Meandering streams in a shallow fluid layer

Abstract

Decaying turbulence in a shallow flow is shown to be characterized by the emergence of long-lived meandering currents, which are closely related to pronounced vertical flows inside the shallow layer. These vertical flows are concentrated in regions that are dominated either by vorticity or by strain of the flow field. Upwelling of fluid is observed in patch-like domains near elliptic points. Downward flow takes place close to hyperbolic points where the hyperbolic nature of the streamlines leads to thin, elongated regions of intense downwelling. The latter results in long, contracting regions in the free-surface flow. Particles that float on the liquid surface will congregate in these strain-dominated regions, thus lining out the large-scale meandering streams.

Studies on quasi-2D turbulence—the effect of boundaries

“…A no-slip condition was prescribed at the bottom, while a stress-free condition was applied at the free surface, which was taken to be flat. These simulations have revealed that the flow throughout the post-forcing stage is essentially 3D, containing locally substantial vertical velocities as well as a vertical structure that is not Poiseuille-like, see Cieślik et al (2009bCieślik et al ( , 2009c. The numerical simulation results show good agreement with the experimentally observed flow evolution.…”

“…Apparently, shallow flows generated under the conditions of the experiments reported by Akkermans et al (2008aAkkermans et al ( , 2008bAkkermans et al ( , 2009) and Cieślik et al (2009bCieślik et al ( , 2009c do not behave in a quasi-2D fashion, as is commonly assumed in experimental shallow-flow studies related to 2D turbulence, see e.g. Tabeling et al (1991), Danilov et al (2002) and Shats et al (2005Shats et al ( , 2007.…”

“…Under the assumption of two-dimensionality, the vortices induced by the magnets would interact and gradually give rise to larger coherent vortex structures, as illustrated for example by the numerical simulations by McWilliams (1984). Recent experiments by Cieślik et al (2009bCieślik et al ( , 2009c on shallow flows driven electromagnetically by a regular array of 10 × 10 magnets have revealed a different flow evolution; however, in the post-forcing stage the flow shows large-scale meandering structures rather than vortices. This is clearly observed in the streak photographs presented in figure 8: during the forcing ( figure 8(a)) the flow is organized in a regular array of 10 × 10 counter-rotating cells, but some time after the forcing has stopped large meandering currents are visible throughout the flow domain ( figure 8(b)).…”

Three-dimensional structures in a shallow flow

“…These studies include experiments on a simple vortical structure, a dipolar vortex (Akkermans et al, 2008a,b;Cie slik et al, 2009a), as well as on decaying turbulence initialised by an array of vortices (Cie slik et al, 2009b). A single dipole freely evolving in a shallow fluid layer exhibits significant and complex vertical motions throughout the flow evolution (Akkermans et al, 2008a).…”

Strain-vorticity induced secondary motion in shallow flows

“…This compressibility leads to inhomogeneous distributions of Lagrangian tracers on such surface flows resulting in a clustering of the tracers in ridge-like structures and meandering streams. [2][3][4] In the present paper, we will quantitatively relate magnitude and spatial distribution of vertical motion inside a shallow fluid layer to the local distribution of strain and vorticity of the surface flow. Furthermore, the compressibility of this surface flow is also quantified in terms of the local strainvorticity balance in the horizontal flow field as described by the Okubo-Weiss function.…”