Effects of Large Particle and Turbulent Scattering on Wavefront Sensor Measurements of the Volume Scattering Function

Woods, Sarah1; Bogucki, Darek1; Freda, Wlodzimierz2

1 Division of Applied Marine Physics, RSMAS, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149 USA

2 Physics Department, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland

INTRODUCTION

Turbulence plays an important role in processes near the surface of the ocean, such as air-sea gas transfer, distribution and mixing of nutrients, resuspension of sediment in shallow waters, and light propagation. Characterization and understanding of turbulence is important to those studying the air-sea interface, near surface ocean processes, the coastal ocean, and optical oceanography. The optical quantity describing light interaction with a water sample is the volume scattering function (VSF). In general, the VSF is strongly influenced by scattering from turbulent inhomogeneities, most effectively at near-forward scattering angles. While the near-forward VSF is also influenced by scattering from particulates, the turbulent effects dominate at the smallest angles.

Most investigations of oceanic turbulence are conducted through observation of the associated turbulent fluctuations of passive scalars such as temperature or salinity. Observation of these fluctuations in the ocean is limited, in part, because it is often difficult to make measurements with a response time fast enough to resolve the temperature gradient spectrum in the dissipation range, many instruments only profile along one of the three coordinate directions, and because measurements often include too much noise (Dillon and Caldwell 1980, Gregg 1999, Lueck et al. 2002). Fortunately, variations in these passive scalars lend well to an optical measurement of the turbulent fluctuations because these passive scalars cause variations in the density of the water, hence deviations in the refractive index of the medium, resulting in the scattering of incident light.

Recent work (Bogucki et al. 1998, Bogucki et al. 2004, Bogucki et al. 2007) shows that these turbulent changes in index of refraction can be quantified by measuring the near-forward scattering of a plane-parallel beam sent through the fluid. The method to measure the small angle scattering of the light beam is based upon measurement of the light beam wavefront using a wavefront sensor (Bogucki et al. 2007). Our experimental setup, similar to the Optical Turbulence Sensor (OTS), is schematically shown in Figure 1.

In this work we aim to quantify the effects of particulates on the wavefront sensor performance and investigate the wavefront sensor ability to characterize the particulate field.

Incident Turbulent Transmitted Wavefront Medium Wavefront

Lenslet CCDFigure 1. Schematic of our experimental setup, resembling the OTS, consisting of an incident

plane-parallel light beam, the non-planar transmitted beam resulting from fluctuations in the index of refraction within the turbulent scattering medium, and the corresponding focal-spot distribution,

as seen by a linear CCD element after focusing by a lenslet array.

MOTIVATION

The Optical Turbulence Sensor (OTS) has been developed to measure in situ the near-forward VSF through scattered wavefront analysis. The OTS thereby presents a unique tool, not only for optical characterization of turbulence, but of particulates as well. Such optical characterization by measuring the VSF of these particles using the wavefront sensor is important for optical light scattering measurements, particularly in coastal regions, where large particles, such as sediment and aggregated particulates, or flocs, are prevalent in the turbid waters. Proper characterization of the VSF for use in such measurements is important because in situ VSF measurements are used to obtain information about the shape, size, and refractive index of the scattering media comprising the water column (Sullivan et al. 2005, Berthon et al. 2007).

Proper parameterization of oceanic turbulence in terms of its VSF and total turbulent scattering coefficient also allows for determination of parameters for an active remote sensing instrument (lidar) capable of measuring the strength, and possibly the depth, of the oceanic mixed layer (Bogucki et al. 2007). The turbulence induced VSF is also important in instrument measurements that rely on near-forward light scattering, such as the Sequoia Scientific LISST Series Laser Diffraction Particle Size Analyzers (Styles 2006), or any light beam transmissometer (beam c). It has been suggested that turbulent scattering may contaminate measurements obtained from these instruments under certain conditions. Therefore, it is important to quantify the effects of turbulence on optical oceanic measurements within the range of observed oceanic turbulence. And conversely, it is also important to quantify how near-forward scattering from particulates influences optical measurements of turbulent scattering. Our laboratory experiments combine observations of near-forward particulate scattering with concurrent observations of near-forward turbulent scattering, for varying strengths of turbulence in a controlled Rayleigh-Bernard convective cell, allowing for an investigation of the interplay between particle dynamics and their optical scattering properties, particularly in the near-forward direction.

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EXPERIMENTAL SETUP

Our measurements are centered upon a Rayleigh-Benard convective cell, consisting of a 30 cm cubic tank, which is heated on the bottom and cooled on the top. The fluid is kept at an ambient average temperature, but the top and bottom are adjusted to maintain a vertical temperature difference, ∆T, about the ambient, inducing a controllable flow capable of generating high Rayleigh Number, Ra > 106, and thus fully turbulent, flow. Pure water is used inside the tank, but is seeded with 10 μm spherical particles for characterizing the flow with a Particle Image Velocimeter (PIV), which will allow for computation of the viscous energy dissipation of the flow from the cell velocity field. A fast response thermistor (FP07) is inserted into the interior of the tank to provide a temperature time series of the turbulent flow from near the center of the convective cell. This measurement, combined with that of the PIV, allows for determination of the temperature dissipation rate, energy dissipation rate, and energy and temperature dissipation spectra. With means for calculating the thermal and energy dissipation of the flow for different ∆T, we are able to characterize the turbulence of the cell, providing a useful tool for investigating the effects of oceanic scale turbulent scattering, as well as particulate scattering on wavefront sensor measurements of the VSF within a controlled environment, utilizing the OTS.

The OTS, or Optical Turbulence Sensor, is comprised of a laser diode light source, lenses providing optical expansion and collimation of the beam, a 30 cm measurement pathlength, focusing optics, and an array of receiving lenslets, which focus the beam onto a CCD (charge coupled device), before the image is fed to a computer. A schematic of this setup was provided in Figure 1. Through the array of lenslets, the instrument is able to capture changes in the initially plane-parallel optical wavefront, induced by inhomogeneities of the refractive index of the scattering medium, which result from the turbulent motion of the fluid. These phase changes are then used to compute the near-forward volume scattering function of the fluid.

The PIV, or Particle Image Velocimeter, consists of a pulsed Nd-Yag laser that illuminates a two-dimensional sheet within the convective cell, and a camera which images the sheet, as depicted in Figure 2 below. By seeding the flow with particles and recording a series of snapshots of the flow within the laser-illuminated sheet, a time series of the velocities within the flow can be obtained by dividing the images into a grid and determining the maximum correlation between grid points in subsequent images, resulting in a series of velocity flow fields. From these velocities, an estimate of the rate of turbulent kinetic energy dissipation (TKED rate), ε, may be obtained. The TKED rate is an indication of the diffusivity of momentum and other scalar quantities of the flow, and is thus a measure of how quickly a velocity disturbance within the flow will be dissipated. A corresponding estimate of the temperature dissipation (TD) rate, χ, which indicates how quickly a temperature disturbance within the flow will be dissipated, is then determined by combining these velocities with the time series obtained form the thermistor in the interior of the cell. These parameters, which are also obtained from the OTS measurements, allow for characterization of the turbulent flow within the convective cell over a range of turbulent regimes.

Figure 2. Experimental setup of the Particle Image Velocimeter (PIV): a pulsed Nd-YAG laser illuminates a two-dimensional sheet of particles across the convective cell, which is imaged by a

camera. A thermistor near the center of the sheet takes concurrent temperature measurements of the flow within the cell.

The diffractometer allows for measurement of the near-forward scattering of a plane-parallel beam from the medium, and is used for investigating the near-forward scattering of the PIV particulates, as well as a variety of other size distributions of particulates, seeded into the flow of the convective cell. The diffractometer also allows for measurement of the linear polarization of the near-forward scattered light. The details of this portion of the experiment may be found in the abstract by W. Freda et al., entitled “Polarization of the near-forward light scattered on particles and a turbulent flow.”

RESULTS

Particle Image Velocimetry measurements of the Rayleigh-Bernard convective cell demonstrated large scale velocity flow structure in agreement with the observations of Xia et al. (2003). The time-averaged flow consists of a mean rotary motion, with an elliptically shaped lower velocity core, and concentrated higher velocity regions around the perimeter of the cell. Figure 3 shows the time-averaged flow for (a) ∆T = 1.4 oC, corresponding to Ra = 1.8*108, and (b) ∆T = 11.7 oC, corresponding to Ra = 1.4*109.

(a) (b)Figure 3. Time-averaged mean velocity field for (a) Ra = 1.6*108 and (b) Ra = 1.4*109. Velocities

shown are in (m/s). The dark blue region near the upper left-hand corner is the zero velocity region corresponding to the thermistor. The dashed black line indicates the approximate part of the flow

seen by the OTS and diffractometer.

The PIV measurements of the convective cell were obtained simultaneously with near-forward scattering measurements from the OTS and diffractometer. A raw OTS measurement is shown in Figure 4. The horizontal axis of the image corresponds to the array of lenslets, and the vertical axis to time, so that the image is composed of sequential readings of the lenslet array. Were no scattering to occur, the image would be composed of evenly spaced straight vertical white stripes overlaying the black background, indicative of the plane-parallel wavefront incident beam, focused through the lenslet array. Two main features are obvious in the raw image, measures of the turbulent and particulate scattering from the seeded turbulent flow. The seemingly elongated features lying across several lenslets, and resembling an image of an internal wave, result from scattering upon the turbulent inhomogeneities, while the rounded, diffraction ringed features lying across only a few lenslets result from scattering on suspended particulates.

Particulate scattering Turbulent scattering

Figure 4. Raw OTS image of near-forward scattering from turbulent inhomogeneities and suspended particulates.

These raw images are then processed to obtain the scattering angle distribution observed from each lenslet as a function of time, as shown in Figure 5. Here, the axes are opposite from that of Figure 4: the horizontal axis is time, while the vertical axis is the lenslet array. The grayscale represents the scattering angle in micro-radians.

Figure 5. Intermediate processing of OTS data, showing the scattering angle distribution for each lenslet as a function of time.

Finally, this information is used to obtain the near-forward VSF, as shown in Figure 6 for ∆T = 6.6 oC, Ra = 7.7*108. Here, measured VSFs are plotted for two cases: turbulent flow in the absence of particulates, and turbulent flow seeded with 10 μm particles. While the overall shape of the two curves is similar, there is an obvious dissimilarity in the tails of the two curves for angles larger than about 4*10-4 μrad. This discrepancy is due to the particulate scattering of the seeded flow, showing the dominance of turbulent scattering at very small angles, and the influence of particles at larger angles. Unfortunately, the turbulent dominated VSFs at the very near-forward do not have better overlap here due to a slight temperature drift in ∆T (and thus a corresponding drift in Ra and the strength of the turbulent flow) during the course of the experiment.

Figure 6. Sample OTS VSF for Ra = 7.7*108. The red curve is the VSF from turbulent flow in the absence of particles. The blue curve is the VSF from turbulent flow with suspended 10 μm particles.

DISCUSSION AND FUTURE WORK

From these results, it is clear that the effects of both turbulent and particulate scattering are evident in wavefront sensor measurements of the VSF, with the former dominating scattering at the smallest near-forward angles, and the latter at larger angles. Utilizing the controllable Rayleigh-Bernard convective cell, for which the turbulent flow is characterizable by means of PIV and thermistor measurements, these turbulent and particulate scattering effects may be investigated more fully over a range of turbulent regimes and particle sizes and concentrations relevant to oceanic measurements of the VSF. Such measurements and characterization will provide insight into in situ optical and turbulence measurements in a variety of oceanic regimes of varying turbulent kinetic energy and thermal dissipation rates: surface breaking waves, the mixed layer, near bottom and coastal, as well as the deep ocean.

To ensure consistency and confidence in these characterization efforts, work is currently underway to reaffirm OTS VSF measurements with those obtained from diffractometer measurements. We will also seek to provide affirmation of these measurements through comparison of measurement results with those analytically derived from Rytov theory.

In addition to the near-forward VSF, OTS measurements may also be used to obtain estimates of the turbulent kinetic energy, ε, and temperature dissipation, χ, rates, as in the plots of Figure 7, showing in situ measured OTS ε and χ depth profiles off the Oregon coast. Future work includes additional in situ OTS measurements that allow for comparison with the optical and turbulent laboratory measurements presented above.

Figure 7. OTS in situ measurements of TKED and TD off the Oregon coast: (a) Depth profiles of ε, χ, temperature, and salinity, (b) scatterplot of ε and χ from (a), overlayed with regions of our current

laboratory and recent in situ coastal (Bogucki et al, 2007) measurements of ε and χ.

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