2 results
Turbulent mass transfer through a flat shear-free surface
- JACQUES MAGNAUDET, ISABELLE CALMET
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- Journal:
- Journal of Fluid Mechanics / Volume 553 / 25 April 2006
- Published online by Cambridge University Press:
- 06 April 2006, pp. 155-185
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Mass transfer through the flat shear-free surface of a turbulent open-channel flow is investigated over a wide range of Schmidt number (1 $ \le $Sc$ \le $ 200) by means of large-eddy simulations using a dynamic subgrid-scale model. In contrast with situations previously analysed using direct numerical simulation, the turbulent Reynolds number Re is high enough for the near-surface turbulence to be fairly close to isotropy and almost independent of the structure of the flow in the bottom region (the statistics of the velocity field are identical to those described by I. Calmet & J. Magnaudet J. Fluid Mech. vol. 474, 2003, p. 355). The main statistical features of the concentration field are analysed in connection with the structure of the turbulent motion below the free surface, characterized by a velocity macroscale $u$ and an integral length scale $L$. All near-surface statistical profiles are found to be Sc-independent when plotted vs. the dimensionless coordinate Sc$^{1 / 2}yu$/$\nu $ ($y$ is the distance to the surface and $\nu $ is the kinematic viscosity). Mean concentration profiles are observed to be linear throughout an inner diffusive sublayer whose thickness is about one Batchelor microscale, i.e. LSc$^{ - 1 / 2 }$Re$^{ - 3 / 4}$. In contrast, the concentration fluctuations are found to reach their maximum near the edge of the outer diffusive layer which scales as LSc$^{ - 1 / 2}$Re$^{ - 1 / 2}$. Instantaneous views of the near-surface isovalues of the concentration and vertical velocity are used to reveal the influence of the Schmidt number. In particular, it is observed that at high Schmidt number, the tiny concentration fluctuations that subsist in the diffusive sublayer just mirror the divergence of the two-component surface velocity field. Co-spectra of concentration and vertical velocity fluctuations indicate that the main contribution to the turbulent mass flux is provided by eddies whose horizontal size is close to $L$, which strongly supports the view that the mass transfer is governed by large-scale structures. The dimensionless mass transfer rate is observed to be proportional to Sc$^{ - 1 / 2}$ over the whole range of Schmidt number. Based on a frequency analysis of the concentration equation and on the Sc$^{ - 1 / 2}$Re$^{ - 3 / 4 }$scaling of the diffusive sublayer, it is shown that the mass transfer rate at a given Sc is proportional to $\langle {\beta ^2}\rangle ^{1 / 4}$, $\langle {\beta ^2}\rangle $ being the variance of the divergence of the surface velocity field. This yields dimensionless mass transfer rates of the form $\alpha$Sc$^{ - 1 / 2}$Re$^{ - 1 / 4}$, where the value of $\alpha$ is shown to result from both the kinematic blocking of the vertical velocity and the viscous damping of the horizontal vorticity components induced by the free surface.
Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow
- ISABELLE CALMET, JACQUES MAGNAUDET
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- Journal:
- Journal of Fluid Mechanics / Volume 474 / 10 January 2003
- Published online by Cambridge University Press:
- 14 January 2003, pp. 355-378
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Statistical characteristics of turbulence in the near-surface region of a steady open- channel flow are examined using new data obtained in a high-Reynolds-number large-eddy simulation using a dynamic subgrid-scale model. These data, which correspond to a Reynolds number Re* = 1280 based on the total depth and shear velocity at the bottom wall, are systematically compared with those found in available direct numerical simulations in which Re* is typically one order of magnitude smaller. Emphasis is put on terms involved in the turbulent kinetic energy budget (dominated by dissipation and turbulent transport), and on the intercomponent transfer process by which energy is exchanged between the normal velocity component and the tangential ones. It is shown that the relative magnitude of the pressure–strain correlations depends directly on the anisotropy of the turbulence near the bottom of the surface-influenced layer, and that this anisotropy is a strongly decreasing function of Re*. This comparison also reveals the Re*-scaling laws of some of the statistical moments in the near-surface region, especially those involving vorticity fluctuations. Velocity variances, length scales and one-dimensional spectra are then compared with predictions of the rapid distortion theory elaborated by Hunt & Graham (1978) to predict the effect of the sudden insertion of a flat surface on a shearless turbulence. A very good agreement is found, both qualitatively and quantitatively, outside the thin viscous sublayer attached to the surface. As the present high-Reynolds-number statistics have been obtained after a significant number of turnover periods, this agreement strongly suggests that the validity of the Hunt & Graham theory is not restricted to short times after surface insertion.