In this study the evolution of initially homogeneous and isotropic turbulence in the presence of a free surface was investigated. The Navier–Stokes equations were solved via direct pseudo-spectral simulation with a resolution of 963. The Reynolds number based on the volume-averaged turbulence kinetic energy and dissipation rate was 147. Periodic boundary conditions were used in two dimensions, and the top and bottom sides of the domain were flat and shear-free. A random, divergence-free velocity field with a prescribed spectrum was used as the initial condition. An ensemble of sixteen separate simulations was used to calculate statistics.Near the surface, the Reynolds stresses are anisotropic and the anisotropy extends a distance from the surface roughly equal to the turbulent lengthscale. The tangential vorticity fluctuations also vanish near the surface, owing to the no-shear condition, causing a corresponding decrease in the fluctuating enstrophy. The thickness of the region in which the surface affects the vorticity distribution is roughly one-tenth the turbulent lengthscale. The stress anisotropy near the surface appears to be maintained by reduced dissipation for the tangential velocity fluctuations, reduced pressure–strain transfer from the tangential to surface-normal velocity fluctuations, and rapid decay of the surface-normal velocity fluctuations due to dissipation. The turbulence kinetic energy rises in the near-surface region owing to a decrease in dissipation at the surface. This decrease in dissipation results from the local reduction in enstrophy owing to the vanishing of the tangential vorticity fluctuations at the surface. At the free surface, the mean pressure rises. This is also due to the reduction in enstrophy.While the tangential vorticity must vanish at the free surface, the flow is fully three-dimensional up to the surface and the production of surface-normal vorticity by vortex stretching attains a maximum at the free surface. The contribution to the total enstrophy by the surface-normal vorticity fluctuations remains relatively constant over depth. The production of the surface-normal enstrophy component due to vortex stretching is roughly balanced by turbulent transport of enstrophy away from the surface. Near the surface, there are elevated levels of production of tangential vorticity by both vortex-stretching and fluctuating shear strains.

Direct numerical simulations of fully developed turbulence in an open channel geometry were performed in which a passive scalar was introduced. The simulations were intended to explore transport at free surfaces in two cases for which (1) the free surface was maintained at constant temperature and (2) the interfacial flux was fixed. These cases can be considered models for mass and evaporative heat transport where buoyancy and surface deformation effects are negligible. Significant differences were found in the thermal fields in these two cases. The turbulent statistics reveal that the surface flux in the constant temperature case was significantly more intermittent compared to the surface temperature field in the constant flux case. The surface temperature field in the latter case formed large patches of warm fluid, reminiscent of the so-called fish scale patterns revealed in recent infrared imagery of the air–water interface. The wake-like structure of the patches was evident despite the absence of surface shear. A model of surface renewal based on the existence of two disparate time scales (a fast hydrodynamic scale, and a slow, diffusional scale) was introduced to explain these differences in a heuristic manner. The model appears successful in explaining, in a qualitative sense, the surface thermal structure in each case. Correlations between the surface thermal fields (flux or temperature) and the subsurface hydrodynamics were also computed. A model based on the hypothesis that hairpin eddies are the dominant kinematic structure responsible for surface renewal is consistent with the correlations. However, these results cannot rule out the importance of other turbulent structures in free surface heat and mass transport processes.

Results from a joint numerical/experimental study of turbulent flow along a corner formed by a vertical wall and a horizontal free surface are presented. The objective of the investigation was to understand transport mechanisms in the corner. Numerical simulations were conducted at NRL to obtain data describing the dynamics of the near corner region. The Reynolds number for the simulations was Reθ ≈ 220. Flow visualization experiments conducted in the Rutgers free surface water tunnel were used to initially identify coherent structures and to determine the effect of these structures on the free surface. Time-resolved streamwise LDA measurements were made for Reθ ≈ 1150. The most significant results were the identification of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. Additional salient results included observations of surfactant transport away from the surface in cores of vortices connected to the free surface, intermittent energetic transport of fluid to the surface, and attenuation of streak motion by the free surface.

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High-resolution DPIV and LDV measurements were made in a turbulent mixed- boundary corner, i.e. a turbulent boundary layer generated by horizontal flow of water along a vertical wall in the vicinity of a horizontal free surface. This work is an extension of an earlier numerical/experimental study which established the existence of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak, slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. The objective of the current investigation, then, was to understand the combined effects of a horizontal, shear-free, free surface and a vertical, rigid, no-slip boundary on turbulent kinetic energy transport. The context of this work is providing physical insights and quantitative data for advancing the state of the art in free-surface turbulence modelling. Experiments were conducted in a large free-surface water tunnel at momentum-thickness Reynolds numbers, Reθ, of 670 for the DPIV studies, and 1150 for the LDV measurements. A high-resolution, two-correlation DPIV program was used to generate ensembles of vector fields in planes parallel to the free surface. These data were further processed to obtain profiles of turbulent kinetic energy transport terms, such as production and dissipation. In addition, profiles of streamwise and surface-normal velocity were made (as functions of distance from the wall) using two-component LDV. Key findings of this study include the fact that both turbulent kinetic energy production and dissipation are dramatically reduced close to the free surface. Far from the wall, this results in an increase in surface-parallel uctuations very close to the free surface. The degree of this anisotropy and the spatial scales over which it exists are critical data for improved free-surface turbulence models.

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to determine the extent of the source layer described Qi = instantaneous vorticity component in the Hunt-Graham model. The energy spectra show qualitative agreement with the model, though higher Subscripts resolution calculations will be required to make more i = 1,2, 3, coordinate directions quantitative comparisons. Additionally, the proxims = value at free surface ity of the free surface to the bottom solid wall of the oo = value in free stream channel evidences itself as a wall-layer streaky strucw = value at wall ture which persists to a noticeably greater distance. away from the wall. Some speculations are offered to 1. INTRODUCTION explain this effect. ,The study of the structure of turbulence near afree surface is obviously important to our understanding of the complex interaction of the atmosphere and upper ocean. It is also of fundamental relevance to the h = channel height -K wall-bounded turbulence problem, since it isolates the k = turbulent kinetic energy' -boundary influence on turbulent fluctuations from the e" = V/u 7 , viscous length scale turbulence production mechanism at the wall. The Reh = -h/v, Reynolds numbr first detailed experiment which addressed itself to this R' = uh/v, wall Reynolds number particular problem was that of Uzkan and Reynolds' Re = U,0/v, momentum thickness (UR). They passed grid generated homogeneous turReynolds number bulence over a wall which moved with the mean flow = V/u2, viscous timescale and therefore generated no mean shear at the bound-U = instantaneous velocity vector ary. They found that the streamwise turbulence inUi = instantaneous velocity component tensity near the shear-free boundary did not peak as u, = fluctuating velocity component it does near a stationary solid wall, but instead deur = V/I, friction velocity creased monotonically from its free stream value to A,, = turbulent microscale zero at the boundary. The simulations performed here were designed to vorticity vector is defined by fl = (V x U). Followrepresent as closely as possible the physics of free suring the solution of equations 1 and 2, the streamwise face/turbulence interaction in which the effects ofsurand spanwise velocity components, Ul and U 3 . are face waves can be safely neglected. For this purpose, recovered from the incompressibility condition. fully developed turbulence between a solid wall and aThe equations of motion are solved in Fourierfree surface is simulated. The physical processes repChebyshev space where Fourier modes are employed resented by these simulations differ in some important in the horizontal plane and Chebyshev modes in the respects from processes involved in the physical experwall normal direction. The calculations are performed iments noted above. First, in these simulations, no on a 64 x 65 x 48 grid in X 1 ,X 2 ,z 3 respectively. viscous layer can develop since u 1 and U3, the fluctuWith the geometry scaled by the channel height, the ating streamwise and spanwise velocity components, streamwise, vertical, and transverse dimensions of the are not forced ...

A Reynolds-stress transport equation model for turbulent drag-reducing viscoelastic flows, such as that which occurs for dilute polymer solutions, is presented. The approach relies on an extended set of Reynolds-Averaged Navier-Stokes equations which incorporate additional polymer stresses. The polymer stresses are specified in terms of the mean polymer conformation tensor using the FENE-P dumbbell model. The mean conformation tensor equation is solved in a coupled manner along with the Navier-Stokes equations. The presence of the polymer stresses in the equations of motion results in additional explicit polymer terms in the Reynolds-stress transport equations, as well as implicit polymer effects in the pressure-strain redistribution term. Models for both the explicit and implicit effects have been developed and implemented in a code suitable for boundary layer, rectangular channel and pipe-flow geometries. Calibration and validation is has been carried out using results from recent direct numerical simulation of viscoelastic turbulent flow.