Use of Turbulent Kinetic Energy and Scalar Variance Budgets to Obtain Directly Eddy Viscosity and Diffusivity from AUV Turbulence Measurements

In this manuscript we examine whether measurements obtained from an Autonomous Underwater Vehicle (AUV) equipped with standard microstructure and fine structure sensors can be used to close the Turbulent Kinetic Energy (TKE) and Temperature Variance TV (heat) budgets. Classical turbulence theory is used to estimate the dissipation rate, ε, and the rate of change of the variance of temperature, χ. The turbulent Reynolds stress production and heat flux terms are also obtained directly from measurements. Examination is made of data obtained from an experiment in Narragansett Bay RI in a strong tidally driven stratified shear field. The turbulent field observed, although of limited spatial extent, can be segmented into three different regimes, a strongly turbulent isotropic regime, an anisotropic regime, and a weakly turbulent regime. For these three regimes the TKE budget can be closed within a factor of 2. Closure of the TV budget is not as good, although there appears to be a trend of increasing closure with decreasing turbulence level. This might be explained by the fact that the spatial filtering effect of the finite size of the AUV, being of order 2.3 meters in length, has more of an impact on the calculation of the heat flux term than on the Reynolds stress term. Mixing efficiencies of order .2 are found for all three regimes, with a slight trend of increasing with increasing buoyancy Reynolds number. 1. Background/Introduction Although there is and has been a great deal of interest in oceanography in turbulent mixing, both for application to the subgrid scale parameterization in ocean numerical models and for process studies, direct measurements of mixing are very limited. To obtain the flux (mixing) of momentum, dissipation rate, ε, is typically calculated from turbulent velocity shear measurements and then combined with a local (finescale) value of the vertical shear field. For the temperature (and salinity fields) indirect methods are typically employed to obtain their fluxes, relying on some version of the Osborn (1980) formulation, and assuming a constant mixing efficiency of typically .2. In the past two decades, there have been increased efforts in the laboratory (Ivy et al., 1998, Itsweire et al., 1986, Stillinger et al., 1983) as well as the field (Fleury and Lueck, 1994, Moum, 1990) to obtain directly and simultaneously the fluxes of momentum and heat without recourse to invoking some specific value for mixing efficiency. However, it should be stated that often values of order .2 are obtained in these studies, lending credence to that assumption. Turbulence mixing has been the subject of many reviews, see, for example, Gregg, 1987, Gargett, 1989, and Caldwell and Moum, 1995. For the past thirty years the standard technique of measuring turbulent quantities in the ocean has been by means of microstructure profilers pioneered by Cox et al., 1969, Osborn, 1974, and Gregg et al., 1982. These techniques provide very high-resolution 144 GOODMAN AND LEVINE vertical distribution of turbulent quantities and more recently, with the advent of rapid loosely tether profilers, some horizontal information on the distribution of the turbulent quantities. Efforts are presently underway to obtain fixed-point time series and horizontal sampling of turbulent quantities. For a review of microstructure observational techniques see the special series of articles in the Microstructure Sensors Special Issue (J. Atmos. Oceanic Tech., 16(11), November 1999) and the recent article by Lueck et al. (2002) on velocity microstructure measurements. Horizontal transects of turbulence can resolve structures on scales not resolvable with vertical profiling (Yamazaki et al., 1990). In the past, horizontal sampling, using towed bodies and submarines, has provided unique views of internal waves (Gargett, 1982), salt fingers (Fleury and Lueck, 1992), and turbulence (Osborn, 1985). Vibration measurements taken aboard the NUWC vehicle Large Diameter Unmanned Underwater Vehicle (LDUUV) in Narragansett Bay (Levine and Lueck, 1999) indicated that this platform was sufficiently stable to obtain horizontal measurements of dissipation rate in shallow water. Following this, Levine et al. (2000) demonstrated that a small AUV could also be used to measure the turbulent dissipation rate. This manuscript addresses the question of how much information on the turbulent fields can be obtained from a small AUV equipped with standard fine and microstructure sensors. Although results are particular to one deployment in a very specific setting, aspects of this study should be generalizable to other similar situations. The key issue addressed is whether one can use an AUV to obtain directly measurements of the fluxes of momentum and heat and thus obtain in situ estimates of the eddy viscosity, kν , and the diffusivity kρ, key parameters in mixing studies and numerical models. To perform these types of measurements a variety of assumptions must still be made. It should be noted that the ability to close the turbulent budgets is an important constraint used in assessing the validity of these assumptions and in the validity of the techniques themselves. Following this introduction the manuscript is organized into the following sections: 2. Description of the Turbulence AUV Vehicle, 3. Estimating the TKE and TV Budgets, 4. Results from the Narragansett Bay September 2000 Experiment, and 5. Summary and Conclusions. 2. Description of the Turbulence AUV Vehicle The Turbulence AUV, shown below in Figure 1, performs synoptic microstructure and finestructure measurements (Levine et al. , 2001). It is an extended REMUS vehicle (von Alt et al., 1994) 2.3 m in length, .18 m in diameter, weighing 56 kg in air. With the first-generation turbulence-measuring AUV, we are currently limited to the mid-water column, for safety, and to an endurance of 4 hours using rechargeable lead-acid batteries. However, modifications to the internal frame enable rapid redeployment with fresh batteries. Figure 1. Turbulent REMUS AUV Sensors include two FSI CTDs, an upwardand downward-looking 1.2 MHz ADCP, a University of Victoria Turbulence Package (two orthogonal thrust probes, three accelerometers and one FP07 fast response thermistor), and a SONTEK ADV-O. Vibration studies have led to reductions in noise transmitted to the shear probes with the use of a damping material and a probe stiffener attached to the forward end of the UVIC pressure case. Also contained in the AUV are a variety of standard REMUS “hotel sensors”, including pitch, roll, heading, depth, latitude, and longitude. In addition, the AUV navigates using a SBL system, using onboard forward-looking and moored transponders. For safety, the AUV is tracked from a surface vessel using a Trackpoint II transponder. For a more complete description of the techniques used to calculate the dissipation rate, see Levine et al., 2001. Absolute velocity is obtained from Upward and Down ward ADCPs Upper CTD Lower CTD Thrust probe EDDY VISCOSITY AND DIFFUSIVITY FROM AUV MEASUREMENTS 145 the bottom tracked mode of the downward-looking ADCP, which combined with Doppler obtained from volume scattering allows very precise absolute water velocity and shear. With these sensors, the AUV is capable of measuring the key finescale gradients of velocity, temperature, salinity, and density, as well as the turbulent temperature and the two-component velocity shear field, the components transverse to the direction of AUV motion. The response of the shear probe and the corrections needed to estimate the unresolved high wavenumber contribution are discussed in Macoun and Lueck (2002). The response of a REMUS vehicle to the larger turbulent scales and the use of the vehicle vertical motion to infer turbulence at these scales using a Kalman filter technique are discussed by Hayes and Morrison (2002). Raw data from the shear probes is processed to remove noise associated with platform vibration. This transfer function method utilizes data from accelerometers mounted in the pressure case, directly behind the probe mounts. The combination of noise limiting vehicle modifications, discussed above, and the use of the all accelerometers has resulted in a noise floor of order 10 W/kg. The addition of the probe stiffener raises the resonant frequency of the probes into the kilohertz range. The frequency response of the FP07 fast thermistor used in the UVIC turbulence package, 25 Hz (Lueck et al., 2002), is too slow for capturing the high wavenumber end of the thermal microstucture using the AUV, typically moving relative to the water at 1 m/s. For calibration, this fast thermistor is compared with synoptic data from the CTD platinum thermometer. To estimate stratification, two Falmouth Scientific Instruments CTDs are mounted above and below the centerline of the AUV. These instruments, 2" FSI MCTDs, utilize an inductive conductivity cell, a platinum resistance thermometer, and a silicone pressure sensor. Correspondingly, the manufacturer claims accuracies of ±0.0002 S/m, ±0.002°C, and 0.02% of full scale pressure (100 db) for these sensors. Because of drift problems with these sensors for the study presented here, stratification was estimated from individual CTD vertical profiles during launch and recovery. To estimate finescale velocity shear, a modified version of the RDI 1200 kHz Workhorse navigator ADCP was integrated in the AUV hull. Upwardand downward-looking transducers share one set of electronics and ping alternatively. The manufacturer claims accuracies for water velocities of ±0.2% ±1mm/s. We selected eight 0.5-m bins for both the upward and downward transducers. Since the vehicle diameter is 0.18 m and the blanking distance is .25 m, the edge of the first bin is located 0.34 m from the AUV centerline. Because of the potential of side lobe scattering we ignore the first bin and use the second and third bins to estimate the finescale shear above and below the vehicle. An average of these upwardand downward-looking estimates represents the finescale shear field over a 4-m scale surrounding the body. This platform has been used in a number of successful studies, which are realizations of Autonomous Ocean Sampling networks (Curtin et al., 1993) Turbulence observations have been made in the LEO summertime upwelling region, offshore of New Jersey, (Levine et al., 2000), as a component of a dataassimilative forecast system (Glenn et al., 1998). In addition, turbulence measurements were obtained in the LOOPS study of patchiness in the biophysical regime of Cape Cod Bay (Levine et al., 2001). Also, turbulence observations have been made, in coastal fronts in the FRONT network near the mouth of Long Island Sound (Levine et al., 2002) in a region strongly influenced by estuarine outflow and tides. In the above turbulence studies, only the dissipation measurements have been used to estimate epsilson, and the estimation of chi has not been attempted. Consequently, the Osborn (1980) formulation has been invoked to obtain the diapycnal density flux. 3. Estimating the TKE and TV Budgets If the turbulent field is steady in time and homogenous in space one can show (Gregg, 1987) that the equations for the turbulent kinetic energy (TKE) budget and temperature variance (TV) budgets are respectively,