Richard Irwin Leighton

Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow

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 surf...

Direct numerical simulations of free convection beneath an air–water interface at low Rayleigh numbers

Direct numerical simulations of a cooling air–water interface were employed to determine the structure of the temperature, velocity, and vorticity fields in the thin thermal boundary layer formed at the free surface. The simulations were performed at low to moderate Rayleigh numbers. In this flow, the turbulence is initiated by the Rayleigh instability at the interface and is maintained by buoyant production. Visualizations of the flow reveal that the temperature field at the interface is composed of large warm patches surrounded by cooler dense fluid which accumulates in thin bands. The cool fluid associated with the bands initially falls in sheets, but rapidly forms descending tubes and plumes. The turbulence statistics were scaled both with outer and inner variables. The latter scaling is based on the so-called surface strain model which is essentially consistent with Townsend’s inner scaling. It is found that the temperature statistics collapse well using inner variables. On the other hand, the vertical velocity scales well with inner variables within the thermal boundary layer, but at greater depths it becomes more appropriate to use outer scaling. The anisotropic nature of the velocity statistics in the core of the flow is ascribed to the relatively low Rayleigh numbers used in the simulations. An explanation for this anisotropy is offered based on a detailed examination of the turbulence kinetic energy balances.

The thermal structure of an air-water interface at low wind speeds

High-resolution infrared imagery of an air–water interface at wind speeds of 1 to 4 ms-1 wasobtained. Spectral analysis of the data reveals several important features of the thermal structureof the so-called cool skin. At wind speeds for which wind waves are not generated, the interfacialboundary layer appears to be composed of buoyant plumes that are stretched by the surfaceshear as they reach the interface. The plumes appear to form overlapping laminae with ahead–tail structure which we have termed fish-scales. At higher wind speeds, gravity wavesappearing on the surface give rise to distinct signatures in the infrared imagery. The wavesystem appears to modulate the surface temperature with sufficient strength so that the lengthand time scales of the waves are readily revealed in a k–ɷ spectrum. A surface drift speed canalso be easily inferred from the spectrum. A direct numerical simulation of the cool-skin of asheared water interface has also been performed. For Richardson numbers less than about 10-3, the simulations reveal a surface temperature pattern dominated by a streaky structure with acharacteristic spanwise length scale on the order of 100l+ where l+=v/u*. The simulationsconfirm that this streaky structure is formed as slow moving fluid originating from belowencounters a surface shear. The thermal structure of the surface appears virtually unchangedwhen buoyancy is turned off in the simulations and shear remains. This indicates that the fishscalepattern has universal features in the sense that it forms independently of the mechanismby which the turbulence is generated. The simulations are found to be in remarkable agreementwith the experimental results for which the same streaky, fish-scale structure was observed andthe same streak spacing was obtained.

Surfactant effects on passive scalar transport in a fully developed turbulent flow

Direct numerical simulations of fully developed turbulence in an open channel were performed. Effects of surfactants on heat transfer and the underlying turbulent structures were investigated. As surface elasticity is increased turbulent fluctuations are damped and the mean surface temperature is decreased. A surface strain model is introduced to explain this behavior in a heuristic manner. A nondimensional parameter representing the ratio of surface elastic forces to local inertial forces is introduced. It is concluded that for values of the parameter of order one, surfactants have strong effects on surface turbulence, whereas an effectively clean surface can be obtained for parameter values less than O(10−3).

The thermal signature of a vortex pair impacting a free surface

The action of a rising vortex pair on the thermal boundary layer at an air–water interface is studied both experimentally and numerically. The objective is to relate variations in the surface temperature field to the hydrodynamics of the vortex pair below. The existence of a thermal boundary layer on the water side of an air–water interface is well known; it is this boundary layer which is disrupted by the action of the vortex system. Experimentally, the vortices were generated via the motion of a pair of submerged flaps. The flow was quantified through simultaneous measurement of both the subsurface velocity field, via digital particle image velocimetry (DPIV), and the surface temperature field, via an infrared (IR) sensitive imager. The results of the physical experiments show a clearly defined disruption of the ambient thermal boundary layer which is well correlated with the vorticity field below. Numerical experiments were carried out in a parameter space similar to that of the physical experiments. Included in the numerical experiments was a simple surfactant model which enabled the exploration of the complex role surface elasticity played in the vortex–free surface interaction. The results of this combined experimental and numerical investigation suggest that surface straining rate is an important parameter in correlating the subsurface flow with the surface temperature field. A model based on surface straining rate is presented to explain the interaction.

A model for the aqueous thermal boundary layer at an air-water interface

A fundamental understanding of the thermal characteristics of the air-water boundary is critical to applications such as remote sensing of the bulk sea temperature and modeling of the heat transfer through the interface. The objective of the current work is to develop a model of the thermal boundary layer on the aqueous side of an air-water interface. This model is based on the surface strain model Csanady [1990] developed for gas transfer. The primary underlying assumption is. that a quasi-steady straining exists at the air-water interface. This quasi-steady straining field maintains a steady state aqueous thermal boundary. With this approach the properties of the thermal boundary layer can then be related to a variety of hydrodynamic conditions. This approach is motivated by experimental evidence and validated with simulation results.

A comparison of simulated and experimental IR measurements at low to moderate wind speeds

The surface temperature field due to free-convection and/or forced turbulence at low to moderate wind speeds is examined experimentally and numerically. The objective of the research is to examine the scaling of the thermal boundary layer as the flow evolves from a free-convection regime to a shear-driven regime. The information will be used to assess models of the thermal boundary layer as the turbulence transitions from free-convection to sheared turbulence at low wind speeds. The experiments were performed at the University of Delawares Air-Sea Interaction Laboratory Wind-Wave-Current facility using an Amber Model 4256 IR Camera sensitive to image the air-water interface. The numerical simulations were performed using a spectral algorithm. A constant heat flux boundary condition is used in conjunction with a rigid lid approximation to model the free-surface. All fluid properties are held constant. A Boussinesq approximation is used to represent the temperature effects on buoyancy. The effect of the wind is modeled as a steady shear stress acting on the free-surface. For the low wind speeds, the dominant physical process is the ascension of a warm plume into the wind-sheared near-surface region. The surface temperature exhibits a characteristic fish-scale pattern. As the flow transitions from free-convection to forced turbulence, a similar, but more complicated thermal pattern evolves. Some of the thermal structure in the laboratory experiments is similar to that observed in simulations of forced turbulence near a free-surface.