Wind effect on gyrotactic micro-organism surfacing in free-surface turbulence

We investigate two-phase free-surface turbulence (FST) associated with an underlying shear flow under the condition of strong turbulence (SFST) characterized by large Froude ($Fr$) and Weber ($We$) numbers. We perform direct numerical simulations of three-dimensional viscous flows with air and water phases. In contrast to weak FST (WFST) with small free-surface distortions and anisotropic underlying turbulence with distinct inner/outer surface layers, we find SFST to be characterized by large surface deformation and breaking accompanied by substantial air entrainment. The interface inner/outer surface layers disappear under SFST, resulting in nearly isotropic turbulence with ${\sim}k^{-5/3}$ scaling of turbulence kinetic energy near the interface (where $k$ is wavenumber). The SFST air entrainment is observed to occur over a range of scales following a power law of slope $-10/3$. We derive this using a simple energy argument. The bubble size spectrum in the volume follows this power law (and slope) initially, but deviates from this in time due to a combination of ongoing broad-scale entrainment and bubble fragmentation by turbulence. For varying $Fr$ and $We$, we find that air entrainment is suppressed below critical values $Fr_{cr}$ and $We_{cr}$. When $Fr^{2}>Fr_{cr}^{2}$ and $We>We_{cr}$, the entrainment rate scales as $Fr^{2}$ when gravity dominates surface tension in the bubble formation process, while the entrainment rate scales linearly with $We$ when surface tension dominates.

Download Full-text

A numerical study of free‐surface turbulence in channel flow

Physics of Fluids ◽

10.1063/1.868483 ◽

1995 ◽

Vol 7 (7) ◽

pp. 1649-1664 ◽

Cited By ~ 100

Author(s):

Y. Pan ◽

S. Banerjee

Keyword(s):

Free Surface ◽

Channel Flow ◽

Numerical Study ◽

Surface Turbulence ◽

Free Surface Turbulence

Download Full-text

Large-eddy simulation of free-surface turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112001004669 ◽

2001 ◽

Vol 440 ◽

pp. 75-116 ◽

Cited By ~ 42

Author(s):

LIAN SHEN ◽

DICK K. P. YUE

Keyword(s):

Boundary Condition ◽

Free Surface ◽

Large Eddy Simulation ◽

Surface Boundary ◽

Eddy Simulation ◽

Large Eddy ◽

Similarity Model ◽

Scale Similarity ◽

Surface Turbulence ◽

Free Surface Turbulence

In this paper we investigate the large-eddy simulation (LES) of the interaction between a turbulent shear flow and a free surface at low Froude numbers. The benchmark flow field is first solved by using direct numerical simulations (DNS) of the Navier–Stokes equations at fine (1282 × 192 grid) resolution, while the LES is performed at coarse resolution. Analysis of the ensemble of 25 DNS datasets shows that the amount of energy transferred from the grid scales to the subgrid scales (SGS) reduces significantly as the free surface is approached. This is a result of energy backscatter associated with the fluid vertical motions. Conditional averaging reveals that the energy backscatter occurs at the splat regions of coherent hairpin vortex structures as they connect to the free surface. The free-surface region is highly anisotropic at all length scales while the energy backscatter is carried out by the horizontal components of the SGS stress only. The physical insights obtained here are essential to the efficacious SGS modelling of LES for free-surface turbulence. In the LES, the SGS contribution to the Dirichlet pressure free-surface boundary condition is modelled with a dynamic form of the Yoshizawa (1986) expression, while the SGS flux that appears in the kinematic boundary condition is modelled by a dynamic scale-similarity model. For the SGS stress, we first examine the existing dynamic Smagorinsky model (DSM), which is found to capture the free-surface turbulence structure only roughly. Based on the special physics of free-surface turbulence, we propose two new SGS models: a dynamic free-surface function model (DFFM) and a dynamic anisotropic selective model (DASM). The DFFM correctly represents the reduction of the Smagorinsky coefficient near the surface and is found to capture the surface layer more accurately. The DASM takes into account both the anisotropy nature of free-surface turbulence and the dependence of energy backscatter on specific coherent vorticity mechanisms, and is found to produce substantially better surface signature statistics. Finally, we show that the combination of the new DFFM and DASM with a dynamic scale-similarity model further improves the results.

Download Full-text