ETC2019 17th European Turbulence Conference Submission

10:45 Two-dimensional Turbulence 1

10:45 15 mins #29	EFFECT OF ROTATION ON TURBULENT THERMAL CONVECTION ON A HEMISPHERE Patrick Fischer, Charles-Henri Bruneau, Hamid Kellay Abstract: In this talk, we present experiments and numerical simulations of rotating two dimensional turbulent convection on a hemisphere. Experiments on a half soap bubble located on a heated plate have shown that such a configuration is ideal for studying thermal convection on a curved surface [1, 2]. For the numerical simulations, two different methods have been used to produce the rotation of the bubble: the classical rotation term added to the velocity equation (Method 1), and a non zero tangential velocity boundary condition (Method 2). These two methods induce different fluid dynamics. While the first method is classically used for describing rotating Rayleigh-Bénard convection experiments, the second method is more coherent with our real rotating half bubble of soap. The first part of the presentation is devoted to the analysis of the influence of the rotation on the temperature fluctuations put forth by studying the second moment of temperature differences across different scales. In this part, the classical method for inducing the rotations has been used in the numerical simulations. For high enough rotation rates, these temperature differences display a transition from a Bolgiano Obukhov scaling to a new scaling regime. This scaling is at odds with expectations from theory, numerics, and experiments in three dimensions, suggesting that the effects of rotation on turbulent flows depend strongly on geometry and spatial dimension. In the second part we compare the two methods for inducing numerical rotations. Our different analysis tools show that moderate rotations obtained with Method 2 (non zero velocity boundary conditions) induce a 15% enhancement of the convective heat flux (measured in particular with the Nusselt number). This enhancement is closely related to instabilities and thermal boundary layers. In contrary to classical three dimensional rotating Rayleigh-Bénard convection experiments, almost no significant improvement of the convective heat flux has been observed with Method 1, with a rotation term in the velocity equation, (at most 5 %). This difference might be explained by the difference of the geometry: a two dimensional hemisphere instead of a three dimensional cylinder. We also observe that the dynamics of the convective heat flux is killed by high rotations with both methods in good agreement with usual three dimensional experiments. References [1] C.-H. Bruneau, P. Fischer, Y.-L. Xiong, and H. Kellay. Numerical simulations of thermal convection on a hemisphere. Phys. Rev. Fluids 3: 043502, 2018. [2] T. Meuel, M. Coudert , P. Fischer, C. H. Bruneau, and H. Kellay. Effects of rotation on temperature fluctuations in turbulent thermal convection on a hemisphere . Scientific Reports 8: 16513, 2018.
11:00 15 mins #135	Condensate in quasi two-dimensional turbulence Stefano Musacchio, Guido Boffetta Abstract: By means of numerical simulations, we investigate the process of formation of large-scale structures (condensate) in a turbulent flow confined in a thin layer. We show that the 3D turbulence at small scales acts as an effective viscosity which arrests the growth of the condensate.
11:15 15 mins #170	Condensates in thin-layer turbulence Adrian van Kan, Alexandros Alexakis, Takahiro Nemoto Abstract: It is well known that turbulence behaves differently in two dimensions (2D) and three dimensions (3D). Since the 2-D Euler equation conserves enstrophy in addition to energy, it gives rise to an inverse energy cascade from small to large scales, as opposed to a forward cascade of energy from large to small scales due to vortex stretching in 3D. Geophysical and astrophysical fluids are often constrained into thin (but 3-D layers), such as Earth's atmosphere and oceans. The anisotropic domain geometry causes the properties of thin-layer flow at large Reynolds number $\mathrm{Re}$ to deviate strongly from those predicted by classical 3-D homogeneous and isotropic turbulence theories. Thin-layer turbulence combines features of the 2-D and 3-D cases, with the large scales behaving like 2-D and the small scales behaving like 3-D. In the idealised case of forced incompressible 3-D flow in a thin triply-periodic box of height $H$ and base length $L$, with spectrally local forcing at $k_f=2\pi/\ell$ at fixed energy injection rate, a "dimensional transition" \cite{smith1996crossover} occurs when $Q = \ell/H$ is increased ($H$ decreased) below $Q_{3D} \approx 2$. For $ Q Q_{3D}$, an inverse cascade spontaneously emerges. Similar transitions have been found as a function of Rossby number Ro when rotation \cite{deusebio2014dimensional} is added. The inverse cascade leads to a growth of total energy at large scales. Even in the absence of large-scale dissipation, this process reaches a steady state after long time. The steady state is a spectral condensate in which energy is concentrated in the largest scale. In 2-D turbulence, this condensate is well understood, \cite{frishman2017jets}, but in thin 3-D layers the condensate phase has not yet been investigated. In this work, \cite{van2018condensates}, we use a large number of direct numerical simulations (DNS) to study the steady state of thin-layer turbulence. We investigate the energy budget at large and small scales as a function of $\mathrm{Re}$, $Q$ and the aspect ratio $A$. Two transitions are found: one at $Q=Q_{3D}$ where the inverse cascade arises and one at $Q=Q_{2D}>Q_{3D}$ where the flow becomes exactly 2-D. Both critical points are studied in detail. Spatio-temporal intermittency is found near $Q_{2D}$ and leads to an anomalous scaling of 3-D energy with distance from threshold. For $Q\approx Q_{3D}$, spontaneous transitions from 3-D turbulence to the condensate state and vice versa are possible, with transition times being distributed exponentially and mean transition time becoming very large ($>10^5$ forcing-scale eddy turn-over times), possibly diverging, near $Q_{3D}$. The dynamics of large-scale energy (amplitude of first Fourier mode of velocity field) is well approximated by a Langevin equation with appropriate coefficients determined by the DNS time series, although small deviations from Markovian dynamics are identified through non-Gaussian tails in the conditional transition probability. For $Q\in (Q_{3D},Q_{2D})$, a flux-loop is identified in which 2-D motions transfer energy inversely, while 3-D motions transfer energy down to small dissipative scales. An effective mean field eddy viscosity model is proposed which incorporates the observed spectrally non-local transfer of energy.
11:30 15 mins #238	Generalised flows and turbulent transport Simon Thalabard, Bec Jeremie Abstract: see pdf File
11:45 15 mins #200	Turbulence-driven rotors in 2D turbulent flows Nicolas Francois, Hua Xia, Horst Punzmann, Michael Shats Abstract: When a laminar flow becomes turbulent, its energy is spread over a range of scales in a process named energy cascade. It has recently been discovered that turbulent flows can be forced by steep Faraday waves at a fluid surface. Those flows possess features of two-dimensional turbulence [1,2,3]. In particular, an inverse energy cascade has been identified and a substantial amount of energy is stored into the turbulent fluctuations. An interesting question is whether it is possible to efficiently use the energy of this strongly out-of-equilibrium state. In the wave driven turbulence, we show how to create floating devices able to extract energy from the turbulent motion fluctuations by coupling with underlying features of the energy cascade. The operational principle of these devices relies on the rectification of the chaotic motion of correlated bundles of fluid trajectories. By changing the shape of the device, we can turn it into a vehicle or a rotor powered by turbulence. [1] A. V. Kameke, F. Huhn, G. Fernandez-Garcia, A. P. Munuzuri and V. Perez-Munuzuri, Phys. Rev. Lett. 107, 074502, (2011). [2] N. Francois, H. Xia, H. Punzmann and M. Shats, Phys. Rev. Lett. 110, 194501, (2013). [3] N. Francois, H. Xia, H. Punzmann, S. Ramsden and M. Shats, Phys. Rev. X 4, 021021, (2014).
12:00 15 mins #561	SUB-SURFACE PIV MEASUREMENTS OF VELOCITY FIELDS IN FARADAY FLOWS Raffaele Colombi, Michael Schlüter, Alexandra von Kameke Abstract: Faraday waves are capillary ripples that form on the surface of a ﬂuid being subject to vertical shaking. The resulting pattern of waves is known to be depending on driving amplitude and frequency, [2]. However, only recent studies, [5, 4, 3], proved the existence of a horizontal velocity ﬁeld at the surface, called Faraday ﬂow, which was shown to exhibit attributes of two-dimensional (2D) turbulence. One of the main features of Faraday ﬂows is the presence of an inverse energy cas-cade, by which energy is introduced at intermediate forcing scales and transferred upwards to larger scales, resulting in a net inverse energy ﬂux. Despite the increasing attention towards the well-validated inverse energy ﬂux in Faraday ﬂows and other not strictly 2-dimensional systems (as presented in [1]), very little is known about the ﬂow structures developing beneath the surface. This study aims at shedding new light on the ﬂow characteristics of the Faraday experiment, with particular focus on the sub-surface velocities. Planar PIV velocity ﬁelds are measured with high spatial and temporal resolution at different horizontal and vertical planes, in order to determine the three-dimensional structure of the Faraday ﬂow in dependence of the ﬂuid depth. This is coupled with further investigations on the temporal and spatial reconstruction of the height of the ripples, in order to reveal possible correlations between the velocity ﬁeld and the waveﬁeld.
12:15 15 mins #5	Turbulence appearance and non-appearance in thin fluid layers Gregory Falkovich, Natalia Vladimirova Abstract: Large-scale flows in thin layers can be considered 2d with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven. We argue that wall-driven (Couette) flow cannot sustain turbulence at however small viscosity and friction. Direct numerical simulations (DNS) up to the Reynolds number 1000000 confirm that all perturbations die in a plane Couette flow. On the contrary, for sufficiently small viscosity and friction, perturbations destroy the pressure-driven laminar (Poiseuille) flow. What appears instead is a traveling wave in the form of a jet slithering between wall vortices. For 3000