Generation of energy and vorticity production by surface waves through two-dimensional turbulence effects.
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Final Report Abstract
Lately, parametrically exited surface waves, so called Faraday waves, have been reported to drive two-dimensional turbulence. The resulting surface flow was termed Faraday-flow. In two-dimensional turbulence energy is transferred from small scales to large scales and finally orders the flow into large vortices when large scale dissipation is low (condensate state). A driving idea for this proposal was to ascertain if this ordering mechanism, induced by the wave forcing, can be exploited as a source of renewable energy. Main initial targets were to investigate the energy cascades and the energy condensation under different boundary conditions, secondly, measure and evaluate the full unsteady three-dimensional fluid flows at and beneath the surface and, thirdly, to evaluate the possibility to retrieve energy from these flows with some kind of mill. A fourth initial objective has been to simultaneously resolve the full unsteady threedimensional fluid flow and the fluids’ surface elevation to unveil the wave-flow interaction that induces the vortices on the fluid surface. The measurements performed in this research study led to the discovery of previously unknown bulk flows beneath Faraday waves. An analysis of the flow clarifies that energy is mostly concentrated in a thin surface layer, in which an inverse cascade causes a 2-D turbulence. A pile up of this energy into a condensate state was, however, only observed in geometrically strongly confined cases and seems unnatural. Despite this, a rotor placed onto the surface of the Faraday flow starts to propel with a mean angular velocity. This motion could in principle be used for energy retrieval. However, an efficient usage of two-dimensional turbulence effects as a renewable energy source is not expected in the near future due to the low ratio of converted energy. Nevertheless, the observed fluid structure interaction opens-up a new field of research and could be important with regard to floater design or passive animal propulsion. A new energy dissipating mechanism of the Faraday flow at the surface was found in downward jets that are sporadically and explosively ejected from the surface. The flows beneath the surface are considerably less energetic than the surface flows. Interestingly, right beneath the surface a direct energy cascade sets in that transfers energy from large to small flow structures and dissipates the energy from the jets. To our knowledge, the measurements are the first experimental observation of a coexistence of two-dimensional turbulence with its corresponding inverse energy cascade and a forward energy cascade. These insights into the interaction of two-dimensional surface flow and three-dimensional bulk flow with energy being transferred from the former to the latter via sparking jets could be used in the future to manipulate flows for mixing or patterning of inertial particles. Since it is still not clear under which circumstances these two flows coexist, more research in this regard is necessary using also gravitational Faraday waves since capillary forces might be a necessary key ingredient. Highly spatiotemporally resolved measurements of the particle tracks further reveal that slow large-scale vortices exist beneath the surface that cannot be explained by current streaming theory.
Publications
- 13th International Symposium on Particle Image Velocimetry, Munich, Germany, 2019: Measuring the Sub-Surface Velocity Field in Faraday Flows
Colombi, R., Rohde, N., Schlüter, M., von Kameke, A.
- European Turbulence Conference, Torino, Italy, 2019, Sub-surface PIV measurements of velocity fields in Faraday flows
Colombi, R., Schlüter, M., von Kameke, A.
- 2020. Three Dimensional Flows Beneath a Thin Layer of 2D turbulence Induced by Faraday Waves. Exp. in Fluids. 62. (8)
Colombi, R.; Schlüter, M., von Kameke, A.
(See online at https://doi.org/10.1007/s00348-020-03099-y) - 14th International Symposium on Particle Image Velocimetry, virtual, 2021, Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves
Colombi, R., Rohde, N., Schlüter, M., von Kameke, A.
(See online at https://doi.org/10.18409/ispiv.v1i1.115)
