L [4]. In unaveraged flows, zonal jets become discernible at R~2 while for the strong jets on the Giant Planets, R~5. Achieving such high values of R in a laboratory is a non-trivial task. Experiments were performed in the 5 m diameter rotating tank at the TurLab laboratory in Turin. The tank, rotating counterclockwise with a variable rotation period Trot in the range 20s-120s, was filled with a 56 cm deep layer of fresh water. The -effect was generated by a rigid, conical bottom boundary (radial slope angle~10°) centered on the axis of symmetry of the tank. Turbulence was excited by a comb of partially immersed, vertically oriented paddles periodically oscillating forward and backward along a single radius and interspaced at 10 cm. The comb speed, ucomb, was varied in the range 5cms-1-10cms-1; the estimated forcing period was always shorter than the corresponding shortest Rossby wave. To perform velocity measurements the fluid was seeded with tracer particles (dp~30μm), the system was lit by a light sheet generated by a 6W solid state green laser, while two Dalsa 4Mpx digital cameras were used to acquire flow images at 3fps, each data acquisition lasting for 2-7h. Each camera covers a 1.3 x 0.9m field of view and they were oriented such that to cover the largest area~90° in azimuth downstream of the axis of the forcing. A schematic showing the set-up and acquisition system is shown in Figure 1. After a calibration procedure, images were processed using the UVMAT software based on a Correlation Image Velocimetry algorithm [5] such as to obtain the time histories of velocity fields in the merged area shown in Fig. 1.. From the acquired data, relative and potential vorticity time evolution, energy spectra and the characteristic length scales were calculated to characterize turbulence and to diagnose the flow’s dynamical regime. Of particular importance, the zonostrophy index was estimated at R~2 thereby marking the onset of the zonostrophic regime[3, 4]. This is one of the highest values of Rachieved in a laboratory so far. The analogy between vertical and horizontal turbulent overturning in stably stratified and quasigeostrophic flows was explored by monotonizing potential vorticity [6]. This methodology allows one to estimate LM, a scale commensurate with L and needed in order to estimate , the key variable for turbulence modeling.