Abstract

An intercomparison study was performed with four Russian-made, electromagnetic probes capable of measuring three components of oceanic turbulent velocities and two single-axis velocity sensors familiar to western scientists, namely, a hot-film anemometer and an airfoil shear probe. The intercomparison measurements were conducted in a water flume tank in the Marine Scientific Production Corporation on Fishery Technology facility in Kaliningrad, Russia. Measurements were obtained in the turbulent region generated behind a grid at three different mean flow speeds (0.7, 1.1, and 1.7 m s−1). In all the intercomparison runs, data from the electromagnetic velocity probes behave in a manner expected from the sensor and filtering characteristics. On the average, turbulent velocity variances from the electromagnetic probes are about ±20% of those from both the hot-film and airfoil probes.

1. Introduction

Electromagnetic velocity probes (hereafter EM probes) capable of measuring the three components of oceanic turbulent velocities (longitudinal, transverse, and vertical, hereafter u′, υ′, and w′, respectively) have been developed in the former Soviet Union since 1983. The probes are based on the electromagnetic induction principle by which an electric field is induced in the region of the interaction of a flow of a conductive liquid with a magnetic field. One of these EM probes was used in the Tropical Ocean Global Atmosphere Comprehensive Ocean–Atmosphere Research Experiment (TOGA COARE) to obtain fluctuating velocity measurements of the flow ahead of the bow of the R/V Moana Wave (Soloviev and Lukas 1997; Soloviev et al. 1998; Soloviev et al. 1999). To evaluate the performance of these probes, velocity measurements of grid-generated turbulence were taken in a water flume tank at the Marine Scientific Production Corporation on Fishery Technology (MARINPO) facility in Kaliningrad, Russia, using several EM probes of different sizes and sensitivities. These measurements are compared with similar measurements taken in the same facility, using two turbulent velocity sensors familiar to western scientists, namely, a one-component DISA hot-film anemometer and an airfoil shear probe. The results of the intercomparison are presented in this paper. The present work provides an extension to that performed by Soloviev et al. (1998).

A general description of the EM probe and the principle of its operation are given in section 2. The calibration facility and calibration of the EM probes are described in section 3. The intercomparison experimental setup, the MARINPO facility, and the two reference sensors are described in section 4. An overview of the data intercomparison is given in section 5, followed by the intercomparison between the EM and reference velocity data in section 6. The three components of turbulent velocity and their use for evaluating isotropy are presented in section 7. The noise levels of the different EM probes are estimated in section 8. The possible effects of data contamination by vibrations is assessed in section 9, followed by a summary and discussion in section 10.

2. General description and principle of operation of EM probes

The EM probes used in this study are manufactured by Dr. A. Arjannikov at ECAR Ltd., St. Petersburg, Russia. A photograph of an EM probe is shown in Fig. 1. A ruler, with dimensions in inches, is included in the photo for scale. The total length of the probe shown is 70 cm. In the photo, the sensor tip is located at the far right, an input/output connector is located on the far left, and a flange for mounting the probe is located one-third of the way from the connector to the sensor tip. The sensor tip contains four permanent magnets with electrodes placed between them (Fig. 2). The electrodes are isolated from the magnets by an epoxy compound (a dielectric material).

Fig. 1.

Photograph of an electromagnetic three-component turbulent velocity probe. The scale of the ruler is in inches.

Fig. 1.

Photograph of an electromagnetic three-component turbulent velocity probe. The scale of the ruler is in inches.

Fig. 2.

Schematic diagram of the magnets and electrodes in the EM probe.

Fig. 2.

Schematic diagram of the magnets and electrodes in the EM probe.

The sensor tip is 40 mm in diameter for the EM probe shown. Other EM probes with a smaller sensor tip (16 mm in diameter), and with magnets of different strength (and therefore different sensitivities), were also used in this intercomparison study.

The probe electronics are located inside the titanium housing. A 10-pin connector on the far left end of the probe carries the ±20 V to power the probe, and it also carries the analog outputs from the sensors. The useful bandwidth of the measurements is between 0.05 and 200 Hz. The range of each of the three turbulent velocities is −1.0 m s−1 to +1.0 m s−1 with a noise level ∼1 mm s−1. In this probe, one or more accelerometers can be placed near the sensor tip to measure motions due to probe vibration.

The operation of the probe is based on the principle of electromagnetic induction. A magnetic field is set up by four permanent magnets located symmetrically on the sensor tip (Fig. 2). In the area of interaction between the flow of the conducting water and the magnetic field, an electrical field is induced. Four electrodes are placed at the centers of the space between the magnets to measure the potentials of the induced electric field. The different potential differences measured by the electrodes are proportional to the different components of the fluctuating velocity field. The closest separation between the electrodes is typically half the sensor tip diameter. In theory, one can derive analytically the relationship between potential differences and the velocity field. In practice, such computation is difficult due to the complex three-dimensional nature of the fluid flow and the inductance field. Instead, these relationships are obtained by a calibration procedure described in the next section.

3. EM probe calibration

a. Calibration facility

The EM probes were calibrated by Dr. A. Arjannikov in the hydrodynamic water channel (HDWC) at the Central Research Institute “GRANIT” in St. Petersburg, Russia, in a turbulent jet at two flow speeds. A drawing of the calibration facility is shown in Fig. 3.

Fig. 3.

Hydrodynamic water channel calibration facility in GRANIT. The numbered features are described in the text.

Fig. 3.

Hydrodynamic water channel calibration facility in GRANIT. The numbered features are described in the text.

The HDWC is a closed-circuit system with two levels. The upper level consists of a test section (identified as 1 in Fig. 3), a turning chamber (2), a vortex depressor (3), a stabilizing section (4), a convergent nozzle (5), a grid (6), and directing blades (7). The lower level consists of three turning chambers (8, 12, and 13), a reversing channel (9), a pump (10), and a motor (11). Deployment of the probe and its proper placement in the jet is provided by a supporting device (14). All parts of the facility containing water are shown shaded in the figure.

The test section is an open tank, with dimensions 3 m (length) × 0.75 m (height) × 0.75 m (transverse). A jet flow with a controllable and reproducible velocity field is generated at the nozzle. The exit hole diameter of the nozzle is 6 cm. Velocity distributions of the jet at the nozzle edge and at the region of developed turbulence are illustrated by arrows in the figure.

The vortex depressor is a cylindrical chamber with grids and honeycombs to suppress the generation of vortices. In conjunction with the nozzle, the cone-shaped stabilizing section homogenizes the velocity distribution of the jet. A grid is placed close to the back wall of the tank to inhibit a reflecting current. Turning blades are used to direct the flow to the lower level and turning chambers are used for smooth continuous rotation of the flow by 90°.

The pumping device consists of a centrifugal pump driven by a DC motor. The number of rotations of the motor, and, therefore, the flow velocity, is controlled by a thyristor controller. After filling the tank with water and degassing, the thyristor controller is switched on and the motor starts. The probe to be calibrated is located along the axis of the submersed jet at a distance of 10 D from the nozzle, where D is the nozzle exit diameter. To monitor the mean speed of the jet, a differential manometer was used to measure the pressure difference between the stabilizing section and the edge of the nozzle.

b. EM probe calibration procedure

Calibration of an EM probe is done in two separate steps. The first step is to obtain a reference turbulent velocity spectrum of the jet in the HDWC with an established and calibrated velocity sensor. This is done using a dual-axis DISA hot-film anemometer that measures two components of the velocity fluctuations. By changing the orientation of the hot-films, all three fluctuating velocity components (u′, υ′, and w′) are measured. The calibrated DISA hot-film probe was placed along the axis of the jet at a distance 10 D from the nozzle. The velocity spectral data at 24 frequency intervals ranging from 2 to 400 Hz were obtained using an Hewlett-Packard 8064A spectrum analyzer that produces filtered output signals, each with a 1/3 octave width centered at a frequency. The averaging time for each set of measurements is 13 s. Data were taken at two mean flow speeds of 1.1 and 2.2 m s−1. The outputs from the spectral analyzer (in dB) are converted to rms velocity values and are shown in Fig. 4. The DISA velocity data indicates that turbulence in the calibration jet is anisotropic. The transverse velocities (υ′ and w′) are similar, and they are lower than the longitudinal velocity fluctuations (u′).

Fig. 4.

DISA rms velocity as a function of frequency in a submerged jet used for EM probe calibration. Data from 2 to 20 Hz are used for calibration.

Fig. 4.

DISA rms velocity as a function of frequency in a submerged jet used for EM probe calibration. Data from 2 to 20 Hz are used for calibration.

The second step of the calibration is performed for each EM probe. The EM probe is placed at the same location in the jet as that of the DISA probe in the first step. The rms values of the observed voltage fluctuations along each of the three axes of the EM probe are obtained with the same HP spectral analyzer. The same frequency bands as the DISA velocity measurements are used. Again data at two mean flow speeds were taken. To stabilize statistics, the measurements are repeated three times for each mean speed.

The reference DISA velocity spectra and the voltage spectra from the EM probe are then used to produce the calibration coefficients for the EM probe. The computation is performed in the following steps:

  1. The measured rms voltage signals of the EM probe are divided by the rms DISA velocity signals at the corresponding frequency. The DISA velocity spectrum for a component is used for the corresponding EM component.

  2. For the initial set of readings, all the points between 2 and 20 Hz are used to compute the average and variance. Outliers are eliminated to reduce the variance.

  3. This procedure is repeated for the second and third sets of readings for the same component.

  4. The three estimates are averaged to get the calibration coefficient for each component.

In this intercomparison study, four EM probes were used: two 16-mm probes (#6 and #7), and two 40-mm probes. The length refers to the diameter of the sensor tip. These probes will be referred to as 16-6, 16-7, 40O, and 40S, respectively. One 40-mm probe (40S) has a magnet about three times stronger than the magnet in the other 40-mm probe (40O). The 16-mm probes all use this stronger magnet. The two 16-mm probes are similar and have similar sensitivity as probe 40O, while probe 40S has about two to three times the sensitivity of the others. Table 1 shows the calibration coefficients for these four EM probes.

Table 1.

Calibration coefficients, in mV cm−1 s−1, for the EM probes used in the intercomparison study.

Calibration coefficients, in mV cm−1 s−1, for the EM probes used in the intercomparison study.
Calibration coefficients, in mV cm−1 s−1, for the EM probes used in the intercomparison study.

4. MARINPO intercomparison experiment

The intercomparison experiment was conducted in the water flume tank at the MARINPO facility in Kaliningrad, Russia (Fig. 5). The test section of the MARINPO tank (the upper level in Fig. 5) is 14 m long, 3 m wide, and 2.5 m deep. Water flow is generated in the tank by revolving propellers. After an initial spinup time, the flow in the tank achieves a stable mean velocity, the value of which is a function of the propeller revolution rate. The flow speed in the tank was measured by a calibrated propeller current meter. A postexperiment calibration of the current meter, performed by timing the motion of neutrally buoyant balls in the tank, indicated that the calibration of the counter is accurate to within 1%. The correlation coefficient between the speeds measured by the current meter and the buoyant balls was 0.99.

Fig. 5.

Schematic diagram of the MARINPO water flume facility.

Fig. 5.

Schematic diagram of the MARINPO water flume facility.

In each intercomparison run, an EM probe and a reference sensor (either a single-axis DISA hot-film probe or an airfoil shear probe) were mounted separately on a carriage at the top of the tank. The EM and reference probes were separated by a horizontal distance of 0.5 m and were located at a depth of 0.5 m below the water surface. A biplane grid made of cylindrical rods was lowered into the tank 1.5 m in front of the probes. The grid was used to generate turbulence that was advected downstream and measured by the probes. The mesh size (M) of the grid is 8 cm and the diameter of the rods is 1.5 cm. Thus, the porosity (M/d) is 5.3 and the locations of the sensors are at an x/M of 19.

In this intercomparison study, each EM probe has a single-axis accelerometer mounted inside a common housing to measure the vertical acceleration due to vibrations in order to provide information on the possible contamination of the velocity data due to vibration.

Two reference velocity probes were used separately in this intercomparison experiment. The first reference probe is a single-axis DISA hot-film anemometer that measures the velocity fluctuations in the longitudinal direction, along the direction of the mean flow. The second reference sensor is an airfoil shear probe made by Dr. R. Lueck at the University of Victoria. This probe was rotated to measure velocity fluctuations either in the transverse or the vertical direction. This type of airfoil probe has been used extensively in obtaining turbulent velocity measurements mounted on vertical profilers (Osborn 1974), towed vehicles (Osborn and Lueck 1985a; Fleury and Lueck 1994), moorings (Lueck et al. 1997), and on the research submarine USS Dolphin (Osborn and Lueck 1985b).

The DISA probe used for this intercomparison experiment was calibrated in the MARINPO water tank by measuring its response to changes in the mean flow that were measured by the current meter. Figure 6 shows the DISA output signal as a function of the mean speed and a second-order polynomial fitted to the data. The gradients of the fitted curve at various mean speeds, namely 0.7, 1.1, and 1.7 m s−1, are listed in the figure. These coefficients are used to convert the DISA voltage signals to fluctuating velocities during intercomparison runs at the corresponding mean speeds (Bruun 1995).

Fig. 6.

Calibration coefficients for the single-axis DISA probe used in the intercomparison experiment. The gradients of the polynomial fit to the calibration data at various mean flow speed were used to convert the DISA signals to fluctuating velocities for data taken during the intercomparison runs.

Fig. 6.

Calibration coefficients for the single-axis DISA probe used in the intercomparison experiment. The gradients of the polynomial fit to the calibration data at various mean flow speed were used to convert the DISA signals to fluctuating velocities for data taken during the intercomparison runs.

The airfoil probe consists of a piezoceramic beam embedded in an axisymmetric body of revolution with a pointed nose. When the axis of the probe is aligned to the mean flow, the beam senses the fluctuating component of the cross-flow velocity perpendicular to the plane of the beam. Thus, depending on the way it is mounted, measurements from the airfoil probe can be compared with either the horizontal (υ′) or vertical (w′) cross-flow velocity fluctuations obtained from the EM probes. Two accelerometers were mounted in the housing of the airfoil probe to measure both the vertical and cross-flow accelerations in order to provide information on the possible contamination of the velocity data due to vibration.

Calibration of the airfoil probes was performed at the Ocean Turbulence Laboratory at the University of Victoria, Canada (Osborn and Crawford 1980). During calibration, the probe is held in a water jet of fixed velocity (1 m s−1). The support holding the probe is mounted such that the angle of attack of the probe can be set to any value from −20° to +20°. The probe is rotated around its axis of symmetry at a constant angle of attack, and its rms voltage in response to this sinusoidal excitation is measured. The speed of the jet is measured with a differential pressure transducer across the nozzle producing the jet. The rms voltage divided by speed squared is regressed against the sine of twice the angle of attack. The slope of this regression is the sensitivity (S) of the probe.

For the MARINPO intercomparison runs, the recorded voltage (E) is converted to cross-flow fluctuating velocity by

 
υ′ (or w′) = E/(22SUG),
(1)

where S is the sensitivity of the airfoil probe for a gain of 1 provided by the Ocean Turbulence Laboratory, G is the gain of the high impedance amplifier used for data acquisition in the intercomparison runs, and U is the mean speed in the tank as measured by the propeller current meter.

The intercomparison runs were performed under three different mean velocity conditions (0.7, 1.1, and 1.7 m s−1). Several runs were performed without the grid with the 16-mm EM probe to examine the background turbulence level in the water tank, and several zero mean velocity runs were performed with the same probe to measure the probe noise level. A summary of the run conditions is given in Table 2.

Table 2.

Summary of intercomparison runs.

Summary of intercomparison runs.
Summary of intercomparison runs.

Data was collected with a PC-based data acquisition system after the flow achieved a stable designated mean flow. For each intercomparison run, time series of 20–30 s duration were collected. Data were digitized with a 12-bit A/D at a sampling rate of 1000 Hz. An antialiasing filter was applied to each analog data channel before converting to digital data. The bandwidths of the antialiasing filters were 1–1000 Hz, and 0.05–200 Hz for the DISA and EM data, respectively. Due to the sensitivity of the airfoil probe and the noisy conditions in the MARINPO water tank, a bandpass filter at 0.2–53 Hz was applied to the airfoil probe signal. No filter was applied to the accelerometer channel.

5. Data intercomparison overview

Due to different sensor characteristics and the horizontal separation between sensors, one should not expect to have meaningful comparisons between the reference and EM probe data by visual inspection of the time series. The data to be compared are band-limited and comparisons are best done using power spectral density. In all the spectra shown in this paper, power spectral densities are computed using the entire recorded time series. The spectra are then band-averaged over 40 bands to produce 80 degrees of freedom for each spectral value. Frequencies (f) are converted to alongflow wavenumbers (k) using the recorded mean flow velocity (U) by k = 2πf/U. In some cases, velocity gradient in the flow direction (∂/∂x) spectra are shown instead of the velocity spectra to reveal the spectral structures in more details. The gradient spectra are computed by multiplying the velocity spectra by the squared of the alongflow wavenumber (k2).

To understand the spectral comparisons, one needs to know how the shape of an observed turbulent velocity spectrum is being governed by actual turbulence, and by sensor and filtering characteristics. This is illustrated schematically in the velocity and velocity gradient spectra in Figs. 7a and 7b, respectively. The solid line represents a typical turbulent spectrum and the dotted line represents modifications to the spectrum as observed by a sensor. A turbulent velocity spectrum typically has a flat region (a +2 slope for the gradient spectrum) at low wavenumbers corresponding to energy-containing turbulent eddies generated by the grid. This region is followed by a region with a −5/3 slope (a +1/3 slope for the gradient spectrum) in the inertial subrange portion of the spectrum. The turbulent spectrum rolls off in the viscous subrange where viscosity dominates the flow. This transition occurs at a wavenumber kν (m−1) = 1/(2πLk), where Lk is the Kolmogorov length scale (ν3/ɛ)1/4, where ν and ɛ are the viscosity and velocity dissipation rate, respectively. The viscous roll-offs are indicated by the local maxima in the gradient spectra.

Fig. 7.

Schematic diagram of a turbulent velocity spectrum (a) and velocity gradient spectrum along the flow direction (b). Turbulent velocity spectra of the flow are shown as solid lines, and those measured by a sensor are shown as dotted lines.

Fig. 7.

Schematic diagram of a turbulent velocity spectrum (a) and velocity gradient spectrum along the flow direction (b). Turbulent velocity spectra of the flow are shown as solid lines, and those measured by a sensor are shown as dotted lines.

Due to finite size, a sensor cannot measure turbulent fluctuations at length scales smaller than its physical size. This results in a drop-off in the observed spectrum at a spatial roll-off wavenumber, nominally πx m−1, where Δx is the size of the sensor. Dependent on the dissipation rate and the sensor size, the spatial roll-off wavenumber can be higher or lower than the viscous roll-off wavenumber. For the EM probes, there is an additional consideration due to the difference between the sensor tip size and the electrode separation. The spatial roll-off wavenumber of EM probes are determined empirically from the half-power points in the calibration data (Fig. 4), and they are listed in Table 3.

Table 3.

Characteristics of the sensors and filters.

Characteristics of the sensors and filters.
Characteristics of the sensors and filters.

Additional modifications of the data are introduced by filters used in the data acquisition system or sensor electronics. These can result in spectral drop-offs in the low wavenumbers (frequencies) and, more typically, in the high wavenumbers (frequencies) as illustrated in Fig. 7. The slope of the observed spectrum is dependent on the filter characteristics and the real turbulent spectrum. If the filtered data drops below the bit-resolution level of the data acquisition system, a flat region will be found at the highest wavenumbers (frequencies).

To facilitate understanding of the data intercomparison described in the following sections, Table 3 summarizes the characteristics of the various sensors and filters, in both frequency and wavenumber.

6. EM and reference data intercomparison

a. Longitudinal velocity (u′) intercomparison

The DISA probe is a single-axis probe that measures the fluctuating velocity along the flow direction only. Thus, we compare DISA velocity measurements with the u′ component of the EM probe. Figure 8 shows the gradient spectra of DISA velocity and the EM u′ component from probe 16-6 under two different mean flow velocities. For comparison, Nasymth’s “universal” ocean turbulence spectrum (Oakey 1982) for ɛ of 3 × 10−4 and 3 × 10−3 m2 s−3 is superimposed on the observed spectra. It should be noted, though, that energy-containing scales in grid-generated turbulence are controlled by the grid size and these scales are absent in Nasymth’s ocean turbulence spectrum. Therefore, the observed EM and DISA spectra are not expected to be similar to Nasymth’s spectrum at those low wavenumbers, which is consistent with that shown in Fig. 8.

Fig. 8.

Comparison of velocity gradient spectra between EM u′ (16-6) and DISA at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 3 × 10−3 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, spatial roll-off wavenumber of the EM probe (ks), and the low-pass filter for the DISA (kLP) probe are identified by the arrows.

Fig. 8.

Comparison of velocity gradient spectra between EM u′ (16-6) and DISA at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 3 × 10−3 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, spatial roll-off wavenumber of the EM probe (ks), and the low-pass filter for the DISA (kLP) probe are identified by the arrows.

In general, the spectra have similar spectral features expected from grid-generated turbulence: the energy-containing region at low wavenumbers, the inertial subrange region with a −5/3 slope, and a drop-off in energy at high wavenumbers (cf. Fig. 7b). The turbulent energy for each component also increases with the mean flow speed, as expected for grid-generated turbulence.

In the wavenumber range between the spatial roll-off of the EM probe (kν) and the lowpass filter for DISA (kLP), the EM u′ spectra are within the 95% confidence limits of the DISA spectra (Fig. 8). There are expected differences between the DISA and EM u′ spectra on either side of this wavenumber range. These differences are consistent with sensor characteristics, filter bandwidths in the data acquisition system, and sensor electronics, as discussed in section 5 and Table 3. The spectral comparisons shown in Fig. 8 are typical of the rest of the data.

The viscous roll-off wavenumbers are 660 and 1200 m−1 for the two flow regimes shown. Because of its small size, the DISA probe can measure turbulence in the viscous subrange, consistent with the close agreement between the DISA and Nasymth’s spectra (Fig. 8). Spatial response function of the longitudinal component of the EM probes can be computed from the ratio of the EM u′ and the reference DISA spectra, after correcting for the filter characteristics. The response function for EM 16-6 at two different mean flows are shown in Fig. 9, together with its analytical representation.

Fig. 9.

Spatial response function for EM 16-6 u′ component. The analytical response function, obtained by curve fitting to Eq. (2), is shown as the smooth line.

Fig. 9.

Spatial response function for EM 16-6 u′ component. The analytical response function, obtained by curve fitting to Eq. (2), is shown as the smooth line.

The analytical representation of the response function is obtained by least-squares fitting the observed transfer function to

 
H(k) = [1 + (k/ks)n]−1,
(2)

where ks and n are parameters determined in the curve fitting. In this representation, ks is the spatial roll-off wavenumber, representing the half-power point in the spectrum. The u′ spatial response function parameters for the four probes used in this intercomparison study are shown in Table 4. The spatial roll-off wavenumbers of the probes are consistent with their different sizes, and they are very similar to those obtained empirically from the calibration data in the jet (Table 3).

Table 4.

Parameters of longitudinal spatial response function, H(k) = [1 + (k/ks)n]−1, for EM probes where ks is the spatial roll-off wavenumber of the probe.

Parameters of longitudinal spatial response function, H(k) = [1 + (k/ks)n]−1, for EM probes where ks is the spatial roll-off wavenumber of the probe.
Parameters of longitudinal spatial response function, H(k) = [1 + (k/ks)n]−1, for EM probes where ks is the spatial roll-off wavenumber of the probe.

b. Transverse (υ′) and vertical (w′) velocity intercomparison

Intercomparison runs were conducted between EM probe 16-6 and the airfoil probe at three mean flow speeds. After the completion of the MARINPO runs, it was found that in the U = 1.7 m s−1 runs, portions of the airfoil data were saturated. The cause of the saturation was due to too high a gain used in the high impedance amplifier for the airfoil channel at this mean flow speed. Although only about 10% of the data were saturated, the airfoil spectra from these high mean flow speed runs were deemed to be not accurate enough for comparison with the EM measurements. Therefore only data from the mean flow speeds of 0.7 and 1.1 m s−1 were used in this comparison.

Figures 10 and 11 compare the υ′ and w′ velocity gradient spectra along the flow direction from the EM 16-6 and airfoil probes at the two mean flow speeds. Superimposed on the figures are the Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 7 × 10−4 m2 s−3, with corresponding kν of 660 and 800 m−1.

Fig. 10.

Comparison of υ′ velocity gradient spectra from EM and airfoil probes at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 7 × 10−4 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, and spatial roll-off wavenumber of the EM and airfoil probes (ks) are identified by the arrows.

Fig. 10.

Comparison of υ′ velocity gradient spectra from EM and airfoil probes at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 7 × 10−4 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, and spatial roll-off wavenumber of the EM and airfoil probes (ks) are identified by the arrows.

Fig. 11.

Comparison of w′ velocity gradient spectra from EM and airfoil probes at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 7 × 10−4 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, and spatial roll-off wavenumber of the EM and airfoil probes (ks) are identified by the arrows.

Fig. 11.

Comparison of w′ velocity gradient spectra from EM and airfoil probes at two different mean flow speeds. Nasymth’s “universal” ocean turbulence spectra for ɛ of 3 × 10−4 and 7 × 10−4 m2 s−3 are shown as dashed lines. The viscous roll-off wavenumber (kν) of the flow, and spatial roll-off wavenumber of the EM and airfoil probes (ks) are identified by the arrows.

The υ′ and w′ spectra have similar spectral features as the u′ spectra in Fig. 8. The airfoil and EM 16-6 spectra show the same spatial roll-off, as expected from the similar sizes of the two probes (Table 3). From the lowest wavenumber to the spatial roll-off (ks), the EM υ′ and w′ spectra are within the 95% confidence limits of the airfoil spectra. The only exception is the w′ spectrum at U = 1.1 m s−1 where the EM w′ spectrum is statistically lower than the airfoil spectrum.

Because of the similar sizes of EM and airfoil probes, spatial response functions for the EM υ′ and w′ cannot be obtained to wavenumbers higher than ks. However, the ratio between the two spectra from the lowest wavenumber to ks provides quantitative comparison. The averages of the spectral ratios from all the runs are 1.23 and 0.81 for the υ′ and w′ spectra, respectively. That means, on the average, the EM υ′ and w′ variances are about ±20% of the corresponding reference airfoil velocity variances.

c. Broadband turbulent velocity intercomparison

Broadband turbulent velocity variances (u2, υ2, and w2) are parameters often used for characterizing turbulent levels and turbulent spectral models (e.g., Hinze 1975). They are obtained by integrating the corresponding spectra from the lowest wavenumber to the viscous roll-off wavenumber. Since the spatial roll-off wavenumbers of the EM and airfoil probes are lower than the viscous roll-off wavenumbers in the turbulence regimes in this intercomparison study, the integration was performed in two parts. In the first part, integration is performed from the lowest wavenumber to the spatial roll-off wavenumber, using the actual observed spectrum. Then, the observed spectrum is extrapolated along the −5/3 slope to the viscous roll-off wavenumber. The second part of the integration is performed from the spatial roll-off wavenumber to the viscous roll-off wavenumber, using the extrapolated spectrum. This procedure is equivalent to using the spatial response functions of the EM and airfoil probes. Because of its small size, no extrapolation is needed for the DISA data in the integration since the spatial roll-off wavenumber for the DISA probe (Table 3) is higher than that of the viscous roll-off in the MARINPO runs.

The broadband EM u2, υ2, and w2 from all the intercomparison runs are plotted against the corresponding reference velocity data in Fig. 12. A straight line fitted through all the points has a slope of 1.08 and an R2 of 0.96. The dotted line in the figure represents one-to-one correspondence between the EM and reference data. The normalized rms deviation of the data from this dotted line is 0.22. That means the broadband EM velocity variances are about 22% of the reference velocity data, a value similar to that found in section 6b.

Fig. 12.

Intercomparison of broadband velocity variances between EM and reference data. The solid line represents a linear least square fit between the EM and reference data. The dotted line represents perfect agreement between the EM and reference data.

Fig. 12.

Intercomparison of broadband velocity variances between EM and reference data. The solid line represents a linear least square fit between the EM and reference data. The dotted line represents perfect agreement between the EM and reference data.

In summary, we note the following:

  1. The EM turbulent velocity spectra compare well with the corresponding reference velocity spectra to within the 95% confidence limits of the measurements.

  2. The differences in the spectra are understood, accountable by the differences in sensor and filter characteristics.

  3. On the average, turbulent velocity variance measured with the EM probes are ±20% of the reference data.

7. Three-component turbulent velocity (u′, υ′, and w′) measurements

The EM probes used in this study measure all three components of the turbulent velocity. This capability makes the EM probe a unique sensor for the study of turbulence isotropy. The velocity gradient spectra of all three components from the 16-6 probe at two different mean flow speeds (0.7 and 1.7 m s−1) are plotted in Fig. 13. The υ′ and w′ spectra are similar to the u′ spectra, with the usual expected roll-offs as described in section 6. Within the wavenumber range where the −5/3 slope is satisfied, spectra from all three components are similar, with u′ slightly higher than υ′ and w′, consistent with the higher alongflow fluctuating velocities often observed in grid-generated turbulence in a flow tank (Liu 1995).

Fig. 13.

Spectra of u′, υ′, and w′ components from EM probe 16-6 at two different flow speeds.

Fig. 13.

Spectra of u′, υ′, and w′ components from EM probe 16-6 at two different flow speeds.

The broadband turbulent velocity variances (u2, υ2, and w2) are often used as indicators of turbulence isotropy (Liu 1995; Hinze 1975). Broadband velocities are obtained by integrating the corresponding spectra from the lowest wavenumber to the viscous roll-off wavenumber in the same way as described in section 6c. The computed EM u2 from all the runs are plotted against EM υ2 and w2 in Fig. 14.

Fig. 14.

Broadband EM u2 vs EM υ2 and w2. The straight line is the linear regression of all the points, with an intercept of zero.

Fig. 14.

Broadband EM u2 vs EM υ2 and w2. The straight line is the linear regression of all the points, with an intercept of zero.

The figure shows that υ2 and w2 have similar values, and u2 is significantly higher than both υ2 and w2. A straight line with zero intercept fitted through these points has a slope of 0.66 and a correlation coefficient, R2, of 0.95, indicating that the grid-generated turbulence in the MARINPO tank is anisotropic, with υ2w2 ∼ 0.66 u2. The ratio of 0.66 between longitudinal and cross-flow turbulent energy is similar to the value of 0.6 reported by Liu (1995) for turbulence generated by grids with similar porosity (M/d) conditions.

8. EM probe noise levels

The best way to compute the noise levels of the EM probes is to acquire data using the probes in a very low turbulence environment, for example, with zero flow velocity in the water tank. Data were obtained under this condition with the 16-6 probe. Figure 15 shows the u′, υ′, and w′ frequency spectra from this probe at U = 0. The flat regions in the spectra between 5 and 200 Hz represent the noise levels. The spectral roll-off at frequencies higher than 200 Hz is due to the filtering in the EM probe electronics. From the flat spectral levels of 2–3 × 10−9 m2 s−2 Hz−1, the rms noise level of this 16-mm EM probe is about 0.1 cm s−1 for all three components.

Fig. 15.

Frequency spectrum of 16-6 probe at zero mean speed without a grid.

Fig. 15.

Frequency spectrum of 16-6 probe at zero mean speed without a grid.

We also performed runs without a grid but with a mean flow to estimate the noise level of probe 16-6. Figure 16 shows the u′-component frequency spectrum from this EM probe in a run with no grid at a flow velocity of 0.7 m s−1. The feature to look for is a flat spectral region (indicative of white noise) that lies between the spatial roll-off wavenumber and the high wavenumber cutoff of the antialiasing filter. This region is marked by A and B in the figure. In this region, the spectral level for probe 16-6 is about 1.5–2 × 10−9 m2 s−2 Hz−1, a value slightly lower than that observed in Fig. 15. The rms velocity corresponding to this spectral noise level is 0.1 cm s−1. Note that the spectral level of the flat region to the right of B is the result of the antialiasing filtering and therefore does not represent the noise level of the probe.

Fig. 16.

Noise levels of EM probes as observed by frequency spectra in low turbulence environments. The noise levels are marked by A, B, and C.

Fig. 16.

Noise levels of EM probes as observed by frequency spectra in low turbulence environments. The noise levels are marked by A, B, and C.

Zero mean speed runs were not performed for the 40O or 40S probes. Nor are there runs without a grid for these probes. However, data from probe 40O in a low turbulence run (U = 0.7 m s−1 with a grid) enable us to estimate its noise level. The spectrum for this run is shown in Fig. 16 (this spectrum is also shown in Fig. 15). Again, the feature to look for in Fig. 16 is a flat spectral region that lies between the spatial roll-off wavenumber and the high wavenumber cutoff of the antialiasing filter. The spectral level of this relatively flat region, marked by C, is about 2 × 10−9 m2 s−2 Hz−1. This is very similar to that of the 16-mm probe, indicating probes 16-6 and 40O have similar sensitivities, as expected.

Probe 40S has a sensitivity about three times larger than the sensitivity of the other probes (Table 2). That means it has a lower noise level and can measure weaker velocity fluctuations. In the MARINPO intercomparison experiment, no flat spectral regions could be found in the probe 40S data to enable us to estimate its absolute noise level. However, the spectral levels of the 40S data at the highest wavenumbers are lower than those from EM 16-6 and 400 by a factor of about 5. This suggests that the noise level of EM 40S velocity measurements is a factor 2.2 lower, that is, about 0.05 cm s−1.

9. Vibration

Analysis of the EM probe data suggests that the measured turbulent velocities in runs with a grid have not been contaminated by vibration of the probes since the observed turbulent spectra from various probes in different flow regimes behaved similar to what we expected. In this section, we will evaluate the accelerometer data collected and perform a consistency check on the possible contamination of the turbulent velocity measurements by vibration.

First, we want to evaluate the accuracy of the vertical acceleration measurements. An EM probe measures both the fluctuating velocity of the fluid motion and the vibrational motion of the sensor relative to the fluid. In a low turbulence environment, portions of the EM data could be dominated by vibrational motion. Such is the case in the observed EM w′ frequency (not wavenumber) spectrum from probe 16-6 in a run without a grid and a flow speed of 0.7 m s−1, shown in the left panel in Fig. 17. In this figure, we observe several significant narrowband peaks. This EM w′ spectrum is compared in Fig. 17 with the vertical vibrational velocity frequency spectrum converted from the observed vertical acceleration spectrum, A(f), by (2πf)−2A(f), where f is the frequency in Hz. A comparison of these two spectra shows similar peaks at 30 and 50 Hz.

Fig. 17.

Spectra of EM w′ component and vertical velocity estimated from accelerometer data.

Fig. 17.

Spectra of EM w′ component and vertical velocity estimated from accelerometer data.

We note that the spectral levels of the vibrational peaks from the EM w′ spectrum is an order of magnitude higher than those from the accelerometer. If the EM probe and the accelerometer undergo the same vibrations, we expect they should have similar spectral levels. One possible explanation is that the EM probe and the accelerometer experienced vibrations of different magnitudes since they are not collocated, even though they are in the same housing.

We also performed a consistency check on the possible contamination of turbulent spectra at higher mean flow speeds. This check was performed by forcing the vibrational peaks at 30 and 50 Hz to have similar values for both the EM w′ data and the accelerometer data at U = 0.7 m s−1. This matching requires an adjustment by a factor of 10 to the observed vertical vibrational velocity spectrum from the accelerometer. This same scale factor was then applied to the observed vibrational velocity in a run with a grid with U = 1.7 m s−1, shown in the right panel in Fig. 17. Despite the adjustment by one order of magnitude, the observed EM w′ spectrum is still much higher than the adjusted vibrational velocity spectrum, indicating that the measured turbulent velocities have not been contaminated by vibration.

10. Summary and discussion

Data collected in a set of runs performed in the water flume tank at MARINPO were analyzed. The overall data quality of the velocity measurements, in terms of accuracy and frequency response, is very good. The data from the EM probes were very consistent with data from a DISA hot-film probe and from an airfoil shear probe. While the hot-film sensor and airfoil shear probe are very fragile, the EM probes appear to be quite robust. This robustness, combined with good measurement capabilities, implies that the EM probes can be very useful for ocean measurements, if uncontaminated by vibration. We note that the spectra from the EM probes are as anticipated, given the spatial sizes of the probes and the time series filtering employed.

From the MARINPO water tank experiment, one may get the false impression that only a very limited useful bandwidth is available from EM turbulent velocity measurements, especially for the 40-mm probe. A significant portion of the turbulent spectrum is not observable by any of the EM probes due to the roll-off corresponding to the sensor spatial resolution (e.g., see Fig. 8). However, this limitation is not significant in the ocean as explained below.

Turbulence generated by the grid in the MARINPO tank has velocity dissipation rates, ɛ, ranging from 3 × 10−4 to 3 × 10−3 m2 s−3. These dissipation rates imply viscous roll-off wavenumbers from 660 to 1200 m−1. These high values mean that a significant portion of the turbulent spectrum cannot be measured by the EM probes with spatial roll-off wavenumbers of 200 and 70 m−1 (16- and 40-mm probes), as indicated in the MARINPO data. However, in the ocean, ɛ ranges from 10−9 to 10−7 m2 s−3. These values imply viscous roll-off wavenumbers from 30 to 90 m−1, which are similar to the spatial roll-off wavenumbers of the EM sensors. Thus most of the turbulent velocity spectra in the ocean can be sampled by the 16- and 40-mm probes.

With a model turbulent velocity spectrum for the inertial subrange

 
Eu(k) = 0.55ɛ2/3k−5/3
(3)

(Grant et al. 1962), the spectral levels of turbulent velocities at the viscous roll-off wavenumbers are expected to be 2 × 10−9 and 6 × 10−9 m3 s−2 for velocity dissipation rates of 10−9 and 10−7 m2 s−3, respectively. These spectral levels are much higher than the noise level of the 1–3 × 10−10 m3 s−2 (converted from the 2–3 × 10−9 m2 s−2 Hz−1 shown in Figs. 16 and 17) for the 16-mm and 40O probes. In fact, the noise level for the 16-mm probes is even lower than that expected (7 × 10−10 m3 s−2) from extremely weak turbulence at dissipation rates of 10−11 m2 s−3. Therefore, while the 40S probe has a lower noise level (section 8), this probe does not appear to have much of an advantage in the ocean since the sensitivity of the 16-mm probe is adequate for measuring extremely weak oceanic turbulence.

Finally, there is another consideration to be taken into account. Oceanic turbulent patches are typically a few tens of centimeters to a few meters thick. The 16-mm probe can resolve these patches better than the larger 40-mm probe.

The ability to obtain accurate measurements of all three components of turbulent velocities simultaneously by an EM probe makes it an attractive sensor for oceanic turbulence measurements. The EM probe measurements should provide understanding of the total turbulent kinetic energy and velocity dissipation rate in the ocean, without using the common practice of assuming isotropy (Oakey 1982). We are currently using the 16-mm probes to measure three-dimensional turbulence in the Baltic. The results of these measurements will be reported at a later date.

Acknowledgments

We wish to thank Dr. Leonid E. Meyler, Chief Designer of MARINPO, Kaliningrad, Russia, for the use of the water flume facility in this study. This work was sponsored by the Office of Naval Research.

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Footnotes

Corresponding author address: Dr. David Y. Lai, Northwest Research Associates, 14508 NE 20th Street, Bellevue, WA 98007.