Edwin A. Cowen

Boundary layer flow and bed shear stress under a solitary wave

Liu & Orfila ( J. Fluid Mech . vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfilas solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

A random-jet-stirred turbulence tank

We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylors frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.

Laboratory observations of mean flows under surface gravity waves

In this paper we present mean velocity distributions measured in several different wave flumes. The flows shown involve different types of mechanical wavemakers, channels of differing sizes, and two different end conditions. In all cases, when surface waves, nominally deep-water Stokes waves, are generated, counterflowing Eulerian flows appear that act to cancel locally, i.e. not in an integral sense, the mass transport associated with the Stokes drift. No existing theory of wave–current interactions explains this behaviour, although it is symptomatic of Gerstner waves, rotational waves that are exact solutions to the Euler equations. In shallow water (kH ≈ 1), this cancellation of the Stokes drift does not hold, suggesting that interactions between wave motions and the bottom boundary layer may also come into play.

Evolution of the turbulence structure in the surf and swash zones

The velocity field and turbulence structure within the surf and swash zones forced by a laboratory-generated plunging breaking wave were investigated using a particle image velocimetry measurement technique. Two-dimensional velocity fields in the vertical plane from 200 consecutive monochromatic waves were measured at four cross-shore locations, shoreward of the breaker line. The phase-averaged mean flow fields indicate that a shear layer occurs when the uprush of the bore front interacts with the downwash flow. The turbulence characteristics were examined via spectral analysis. The larger-scale turbulence structure is closely associated with the breaking-wave-and the bore-generated turbulence in the surf zone; then, the large-scale turbulence energy cascades to smaller scales, as the turbulent kinetic energy (TKE) evolves from the outer surf zone to the swash zone. Smaller-scale energy injection during the latter stage of the downwash phase is associated with the bed-generated turbulence, yielding a ―1 slope in the upper inertial range in the spatial spectra. Depth-integrated TKE budget components indicate that a local TKE equilibrium exists during the bore-front phases and the latter stage of the downwash phases in the outer surf zone. The TKE decay resembles the decay of grid turbulence during the latter stage of the uprush and the early stage of the downwash, as the production rate is small because of the absence of strong mean shear during this stage of the wave cycle as well as the relatively short time available for the growth of the bed boundary layer.

Plume dispersion in a stratified, near-coastal flow: measurements and modeling

Abstract Dispersion of a passive scalar released from a near-bed source is examined in coastal waters, (O(10 m) deep), just off San Clemente Island, California. Rhodamine WT dye was released continuously for several hours from a bottom source on May 8, 1997. Surveys of the hydrodynamic fields (currents and density) are combined with dye concentration measurements made from a towed fluorometer array to characterize the plume. The plume developed along the 12 m isobath (the depth of the source), to the southeast of the release location. It was largely confined to the near-bed region by a thermocline located at a depth of about 9 m. Therefore, the plume can be loosely characterized as advecting along the isobaths and dispersing throughout the layer below the thermocline (layer thickness of about 3 m). An analytic expression for plume concentration as a function of radial distance from the source was developed for a scale-dependent dispersion coefficient. This model agrees with the data and indicates that the dispersion coefficient obeys a “4/3-law”. This approach is contrasted by a finite difference model in an Eulerian reference frame, illustrating the challenges associated with the modeling of a meandering plume.

The Information Content of a Scalar Plume – A Plume Tracing Perspective

The ability of many animals and insects to track a plume to its source is a particularly impressive feat when the fluid dynamics is considered. Inspired by this observation this research seeks to identify the information in a passive scalar plume suitable for developing robust and efficient plume tracing algorithms. The subject of this study is a scalar plume emanating from a point source in a turbulent boundary layer which has been modeled in a laboratory facility built specifically for this purpose. A coupled PIV-LIF technique is used to measure the velocity and scalar field in a time resolved fashion. This data set is analyzed and the convergence rates of five single-point statistics, suitable as kernels of plume tracing algorithms, are investigated. The experimental data shows that the scalar fluctuations over long downstream distances from the source are characterized by filamentary structures that lead to relatively slow convergence rates for any statistic that is based on mean concentrations. The scalar intermittency, however, converges rapidly toward its true value, in fact converging to a testable hypothesis for source location direction faster than the time scale of the larger scale plume meander.

Chemical Plume Tracing

Given a measurable concentration of a dissolved substance at a point within a fluid flow, where is the source? As physicists and engineers we often look at this problem from a more traditional perspective given a point source release of a substance, we seek to describe the temporal and spatial evolution of the effluent plume. Animals, seeking to evade predators or to locate mates or sources of food, contend with this problem routinely every day, and they have evolved a keen ability to locate these sources. Thus whereas our traditional approach when studying point source releases in the field of fluid mechanics is to seek to understand the fate of the source material and hence to study the forward problem, animals, and hence the biologists who study them, traditionally approach the study of the point-source-in-a-fluid as an inverse problem. This Special Issue on chemical plume tracing presents the work of an interdisciplinary research team, assembled by the Defense Advanced Research Projects Agency (DARPA) and the Office of Naval Research (ONR) to develop the ability to track chemical plumes to their sources. The fundamental approach to this research has been biomimetic. Both ONR and DARPA currently support research programs that seek either to integrate biological sensors or materials directly into new technology, or to capitalize on our knowledge about biological systems and processes to design new technological approaches to meet the demanding capability requirements of many armed services applications. This “biocentric” approach spans many disciplines and length scales. Some workers seek to enhance the performance of Navy surface and underwater platforms by a careful hydrodynamic analysis of swimming animals (Triantafyllou and Triantafyllou, 1995; Gordon et al., 2000; Bandyopadhyay, 2002). Others attempt to harness the power of single molecular motors to provide new energy sources (Montemagno and

Longitudinal vortices beneath breaking waves

The formation of longitudinal vortices has been observed in a wavy channel flow and appears to be linked to spilling breaking and/or to vertical vorticity generated by a wave instability at the wave maker. Both conditions were present when the wave slope, ak exceeded 0.25. The wave instability produced velocity jets beneath and just downstream of the plunger that could provide the initial perturbation for the CL2 instability mechanism (Faller and Caponi, 1978). The breaker activity could also contribute to the CL2 production mechanism by eliminating the negative, stabilizing shear observed within the wave maker wake and by providing seed perturbations to the vorticity field. As the cells evolved downstream, they were maintained through interaction with the bottom boundary layer. When the vortices were present, both vertical mixing and turbulent kinetic energy were enhanced. Despite some differences in scale these results suggest that Langmuir circulation may produce similar changes in the mixed layer.

Tripton, trophic state metrics, and near-shore versus pelagic zone responses to external loads in Cayuga Lake, New York, U.S.A.

An analysis of limnological and input monitoring data for Cayuga Lake, New York, U.S.A., is presented that addresses differences in trophic state metrics and turbidity between pelagic waters and a shallow (< 6 m) near-shore area (shelf) that receives multiple inputs. The effects of tripton (inanimate particles) on the observed patterns, and the contrasting responses of the shelf to local inputs of tripton versus phosphorus (P), are demonstrated. The analysis is based on a combination of long-term monitoring and shorter-term studies, including: (1) 10 to 20 years of concentrations of chlorophyll-a (Chl), total P (TP), and other forms of P; (2) 10 years of Secchi disc (SD) and surrogates of the light scattering coefficient, including turbidity (T n ) and the beam attenuation coefficient at 660 nm [c(660)]; (3) loading estimates of T n and forms of P in point sources and tributaries to the shelf (4 to 10 y) and; (4) longitudinal patterns of thermal stratification, fluorometric Chl, and c(660) from a lake-wide 40 site transect; and (5) 10 years of hourly measurements of near-surface temperature on the shelf. The generally higher TP, particulate P, c(660), and T n , and lower SD on the shelf compared to pelagic waters, particularly after runoff events, is shown to reflect higher tripton levels in the near-shore area. Tripton was also an important regulator of these attributes in pelagic waters. The effects of tripton compromise TP and SD as trophic state metrics in this lake. The light scattering and clarity impacts of tripton are demonstrated to be primarily attributable to clay mineral particles in the 1-10 μm size range. Despite the P loads received from local sources, summer average Chl levels on the shelf were not significantly higher than in bounding pelagic waters because the flushing rate associated with mixing processes, particularly from seiche activity, was high compared to phytoplankton growth rates.

Remote monitoring of volumetric discharge employing bathymetry determined from surface turbulence metrics

Current methods employed by the United States Geological Survey (USGS) to measure river discharge are manpower intensive, expensive, and during high flow events require field personnel to work in dangerous conditions. Indirect methods of estimating river discharge, which involve the use of extrapolated rating curves, can result in gross error during high flow conditions due to extrapolation error and/or bathymetric change. Our goal is to develop a remote method of monitoring volumetric discharge that reduces costs at the same or improved accuracy compared with current methods, while minimizing risk to field technicians. We report the results of Large-Scale Particle Image Velocimetry (LSPIV) and Acoustic Doppler Velocimetry (ADV) measurements conducted in a wide-open channel under a range of flow conditions, i.e., channel aspect ratio (B/H = 6.6–31.9), Reynolds number (ReH = 4,950–73,800), and Froude number (Fr = 0.04–0.46). Experiments were carried out for two different channel cross sections (rectangular and asymmetric compound) and two bathymetric roughness conditions (smooth glass and rough gravel bed). The results show that the mean surface velocity normalized by the depth-averaged velocity (the velocity index) decreases with increasing δ*/H, where δ* is the boundary layer displacement thickness and that the integral length scales, L11,1 and L22,1, calculated on the free-surface vary predictably with the local flow depth. Remote determination of local depth-averaged velocity and flow depth over a channel cross section yields an estimate of volumetric discharge.