We study energy condensation in quasi two-dimensional turbulence that is driven by surface waves. This physical mechanism is investigated with regard to its potential for energy production. In two-dimensional turbulence the net energy is transferred from small scales to large scales. Energy condensation develops when large scale friction is low and energy piles up at large scales. In this way, energy condensation produces large ordered flow structures from disordered small scale forcing that drives the two-dimensional turbulence. It was shown only recently that two-dimensional turbulence can also be driven by surface waves [von Kameke et al. 2011].
However, it is unclear if two-dimensional turbulence and energy condensation can also be driven by more naturally occurring unordered forcing as for instance provided by oceanic surface waves. Further, it is not yet fully understood how non-breaking surface waves generate horizontal vorticity, and if the waves have to possess certain properties, i.e., if they need to be standing, non-linear or monochromatic [Francois et al. 2014, Filatov et al. 2016]. Additionally, the necessary boundary conditions for energy condensation are vague and need clarification. And, it needs to be addressed if the process of energy condensation is stable to the introduction of further sources of drag, i.e., when a turbine is plugged into the fluid flow in order to retrieve energy.
Here, these open points are to be investigated using a Faraday experiment [von Kameke et al. 2010, von Kameke et al. 2011, von Kameke et al. 2013]. The generation of vorticity by the surface waves and the influence of the boundary- and forcing- conditions on energy condensation will be studied as well as the velocity statistics. To this end the full unsteady three-dimensional velocity field at the water surface and below the water surface needs to be recorded which has not been investigated so far. The latest optical methods will be used, such as time-resolved high speed planar particle image velocimetry and time-resolved three-dimensional particle image velocimetry and particle tracking. The complete velocity data allows to doubtlessly verify, if the flow obtained in each case is two-dimensional and, if energy condensation takes place. Two-dimensionality is analyzed on the basis of energy and enstrophy spectra and spectral fluxes, calculated with the aid of a novel filtering method [Eyink, 1995, von Kameke et al. 2011, von Kameke et al. 2013]. Moreover, existing three- dimensional flow structures will be identified and characterized. The forcing, exerted by the surface waves on the fluid-particles, and the resulting vorticity generation will be quantified by measuring the fluid surface elevation simultaneously to the PIV measurements and the subsequent usage of Lagrangian methods [von Kameke et al. 2011, von Kameke et al. 2013, LaCasce 2008] that allow to correlate both movements. The objective of this study is to uncover a new effective mechanism to retrieve renewable energy and will broaden insight into surface wave physics and two-dimensional turbulence.
The details about the creation and the sub-surface velocity field of the Faraday flow, are to date not well understood. Especially intriguing is that the 2D turbulence at the liquid surface is produced by agitation in the vertical direction. For a thick layer of 3 cm liquid height the system is by no means shallow in comparison to the typical scale of energy injection (of the order of the half Faraday wave length) and pronounced three dimensional flows occur in the bulk.
The initial steps in understanding the interplay of 2D turbulence at the fluid surface and the 3D fluid flow beneath for the Faraday flow are reported in [Colombi et al., 2020]. For the first time we measured the sub-surface velocity fields by means of planar PIV with high spatial and temporal resolution at multiple horizontal planes at different depths below the surface. An impressive exponential decrease with depth was observed for the mean of the absolute values of the velocities, as well as the turbulent kinetic energy, proving that the forcing mechanism is confined to a thin layer below the surface. Furthermore, the increasing three-dimensionality of the flow as indicated by an increase of the compressibility with depth suggests that there might be a transport of energy to lower depths. Additional observations suggest that the high peaks of the divergence at the fluid surface stem from small and fast vertical jets that are pushed from the surface downwards and might actually drive the bulk flow.
|Title: Three Dimensional Flows Beneath a Thin Layer of 2D turbulence Induced by Faraday Waves.|
|Written by: Colombi, R.; Schlüter, M.; Kameke, A.v.;|
|in: <em>Experiments in Fluids</em>. (2020).|
|Volume: <strong>62</strong>. Number: (8),|
|Publisher: Springer Link:|
Note: 2D Farady Flows
Abstract: Faraday waves are capillary ripples that form onthe surface of a fluid being subject to vertical shaking. Al-though it is well known that the form and shape of the wavespattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal veloc-ity field at the surface, called Faraday flow, which exhibitsattributes of two-dimensional turbulence. However, despitethe increasing attention towards the inverse energy flux inthe Faraday flow and other not strictly two-dimensional sys-tems, very little is known about the velocity fields develop-ing beneath the fluid surface. In this study planar velocityfields are measured by means of particle image velocime-try (PIV) with high spatial and temporal resolution on thewater surface and below it. A sudden drop in velocity isobserved immediately below the water surface, such that at5 mm below the water surface the mean absolute velocitiesare already about 6.5 times smaller than the surface veloc-ity. Additionally, the flow structures below the surface arefound to comprise much larger spatial scales than those onthe surface. These large structures are also found to be slowand temporarily persistent, as proven by analysing the auto-correlation of the velocity fields in time.
The authors gratefully acknowledge the financial support provided by the Deutsche Forschungsgemeinschaft (DFG) within the project 395843083 (KA 4854/1-1).