sensor finite size. Microstructure measurements are also limited by the operational ability to deploy instrumentation to perform such measurements.

Transcription

1 Measurements of the turbulent microstructure of a buoyant salinity plume using acoustics Marcos M. Sastre-Córdova, Louis Goodman, and Zhankun Wang Intercampus Graduate School of Marine Science University of Massachusetts School of Marine Science and Technology 706 South Rodney French Boulevard, New Bedford, MA 0744 USA Abstract- A study has been undertaken to examine the nature of acoustic scattering from salinity fluctuations. A theoretical relationship between acoustic backscattering and salinity fluctuation has been developed. This relationship is expressed in terms of measurable oceanographic variables, namely the turbulent kinetic energy dissipation rate, ε, and the salinity gradient variance rate, χ S. Acoustic and oceanographic data taken from an autonomous underwater vehicle, the SMAST T- REMUS, operating in a naturally occurring freshwater plume was used to compare theoretical and observed backscattering strengths. Observations were found to be in qualitative agreement with predictions. I. INTRODUCTION Acoustics has the potential to provide an inexpensive and easy way to make quick synoptic measurements of turbulence (Seim et. al., 995). This technique is currently not used routinely for this purpose because direct observations needed to validate the theory are difficult to obtain. Much work remains to be done to test the validity of the assumptions made in the derivation of the theory and its applicability to the study of small scale turbulence and dissipation processes in the ocean. The observations and theory presented here are aimed at providing insight into the nature of acoustic scattering from salinity fluctuations. The study of ocean microstructure (typical length scales of millimeters to centimeters) is severely limited by the ability to make measurements of physical parameters at such small scales. Microstructure refers to scalar and vector ocean quantities (i.e., salinity, temperature, and velocity) occurring at spatial scales directly influenced by molecular diffusivity, and viscosity. For velocity, the smallest scales are typically of the order of centimeters; while for temperature and salinity they are of order millimeters. The spatial sampling rates required for such direct measurements for the case of temperature and salinity typically exceed current technology and operational capability except in some very limited cases and then by using specially equipped slow dropped instrumentation. Conventional instruments such as a high resolution fast response CTD (Conductivity Temperature and Depth) probe are limited by sensor relaxation time and of the sensor finite size. Microstructure measurements are also limited by the operational ability to deploy instrumentation to perform such measurements. Autonomous underwater platforms allow measurements of a variety of ocean parameters with acceptable collocation errors in space. This type of observation is important when studying time and space dependent processes. For the problem of acoustic scattering due to small scale volume variability this is particularly important. II. BACKGROUND A. Acoustic Scattering from Volume Variability Acoustic scattering from ocean turbulence is possible because turbulent motions in the ocean act on distributions of density and sound speed - the components of the acoustic impedance of the medium. The key physical quantity used to examine scattering processes is the scattering cross section. It can be shown for scattering from volume variability (Goodman and Kemp, 98) that the scattering cross-section σ V, is given by: π σ V = Φ( K ) κ () Φ is a function of the scalar variance dissipation rate and is a three dimensional spectra which can be expressed as (Goodman, 990) ( K ) Φ ( K) ( ) ( K) ρ Φ c K c + 4κ ( e K) κ Φ ρ ρ0 c0 ρ 0c0 Φ = ( e K) () where K is the Bragg wavenumber. Note that typically one defines the volume scattering strength S v =0log 0 (σ V ) expressed in terms of the units db. The product ( e K ) adds an extra angular dependence for scattering due to density, which is contained in the st and rd terms of equation (). The second term is the sound speed term whose angular dependence is contained in within the Bragg wavenumber K= κ sin( θ / ). At present, direct measurement of the terms in () is severally limited in wavenumber space and typically cannot be made at Bragg wavenumber ranges of practical Also with Raytheon Company Maritime Mission Center, 847 West Main Rd, Portsmouth, Rhode Island 087, USA Electronic mail: sastrem@raytheon.com

2 interest in high frequency scattering regimes above 00 khz. It is convenient to express () in terms of the temperature and salinity spectra Φ Τ, Φ S, and their cross spectra cross-spectrum Φ ΤS. Because variations around the mean quantities are small only the linear dependence between salinity and temperature and density and sound speed need to be considered (Lavery et. al. 00): 4 σ V = πκ [ A Φ T + ABΦ TS + B Φ S ] K () The coefficients A and B are given by θ θ A = a α sin B = b + γ sin (4) where c c a = b = (5) c0 T c0 These represent the fluctuations in sound speed c with variations in T and S (with c 0 the reference or background sound speed). The coefficients α and γ are the thermal expansion and haline contraction, and have typical values of approximately 0. x 0 - (C - ) and 0.8 x 0 - (psu - ), respectively. The spectra in equation () are evaluated at the Bragg wavenumber K. The wavenumber κ is the acoustic wavenumber which is related to acoustic frequency, ω, byω = c0κ. Since in general the three dimensional wavenumber spectra Φ T, Φ S, and Φ TS are not typically measured, but one dimensional versions of these are, we need to use some relationship between the one dimensional spectra and the three dimensional spectra. This only can be done if some assumption on the symmetry of the turbulent field is made. Assuming that the fluctuations are isotropic and homogeneous at the scales of interest, the -D spectrum φ can be related to the -D spectrum Φ by (Tatarski, 96): dφ Φ = (6) πk dk where φ can be obtained from the gradient spectrum at wavenumber k, S(k) by φ = S( k) (7) k S(k) is the one dimensional gradient spectrum (i.e., the spectrum of Θ). In the case of a single scalar, like temperature, S(k) can be both measured and modeled. In the context of variability spectrum, k represents the wavenumber of the media variability not the acoustic wavenumber κ. Using the concepts of an equilibrium range for turbulent field (Batchelor, 95) the gradient spectrum for a scalar is given by (Dillon and Caldwell, 980): / / S( k) = βχε k (8) for the inertial sub-range or k 0 <<k << k ν, is with k 0 the energy containing wavenumber scale and k ν the Kolmogorov wavenumber, where molecular dissipation of kinetic energy occurs at even smaller scales or higher wavenumbers in the range (k B >> k>> k ν ), the gradient spectrum is given by / ( q / ) χ S( α) = f ( α) k BD (9) = α / x / f ( α ) α e α e dx α Equation (9) is written as a function of the non dimensional wavenumber α defined by: k α = ( q) (0) kb The Batchelor wavenumber is defined as k B =(ε/νd ) /4 represents the wavenumber where diffusive effects are dominant; q is a proportionality constant which needs to be estimated from laboratory measurements (Grant, et. al., 968) and D is the scalar diffusivity. The constant β is chosen such that (8) and (9) are the same at k*. Seim (999) suggests a value of The turbulent kinetic energy (TKE) dissipation rate, ε, represents the transfer of kinetic energy by turbulent processes from the larger scale of the turbulent field /k 0 into the smaller scale and eventually into heat. χ is the scalar analogue of the dissipation rate, and represents the amount of variance being transferred into smaller scales and eventually diffused away by molecular diffusive processes. These two quantities are theoretically independent, but the mechanisms governing one may influence the other. We can eliminate the angular dependence in () since we are scattering monostatically at 80 (backscatter). We can also safely ignore the contributions of temperature and temperature-salinity variance since the operating acoustic frequency of 00 khz corresponds to a Bragg wave number of about 0 4 rads/m, which is two orders of magnitude higher than the Batchelor wave number for temperature variance. Figure shows volume backscattering predictions made from typical expected values of ε, and indirect measurements χ T, and χ S. For salinity dominated scattering equation () reduces to B 4 σv = πκ ( b + γ ) ΦS (κ ) () The superscript B is for backscatter. Using the definition of the scalar gradient spectrum (8) and (9), taking f(α)~α, and converting the -dimensional spectrum to a one dimensional wavenumber spectrum using (6) and (7) we get / / q ε S Φ S ( k ) = χ k () π ν Combining equations () and () yields / B 5 / ε σ / V = q ( b + γ ) χs κ () ν which can be written in terms of ε and the buoyant frequency, N, as

3 / B q Γ( b + γ ) / σ = ( εν ) κ (4) V N z Γ is the mixing efficiency, generally assumed to have a value of about 0.. Note that the scattering cross-section is then proportional to the square root of ε (i.e., σ ε / ). Volume Scattering Strength (S v ) Temperature Salinity Acoustic Frequency (Hz) f ADCP =8 khz Figure. Theoretical volume backscattering strength at high TKE dissipation rate. Note that even under high turbulence conditions observed no volume scattering contribution from temperature variance is expected. This suggests that any volume scattering variance observed at 8 khz is due to salinity microstructure. Estimated microstructure parameters for this plot were ε=.6x0-6 W kg -, χ T=.46x0-5 C s -, δ =0.586 C psu -, and χ S=.8x0-4 psu s -. B. Merrimack River Plume Studies The Merrimack River discharges into the Gulf of Maine approximately 6 km south of the New Hampshire - Massachusetts border with a watershed covering a significant portion of the New Hampshire and northeast Massachusetts land area. Discharge during the late spring time is typically between 500 and 000 m s -. The near-field river plume generated by Merrimack River discharge is characterized by a supercritical Froude numbers, enhanced mixing, and rapid water mass modification. This supercritical outflow region separates the estuary from the subcritical far-field plume downstream. The supercritical flow is typically initiated by topographic control at the estuary mouth and results in intense mixing and high flow speeds that are typically not present in the coastal ocean. Whereas the far-field plume is influenced strongly by the Earth s rotation and local wind stress, the supercritical outflow region is dominated by local advective processes and internal shear instabilities. The area over which the estuary outflow is supercritical is only a small fraction of the entire river plume area, but salinity changes occurring within the region of supercritical flow may be similar in magnitude to salinity changes that occur within the estuary or the far-field plume. However, despite the importance of these salinity changes in determining the water mass characteristics and structure of the river plume as a whole, there is no theory that describes the nature of these transformations, or their dependence on varying forcing mechanism. III. METHODS A. T-REMUS AUV The SMAST T-REMUS (Turbulence Remote Environmental Measuring UnitS) is a custom designed extended REMUS vehicle containing the Rockland Microstructure Measurements System (RMMS) developed by Rockland Electronics of Victoria, BC. The RMMS turbulence package consists of two orthogonal thrust probes, two FP07 fast response thermistors, three orthogonal accelerometers and a fast response pressure sensor (Lueck et al., 00). Also contained on the T-REMUS vehicle are an upward and downward looking. MHz ADCP, a FASTCAT CTD, a Wet Labs BBF Combination Spectral Backscattering Meter/ Chlorophyll Fluorometer, and a variety of hotel sensors measuring pitch, roll, yaw, and many other internal dynamical characteristics of the T-REMUS vehicle. This suite of sensors allows quantification of the key dynamical and kinematical turbulent and fine scale physical processes throughout the water column. The data presented here corresponds to two passes of the AUV along the river plume. The first pass is performed following a yo-yo pattern (see Figure 4) and is meant to capture vertical profiles across the freshwater interface. The second pass is the return flight at a constant depth below the river plume towards the mouth (see Figure 5). This pass provides good acoustic coverage of the upper section of the water column. Figure. The T-REMUS AUV. T-REMUS is equipped with a team of sensors: hotel sensor suite, a conductivity, temperature and depth appendage (CTD), an acoustic Doppler current profiler (ADCP), dual side mounted scanning sonar transducers (port and starboard), a shear, temperature, and acceleration probe module (UVSP), and a combination fluorometer/backscattering meter (BBF). B. Estimating TKE Dissipation Rate (ε) Advances in measurement techniques now allow direct estimation of the turbulent dissipation rate, ε,defined by ε u' i u' i = ν (5) x x j j

4 6 where ε is the dissipation rate, ν 0 ms is the kinematic molecular viscosity, u i is the velocity fluctuations, u' i / x j is the fluctuation gradient, i, j are the tensor indices which when repeated indicate a summation. The prime on a variable denotes the turbulent fluctuation and the overbar indicates an ensemble average. In isotropic turbulence, the dissipation rate Eq. (5) can be written as (Osborn, 980) ε = 5/ ν( ui'/ xj) (6) with i j. The derivation of (6) follows from the fact that (5) is a sum of 9 terms in a tensor. For an isotropic turbulent field (Batchelor, 95) the diagonal and off diagonal terms are equal to each other, respectively. The off diagonal term can be shown to be twice that of the diagonal term. C. Scalar Variance Dissipation Rates (χ T and χ S ) Accurate estimation of scalar variance dissipation rates requires full spectral resolution, to the Batchelor wavenumber. It is particularly difficult for the case of salinity variance which has a dissipation scale two orders of magnitude smaller than of temperature and velocity. Since temperature variance dissipates at somewhat larger scales it is possible to obtain indirect estimates of χ T from high resolution temperature data enough to cover the inertial-convective range for known values of ε. The spectrum for the inertial-convective range for a scalar goes as / 5 / φ = βχε k (6) where k is the wavenumber in rads/m and all other parameters are as defined earlier. Equation (6) can be fitted to measured spectra of temperature using least-squares optimization to obtain χ T. Φ / α r α Figure. Fast Response Thermistor Spectrum shown here in nondimensional space, α=(q) / k/k B. The thermistor s response rolls-off at α r, making spectral estimates at large wavenumber unusable. The inertialconvective subrange following a -5/ power law is indicated by the red line. Several methods have been suggested to make direct and indirect measurements of χ S. It is sometimes assumed that salinity variance has the same spectral characteristics temperature but at much smaller scales. No measurements of the salinity dissipation spectrum have been made to date in support of this hypothesis. It has become common to assume that (Lavery et al., 00) χ S =χ T /δ, where δ is defined as T z δ = (7) z A direct method for estimating χ S is possible using the instrumentation presented here, but requires careful spectral corrections to account for AUV motion. The approach consists of measuring the correlating vertical velocity fluctuations w and CTD derived salinity to obtain χ S = w' S' (8) z The quantity in < > represents an ensemble average of the variations in vertical speed and salinity. For such calculation, w must be resolved at very high wavenumbers where contamination from the AUV motion is expected (Goodman et al., 006). This method was not applied to the data presented here, but will be the subject of a future study. TKE/Scalar Dissipation Rate Mission Time (s) AUV Depth (m) Mission Time (s) Figure 4. TKE and scalar variance dissipation rates derived from spectral measurements. Dissipation rates are in units of Watts/kg, C/s, and psu/s for ε, χ T, and χ S, respectively. ε and χ T were estimated from spectral analysis of high resolution shear and temperature data. χ S was estimated from χ T /δ. The bottom figure shows the AUV depth corresponding to the measurements made. Increasing time corresponds to downstream measurements (i.e., away from the river mouth). D. Acoustic Backscatter at 8 khz It is possible to obtain calibrated measurements of the volume backscattering strength from ADCP intensity data. The quality of such measurements relies on how well the instrument characteristics are known. Sometimes data provided by the manufacturer might be sufficient for reasonable absolute estimates of volume scattering, but it might be worthwhile to recalibrate the ADCP unit to validate those parameters, as they could change over time and are different from unit to unit. The reader is referred to Deines (999) for a detailed description on how to convert from acoustic intensity to χ T χ S ε

5 volume backscatter. In essence, the ADCP intensity data is usually captured as counts and the converted to db by a scaling factor, K c, (usually 0.45 db/count). All measurements are relative to a reference value E r which hovers around 40 counts and is different for each ADCP beam (4 upward / 4 downward). From the monostatic active sonar equation the volume scattering strength, S v, is given by Sv = C + 0log 0 (( Tx + 7.6) R ) L DBM P DBW + αr + Kc ( E Er ) (9) The first term on the RHS, C, accounts for losses due to receiver characteristics and is taken as -9. db for the ADCP in use. The second term includes temperature (T x ) dependent receiver and spreading losses. L DBM is 0Log 0 (Pulse Length), which is 0.5 m. The source level term is P DBW and is 4.8 db. The range dependent absorption loss is given by αr and the received intensity in db units is obtained by K c (E-E r ), where E is the intensity level in counts measured by the ADCP. Figure 5. CTD derived temperature, salinity, and density anomaly (Top), and volume backscattering strength measured with the ADCP (Bottom). Increasing time corresponds to upstream measurements (i.e., towards the river mouth). Note that the density gradient features between seconds coincide with acoustic features resolved by the ADCP. IV. DISCUSSION From Figure (4) observed TKE dissipation rates ranged from.4x0-9 to 4.6x0-6 Watts/kg. Values typically decreased both with depth and distance from the river mouth. Using the CTD data for temperature and salinity we were able to calculate δ at the locations of the spectral estimates of χ T, which produced χ S values ranging from 6.0x0-8 to 9.8x0-4 psu/s, with a median at 5.x0-6 psu/s. χ T and χ S are lognormally distributed, so the ranges presented here correspond to the 5% and 75% percentiles. ADCP derived scattering strengths ranged from -0 to -50 db, with intense scattering activity closer to the river mouth, presumably from particulates. Downstream the scattering structure seems more uniform and homogenous, suggesting that volume variability scattering could be dominant over particulate scattering. Particular attention was made to scalar gradient features observed towards the edge of the data set that were observed to coincide in space with anomalies in the scattering structure (see Figure 5). Although not confirmed to be strictly volume variability scattering, these feature do coincide with sudden dips in density due to changed in salinity. This is suggestive that high-frequency volume scattering may be playing a role. Predicted values of backscattering strength due to observed salinity microstructure and turbulence activity ranged from - 0 to -58 db in depths between and meters. Only in one instance was the predicted scattering strength higher than -58 db but the observation was discarded as an outlier since the quality of the measurements at that particular location was in question. Maximum values were predicted closer to the surface averaging -65 db, and lowest at the plume deeper boundary at about m averaging -85 db. Preliminary variance calculations show that only about 5% (i.e., R ~0.5) of the variance observed in backscattering strength is actually explained by volume variability, so the hypothesis of volume variability scattering being dominant is still in question. This was done calculating correlation coefficient between the observed and predicted scattering at depths where acoustic and in-situ measurements were available. The comparison was made from ADCP intensity data that is not perfectly co-located with volume variability measurements, so part of the low correlation might be due to this fact. This can be addressed and will be further explored. The correlation analysis does reveal two regimes or cluster regions that will be further investigated. One of the clusters clearly shows an uncorrelated regime, where it can be seen that the measured scattering is not described by the theory prediction, and a regime that follows a ε / slope. This characteristic can be explored to isolate turbulent contributions to scattering from that of particulates. Spectral calculations of χ T produced values ranging from 6.0x0-8 to.x0-5 C/s, with a median at 8.x0-7 C/s.

6 Depth (m) Depth (m) ds/dz dt/dz δ δ Scalar Gradient ( o C m - / psu m - ) dt/ds ( o C/psu) Figure 6. CTD derived temperature and salinity gradients (Top) and dt/ds (Bottom) for a vertical profile of the plume. V. CONCLUSIONS A data set containing near co-located and synchronized volume variability and acoustic data collected by an AUV was analyzed to compare predicted backscattering strengths due to salinity microstructure with observed scattering by an ADCP. Spectral techniques were employed to estimate TKE and temperature dissipation rates, and CTD gradient data was used as a proxy for estimating salinity variance dissipation. Values obtained for ε, χ T, and χ S are within the range expected for a high turbulence / high scalar gradients regime, as in a freshwater river plume. These parameters were used to predict volume backscattering strengths at 8.8 khz to be compared to measured intensity data. Theory predicts scattering strengths of the same order as those observed with the ADCP. However, preliminary covariance analysis shows that only about 5% of the variance is truly explained by the theoretical predictions. Qualitatively, predictions and observations are in good agreement but in order to make quantitative comparisons the issue of co-location of acoustic and measured data has to be resolved. The data set obtained is very rich and we have the means of accounting for co-location errors, so it is expected for the correlation estimates to improve considerably. As for future work, errors on the estimates of ε and χ T must be quantified, as well as direct estimates of χ S need to be produced. χ S will be calculated using fast response shear probe measurements, vehicle accelerometer data, and CTD data. Scattering from particulates must be accounted for and can be done using optical scattering data as a proxy, which was also collected for the data set here presented. ACKNOWLEDGMENT This work was supported in part by ONR Grant # OA and by the Raytheon Company Advanced Study Program Fellowship. REFERENCES [] Batchelor G. K., 95 The theory of homogeneous turbulence [Book]. Cambridge university press. [] Dillon and Caldwell, 980: The Batchelor spectrum and dissipation in the upper ocean. J. Geophys. Res. 85 (C4), [] Deines, Kent L., 999 Backscatter Estimation Using Broadband Acoustic Doppler Current Profilers. Proceedings of the IEEE Conference San Diego, California. [4] Goodman and Kemp, 98: Scattering from volume variability. J. Geophys. Res. 86 (C5), [5] Goodman and Levine, 006: On measuring the terms of the turbulent kinetic energy budget from an AUV, J. Atoms. Ocean. Tech. (July), , 006. [6] Goodman, L. 990: Acoustic scattering from ocean microstructure. J. Geophys. Res. 95,,557-,57. [7] Grant et. al., 968: The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech. 4: [8] Kocsis, O., H. Prandke, A. Stips, A. Simon, A. Wueest. Jun 999 Comparison of dissipation of turbulent kinetic energy determined from shear and temperature microstructure, Journal of Marine Systems [J. Mar. Syst.]. Vol., no. -4, pp [9] Lavery et. al., 00: High-frequency acoustic scattering from turbulent oceanic microstructure: The importance of density fluctuations. J. Acoust. Soc. Am. 4(5), [0] Lueck, R.G, F. Wolk and H. Yamazaki. 00 Oceeanic Velocity Microstrcutre Measurments in the 0th Century, J. Of Ocean., Vol, 58, pp.5-7 [] Osborn, T.R., 980. Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 0, [] Seim, H. E. 999: Acoustic backscatter from salinity microstructure. J. Atmos. Ocean. Tech. 6, [] Tatarski, V. I., 97: The effects of turbulent atmosphere on wave propagation, Israel Program for Scientific Translations, Jerusalem.