Comparison of Dissipation Estimates

The rate of dissipation of turbulent kinetic energy can be determined using both velocimetry and
temperature microstructure methods.  Others have compared results from the two methods using
data collected in the field (e.g., Oakey 1982, Etemad-Shahidi and Imberger 1998, Kocsis et al. 1999).
In our first set of experiments, we measured dissipation of turbulent kinetic energy using a Micro-
Acoustic Doppler Velocimeter (ADV) from Sontek and a Self-Contained Autonomous MicroProfiler
(SCAMP) from Precision Measurement Engineering.  We first compared measurements from the
instruments in a semi-controlled environment, a field scale bubble plume experiment.  To improve
upon this comparison , we performed a controlled laboratory experiment in which both instruments
measured at the same point .


 Since the original experiments, I have compared the SCAMP with Particle Image Velocimetry, Laser Doppler Velocimetry, and Hot Wire Anemometry. Generating a wide range of dissipation values in the lab has proved to be difficult. Below discusses just the results from the ADV.

The SCAMP and the HWA in a recirculating flume.

EXPERIMENTS
Bubble plume experiments (measurements done by Cheeta Soga and Carlos Garcia)
  • Compressed air released at the center of the bottom of a round tank    
  • Tank dimensions: 13.7 m (radius), 8.3 m (maximum depth)
  •  Air flow rates: 0.1 – 0.6 L/s
  •  Measurements taken at r = 1.2, 2, and 4 m
  •  SCAMP and ADV measured at locations  equidistant from the plume on opposite sides
  • Six SCAMP datasets, with 18 – 51 profiles
  • Six ADVs located 1.2, 1.6, 3.9, 5.3, and 6.8 m above the air diffuser

Laboratory experiments    
  • Recirculating flume
  • Channel width: 30 cm    
  • The ADV run simultaneously with the SCAMP for 15 minutes.
  • Cylinder placed perpendicular to the flow to  produce a range of dissipation rates.
  • SCAMP sampling rate: 100 Hz
  • ADV sampling rate: 25 Hz
  • Eleven datasets
ADV data

The dissipation was computed from the inertial subrange of the spectrum of the vertical velocity fluctuations (used because the noise is lowest in this direction) derived using Welch’s averaged, modified periodogram method.
 
SCAMP data

The dissipation was computed in segments of 512 points by fitting the spectrum of the fluctuations of the temperature gradient to the Batchelor spectrum using the maximum likelihood spectral fitting method of Ruddick et al. (2000), which employs three goodness of fit measures:  the log of the likelihood ratio (LLR), the mean absolute deviation (MAD), and the signal to noise ratio (SNR).

RESULTS

The measurements in the bubble plume agree within a factor of 2 throughout the range of dissipations measured.  Only two sets of measurements did not fall within a factor of two.  In both these runs, the velocity of water past the sensors was not optimal for the SCAMP.

The low data point had a velocity of 13 cm/s, which is higher than the typical fall velocity of the SCAMP. In this run the percent resolution of χT was only 70% (while all the other good runs were 90% or better). If χT is not resolved well, then the dissipation will be underestimated.

The high data point had a velocity of 5 cm/s.  Almost half of the segments were rejected in this dataset. Many of the segments failed the likelihood ratio criterion, which is a measure of how much closer the measured spectrum is to the Batchelor spectrum than to a power law.  The rejected segments tended to have SNR that was low but still above the criterion of Ruddick et al. (2000). Because segments with stronger signals passed, the dissipation estimate is high.

Comparison between dissipation estimated with the SCAMP and an ADV. Open circles come from the bubble plume experiment; closed circles come from the lab experiment.  Dotted lines indicate a factor of 2 away from the line εSCAMP = εADV.