• Campbell Scientific Inc., 2012: CSAT3 three-dimensional sonic anemometer. Campbell Scientific Instrument Manual, 72 pp.

  • Kravchenko, A. G., and Moin P. , 2000: Numerical studies of flow over a circular cylinder at ReD = 3900. Phys. Fluids, 12, 403417.

  • Marks, L. S., 1934: The determination of the direction and velocity of flow of fluids. J. Franklin Inst., 217, 201212.

  • Moller, A. R., 1978: The improved NWS storm spotters' training program at Ft. Worth, Tex. Bull. Amer. Meteor. Soc., 59, 15741582.

  • Prandtl, L., 1952: Essentials of Fluid Dynamics: With Applications to Hydraulics Aeronautics, Meteorology, and Other Subjects. Hafner, 452 pp.

  • Rennó, N. O., 2008: A thermodynamically general theory for convective vortices. Tellus,60A, 688–699.

  • Rennó, N. O., Burkett M. L. , and Larkin M. P. , 1998: A simple thermodynamical theory for dust devils. J. Atmos. Sci., 55, 32443252.

  • Rennó, N. O., Halleaux D. G. , Saca F. , Rogacki S. , Gillespie R. , and Musko S. , 2010: A generalization of Bernoulli's equation to convective vortices. Extended Abstracts, 41st Lunar and Planetary Science Conf., The Woodlands, TX, Lunar Planetary Institute, 1745.

  • Saca, F. A., Rennó N. O. , Halleaux D. G. , Rogacki S. , Gillespie R. , and Musko S. , 2010: A portable instrument for atmospheric measurements. Extended Abstracts, 41st Lunar and Planetary Science Conf., The Woodlands, TX, Lunar Planetary Institute, 1767.

  • Wieringa, J., 1967: Evaluation and design of wind vanes. J. Appl. Meteor., 6, 11141122.

  • Zucrow, M. J., and Hoffman J. D. , 1976: Gas Dynamics. Wiley, 772 pp.

  • View in gallery

    The Michigan Prandtl System (MPS). The MPS includes the Prandtl tube subsystem shown at the top and a 3D sonic anemometer (denoted as CSAT3) shown on the right. The Prandtl tube assembly freely rotates at the top of the mast and provides static and total pressure measurements in the wind flow, while the wind direction (used to verify proper alignment of the Prandtl tube to the wind flow direction) and speed are measured with the sonic anemometer. The data processing and storage electronics are located in a box (not drawn to scale) near the base of the mast.

  • View in gallery

    The pressure sensing portion of the MPS. Static pressure is measured via a port on the tip of this modified Prandtl tube, and total pressure is measured via eight orthogonal ports, all connected to a single pressure transducer. The vane on the aft portion of the tube aligns the tube with surrounding wind direction.

  • View in gallery

    Predicted oscillation behavior of the MPS rotating frame. For an initial angle between the MPS vane and wind flow of θ = 11°, the damped harmonic oscillation of the vane has a period of td = 1.4 s with an overshoot of 65.5%.

  • View in gallery

    Calibration of the Michigan sensor. The solid line indicates theoretical pressure differences between static and total pressure from Eq. (2). Data points (crisscross) are pressure differences calculated from the static and total pressures measured by the MPS. The data deviate from the expected pressure differences by an average of 7.7% over the entire range of use. Mean relative error for tests at wind speeds faster than 5 m s−1 is 4.9%.

  • View in gallery

    Time scale for the MPS to align with the wind flow when subjected to abrupt changes in wind direction. The Prandtl tube was locked at angles to the wind flow, then released at t = 0 s to test its response to rapidly changing wind directions. Even the most extreme wind test here—nearly 90°—displays the sensor's orientation, returning to a small angle from the wind flow direction within 1.5 s of release of the sensor.

  • View in gallery

    MPS alignment with wind direction during measurements in a dust devil. The differences in wind direction measured by the MPS vane and those measured by the 3DSA show misalignment is rare, even during the passage of a dust devil over the sensors, as is shown here. The difference between directional measurements (blue) remains below 30° for all but the most extreme wind shifts in the dust devil. Static pressure readings (green) as the dust devil passes the sensor are shown as a reference.

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The Michigan Prandtl System: An Instrument for Accurate Pressure Measurements in Convective Vortices

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  • 1 Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan
  • | 2 Department of Earth and Atmospheric Science, Cornell University, Ithaca, New York
  • | 3 Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan
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Abstract

This article describes a Prandtl tube system developed at the University of Michigan to measure the static pressure, the total (or stagnation) pressure, and the velocity in flows whose direction and intensity change rapidly. The ever-changing wind vectors in convective vortices are a challenge for making accurate measurements on them. Accurate measurements of the static pressure are particularly problematic because they require the sensor air intake to be aligned perpendicular to the wind direction. This article describes calibrations and tests of the Michigan Prandtl System (MPS) and, in particular, the characterization of the errors in the static pressure measurements as a function of misalignments between the Prandtl tube and the wind vector. This article shows that the MPS measures the pressure with a relative error of 3.5% for wind flows whose direction is within about 10° of the MPS tube direction. It also shows that the MPS adjusts to changes in wind direction of 90° in about 1.5 s, the average rate of change expected in a typical dust devil of about 15 m of radius traveling at 10 m s−1 (Rennó et al.). Field tests indicate that misalignments between the MPS and the wind vector are usually smaller than ~30° during measurements in dust devils and that these misalignments always cause increases in the static pressure measured and decreases in the total pressure measured.

Corresponding author address: Douglas G. Halleaux, Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, 2455 Hayward St., Ann Arbor, MI 48109. E-mail: dgossiau@umich.edu

Abstract

This article describes a Prandtl tube system developed at the University of Michigan to measure the static pressure, the total (or stagnation) pressure, and the velocity in flows whose direction and intensity change rapidly. The ever-changing wind vectors in convective vortices are a challenge for making accurate measurements on them. Accurate measurements of the static pressure are particularly problematic because they require the sensor air intake to be aligned perpendicular to the wind direction. This article describes calibrations and tests of the Michigan Prandtl System (MPS) and, in particular, the characterization of the errors in the static pressure measurements as a function of misalignments between the Prandtl tube and the wind vector. This article shows that the MPS measures the pressure with a relative error of 3.5% for wind flows whose direction is within about 10° of the MPS tube direction. It also shows that the MPS adjusts to changes in wind direction of 90° in about 1.5 s, the average rate of change expected in a typical dust devil of about 15 m of radius traveling at 10 m s−1 (Rennó et al.). Field tests indicate that misalignments between the MPS and the wind vector are usually smaller than ~30° during measurements in dust devils and that these misalignments always cause increases in the static pressure measured and decreases in the total pressure measured.

Corresponding author address: Douglas G. Halleaux, Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, 2455 Hayward St., Ann Arbor, MI 48109. E-mail: dgossiau@umich.edu

1. Introduction

This article describes the University of Michigan Prandtl System (MPS), developed to measure the wind vectors and the static and total pressures in flows with rapidly changing direction and intensity and reports results of its characterization in a wind tunnel to

  1. accurately measure static and total pressures within convective vortices;

  2. make high-frequency (10 Hz) measurements of these pressures; and

  3. study the relationships between changes in static pressures and kinetic energy.

The MPS was developed to make in situ pressure measurements in dust devils and dust plumes. Rennó (2008) proposed a theory for convective vortices that predicts decreases in static pressure when the kinetic energy increases along streamlines of the inflow to the center of these vortices by
e1
where γ ~ 1 is the fraction of the mechanical dissipation of energy occurring at the heat input branch of the convective circulation, η is the thermodynamic efficiency, is the change in enthalpy, is the irreversible work of expansion, ρs is the density of the air at the surface, is the change in potential energy, and is the change in kinetic energy. Equation (1) is a generalization of the Bernoulli equation, which sheds light on the formation of the spiral bands that lift dust particles. In moisture-rich convective vortices, such as tornadoes, the lifting condensation level lowers in these spiral bands while they intensify, producing the “wall clouds” (Moller 1978).

Here, dust devils are defined as low-pressure warm-core vortices strong enough to initiate saltation and lift dust particles (Rennó et al. 1998). Rennó et al. (2010) show evidence that in dust devils the changes in kinetic energy and static pressure are consistent with those predicted by the generalized Bernoulli equation, that is Eq. (1). The center of the typical dust devil analyzed by Rennó et al. (2010) passed over stationary instruments in about 20 s. During the passage of the dust devil, the wind direction changed by as much as 22° between individual measurements 100 ms apart, and the wind direction typically changed by nearly 90° in about 3 s. The vortex that passed directly over the instruments caused a pressure drop of 1.1 hPa from the static pressure in the nearby environment to the lowest static pressure in the vortex walls. A more complete analysis of the data collected during our field campaigns will be described in a companion article.

Accurate pressure measurements are critical for testing theories such as that proposed by Rennó (2008) but are difficult to obtain because of the rapid changes in wind direction and intensity observed in dust devils and the modest changes in the static and total pressures [less than 0.5% of the atmospheric pressure in the strongest dust devils (Rennó et al. 1998)]. Previous measurements of static pressures and kinetic energy, though prevalent in the quasi-steady flows of wind tunnels, have been problematic in natural phenomena such as convective vortices because current instruments do not make simultaneous measurements of pressure and wind velocity with sensors that have the air intake aligned with the flow. We show that the MPS described in this article is capable of making accurate measurements of static pressure, total pressure, and the wind vector in natural phenomena such as convective vortices.

2. Measurement approach

Accurate measurements of static pressure and the wind vector are critical for testing theoretical ideas such as the generalized version of the Bernoulli equation proposed by Rennó (2008). Even though existing instruments, such as sonic anemometers, are capable of performing accurate wind measurements even when the wind directions change rapidly, measurements of the static pressure are a challenge because they require the air intake of the pressure sensor to be aligned perpendicular to the wind. The MPS accomplishes this through a Prandtl probe capable of quickly aligning with the wind as its direction changes.

Prandtl probes measure the total pressure with a port directed into the flow and the static pressure with ports orthogonal to the flow. These measurements are generally used to calculate the flow speed in wind tunnels and airplanes and do so using the classical Bernoulli equation
e2
where is the difference between static and total pressures, ρ is the fluid density, and υ is the flow speed (e.g., Zucrow and Hoffman 1976). In the MPS, the static and total pressures are measured with a Prandtl probe (Prandtl 1952), and the static pressure is the primary measurement of interest. The total pressure is measured only to determine the alignment of the MPS with the flow through comparison with the measurements of the wind speed made with a Campbell Scientific 3D sonic anemometer (3DSA; Campbell Scientific Inc. 2012).

In addition to independent measurements of the 3D wind vectors and the static and total pressures, the MPS measures the wind direction with the vane, which points the instrument toward the flow. Saca et al. (2010) have successfully used the sensor to study dust devils.

3. Science requirements

The requirements for studies of kinetic energy and pressure perturbations in terrestrial dust devils are:

  1. Pressure ranging from 850 to 1100 hPa. This range is required for making measurements in dust devils in areas with altitudes ranging from slightly below sea level, such as Death Valley, to elevations exceeding 1000 m, such as California's High Desert where dust devils are ubiquitous.

  2. Pressure measurement with a resolution of ±1 Pa. Measurements should be accurate enough to describe typical dust devils' pressure perturbations of about 2.5 hPa (Rennó et al. 1998).

  3. Time with resolution of 0.1 s. This resolution is high enough for sampling typical dust devils with diameter of 15 m traveling at about 5 m s−1 (Rennó et al. 1998).

  4. Wind speed ranging from 0 to 35 m s−1. This range is necessary for making measurements in typical dust devils, which have peak tangential velocity of about 15 m s−1 (Rennó et al. 1998).

4. The prototype instrument

The MPS consists of a Prandtl tube, a 3D sonic anemometer, and the supporting data processing electronics and mounting hardware shown in Fig. 1. A standard Prandtl tube, developed for measuring the static and the total pressures on aircraft (Marks 1934), measures pressures in the MPS. As shown in Fig. 2, a single sensing port with a radius of 0.85 mm at the forward tip of the sensor measures the total pressure, while eight ports with radii of 0.25 mm orthogonal to the longitudinal axis of the tube and 33 mm from the tip measure the static pressure. The static pressure ports are connected to a single pressure sensor. The Prandtl tube is attached to a trapezoidal double panel with a surface area of 710 cm2, which acts as a vane to orient the tube toward the wind.

Fig. 1.
Fig. 1.

The Michigan Prandtl System (MPS). The MPS includes the Prandtl tube subsystem shown at the top and a 3D sonic anemometer (denoted as CSAT3) shown on the right. The Prandtl tube assembly freely rotates at the top of the mast and provides static and total pressure measurements in the wind flow, while the wind direction (used to verify proper alignment of the Prandtl tube to the wind flow direction) and speed are measured with the sonic anemometer. The data processing and storage electronics are located in a box (not drawn to scale) near the base of the mast.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

Fig. 2.
Fig. 2.

The pressure sensing portion of the MPS. Static pressure is measured via a port on the tip of this modified Prandtl tube, and total pressure is measured via eight orthogonal ports, all connected to a single pressure transducer. The vane on the aft portion of the tube aligns the tube with surrounding wind direction.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

Plastic tubing connects the static and total pressure ports to pressure transducers mounted in the electronics cylinder on the instrument post. The pressure transducers convert pressures into DC voltage for transmittal to a datalogger with a time response of about 500 ms.

The entire pressure measuring system, including the Prandtl tube, vane, and cylinder, rotates freely as a single unit with changes in wind direction. A slip ring provides power to the rotating portion of the MPS.

The Prandtl tube system's response to change in wind direction depends on the moment of inertia of the entire rotating portion of the MPS. We first calculate moments of inertia for each separate component of the rotating portion of the MPS by integrating the product of the individual masses with their distance from the axis of rotation. We then calculate the total moment of inertia of the vane by adding the components' moments of inertia. The total moment of inertia is indicated in Table 1.

Table 1.

Physical parameters of the MPS vane used in Eq. (3).

Table 1.

The vane responds as a damped oscillator to changes in wind direction. That is,
e3
where θ is the angle of the vane to the wind vector, θ0 is the initial angle of the vane, J is the moment of inertia of the rotating portion of the MPS, D is the aerodynamic damping of the vane, and ω is the damped oscillation frequency (Wieringa 1967).
The damping ratio ζ, defined as the ratio of the actual aerodynamic damping of the vane to its critical damping value D0, is
e4
It follows from Wieringa (1967) that it is given by
e5
where rυ is the distance from the axis of rotation to the center of mass of the vane panel, S is the area of the panel, and aυ is the torque parameter of the vane, determined experimentally to be approximately 7 for a flat-plate fin with an angle of attack of 10°.
Neglecting the friction in the bearings, the MPS vane has a damping ratio of 0.13, implying that it is a subcritically damped oscillator. From this damping ratio, the natural oscillation period of the vane is found to be
e6
where υ is the wind speed. The torque parameter aυ can be used to calculate the torque on the vane as a function of wind speed
e7
where ρ is the air density. It follows from Wieringa (1967) that the damped oscillation period of the vane is
e8

Table 1 lists the values of the parameters used in Eq. (3) to calculate θ(t) for the MPS. The method proposed by Wieringa (1967) simplifies the second-order differential equation governing the motion of the vane by approximating sin(θ) to θ. Thus, we apply this method only for small angles. Figure 3 displays the expected angular response of the vane, indicating that the damped oscillation period is 1.4 s and the overshoot is 65.5%.

Fig. 3.
Fig. 3.

Predicted oscillation behavior of the MPS rotating frame. For an initial angle between the MPS vane and wind flow of θ = 11°, the damped harmonic oscillation of the vane has a period of td = 1.4 s with an overshoot of 65.5%.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

Measurements of the total pressure with the MPS when its tube is not aligned with the wind will always be smaller than those obtained with a tube in perfect alignment. This results from the decrease in the component of the flow into the pressure port as the angle of misalignment increases. In a flow of velocity υ when the misalignment of the MPS vane with the flow is 90°, the decrease in the total pressure ptot is the dynamic pressure pd found by
e9
where ps is the static pressure. The decrease in the total pressure is estimated to be 133 Pa for dry air at 25°C in a typical dust devil, whose peak wind speed is υ ≈ 15 m s−1.
Measurements of the static pressure by the MPS when its tube is not aligned with the wind will always be larger than those obtained with a tube perfectly aligned with the flow. For a misalignment of 90°, the MPS tube acts as a cylinder with the longitudinal axis perpendicular to the flow. The Reynolds number of the flow around this cylinder is
e10
where the cylinder diameter is d = 0.005 m and, for dry air at 25°C, the kinematic viscosity is v = 15.7 × 10−6 m2 s−1. A flow speed of υ = 15 m s−1, the peak flow speed in an average dust devil, yields a Reynolds number of Re = 4.8 × 103. Table 2 lists pressure coefficients along the surface of a cylinder in a flow with a Reynolds number of this order of magnitude (Kravchenko and Moin 2000). As the misalignment between the MPS vane and the flow increases, the total pressure decreases and the static pressure increases.
Table 2.

Pressure coefficients along the surface of a cylinder whose longitudinal axis is perpendicular to a fluid flow at Re = 3900. The term θ is the angle made from the forward-most point of the cylinder, relative to the fluid flow (Kravchenko and Moin 2000).

Table 2.

A 3DSA is integrated into the MPS, providing high-frequency measurements of the wind vector. The measurements with the 3DSA are used to detect and quantify misalignments between the Prandtl tube direction and the wind direction, in addition to the wind speed values used for the calculation of the kinetic energy of the flow. The 3DSA provides wind speed measurements with an accuracy of 0.08 m s−1 and wind direction measurements with accuracy of 0.2° on a typical dust devil peak wind speed of 15 m s−1 (Campbell Scientific Inc. 2012).

5. Instrument characterization

a. Tests

Three sets of measurements are made to characterize the MPS. They determine the accuracy of the static and total pressure measurements made with the MPS. To assess the MPS's accuracy when subjected to the abrupt changes in wind direction observed in convective vortices, we determine the accuracy of the MPS measurements when the sensor is not properly aligned with the wind flow. The wind tunnel used for our tests is large enough to avoid boundary layer effects of the tunnel walls on the measurements.

The first set of measurements is conducted to calibrate the MPS in the range of conditions that the instrument will encounter during measurements on dust devils. To achieve this goal, the MPS is subjected to wind speeds ranging from 5 to 35 m s−1. The flow speed is calculated using the MPS pressure measurements, which is compared to the wind tunnel flow speed measured with a Dwyer 641RM hot-wire anemometer, whose accuracy is 3%. The air density is used to estimate the flow velocity using Eq. (2), and is calculated using the air temperature measured inside the wind tunnel, and the atmospheric pressure measured by a mercury barometer at the wind tunnel facility. As explained below, this indicates that the flow speed calculated using the MPS pressure measurements is accurate over the full range of wind conditions expected in dust devils, beyond 15 m s−1, the peak tangential velocity expected in typical dust devils (Rennó et al. 1998).

The sensor is then tested for errors in pressure measurements resulting from the misalignment between the wind flow and the Prandtl tube. Pressure measurements are made while the sensor is locked at angles ranging from 0° to 90°, both to the left and to the right of the wind direction with respect to the flow. The measurement error is calculated from the deviation of the pressure measurements made at the misaligned angles from those obtained when the sensor is aligned with the flow. These data are useful for estimating the measurement error when wind directions shift more rapidly than the sensor can respond.

Finally, a set of measurements is made to determine the response time of the MPS to changes in the wind direction. The MPS wind vane is placed at angles relative to the wind tunnel's flow ranging from 0° to 90°, locked in this position, and then released. The change in the direction of the vane as a function of time is recorded while it adjusts to the flow direction.

b. Results

The difference between static and total pressures measured by the MPS is found to have a mean error of 7.7% from the pressure differentials estimated by Eq. (2). This deviation between the expected pressure drop and the pressure drop measured by the MPS decreases as the flow speed increases, reducing to 4.8% at flow speeds above 5 m s−1 (Fig. 4). We hypothesize that this deviation is mostly the result of flow perturbations around the Prandtl tube and imperfect seals between the pressure ports on the tube and the pressure transducers.

Fig. 4.
Fig. 4.

Calibration of the Michigan sensor. The solid line indicates theoretical pressure differences between static and total pressure from Eq. (2). Data points (crisscross) are pressure differences calculated from the static and total pressures measured by the MPS. The data deviate from the expected pressure differences by an average of 7.7% over the entire range of use. Mean relative error for tests at wind speeds faster than 5 m s−1 is 4.9%.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

Measurements of the static pressure always increase as misalignments between the Prandtl tube and the wind increase. Therefore, the correct static pressure is the minimum value that can be measured. The tests show that when the sensor is placed at angles with the flow direction that does not exceed 18°, the error in the differences between the static and total pressures from those measured at the zero-degree reference are smaller than +12% (Table 3). When placed at an angle of 12° to the flow, the error in the differences between static and total pressures is about +3.5%. As expected, increases in the angles produce larger errors; at angles of 27° the error is +37%. At greater angles, the error increases significantly. More importantly, the error is always positive, indicating that misalignments of the Prandtl tube with the flow always produce decreases in the difference between the static and total pressures under the conditions tested here.

Table 3.

Measurement error as a function of misalignments between the Prandtl tube and the wind vector. The MPS vane direction was locked at various angles to the left and right of the flow direction while the static and total pressures were measured. Deviation is from the difference between the static and total pressures when the Prandtl tube is aligned with the flow Δp(0°) and when misaligned by an angle α with respect to the flow Δp(α). The wind tunnel flow speed was maintained at 5.0 m s−1 during these measurements. The measurement error increases strongly for angles larger than 30°.

Table 3.

Figure 5 shows the time scale for the MPS to adjust to changes in the flow direction as a function of flow speed. In the most extreme case studied here (the gold-colored line in Fig. 5), the MPS wind vane rotates 25° in 1 s. The wind vane operates like a damped oscillator; within 3 s of release the Prandtl tube aligns with the flow direction even in flow speeds as slow as 5.0 m s−1, a lower limit for the values expected in a dust devil. Our test at small angles with the flow shows a smaller overshoot than predicted in section 4. We hypothesize that this is caused mostly by friction within the bearings of the rotating base. Under the test conditions, the Prandtl tube changed direction with a maximum rate of 14° in a single measurement interval of 100 ms. Typical dust devils produce changes in wind direction at similar rates. For example, the case analyzed by Rennó et al. (2010) shows average wind shifts of 1.4° in 100 ms with a standard deviation of 5.7°. Statistically, 95% of values fall within two standard deviations of the mean value, therefore 95% of the 100 ms wind shifts in this strong dust devil are smaller than 11.4°. Our results indicate that the error caused by the misalignments expected during measurements in this dust devil, of which 95% are 11.4° or less, is not larger than 4%. Moreover, comparison of the flow direction measured with the sonic anemometer to that collected from the vane can be used to quantify misalignments between the Prandtl tube and the wind flow during field measurements, as shown with data from Rennó et al. (2010) in Fig. 6.

Fig. 5.
Fig. 5.

Time scale for the MPS to align with the wind flow when subjected to abrupt changes in wind direction. The Prandtl tube was locked at angles to the wind flow, then released at t = 0 s to test its response to rapidly changing wind directions. Even the most extreme wind test here—nearly 90°—displays the sensor's orientation, returning to a small angle from the wind flow direction within 1.5 s of release of the sensor.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

Fig. 6.
Fig. 6.

MPS alignment with wind direction during measurements in a dust devil. The differences in wind direction measured by the MPS vane and those measured by the 3DSA show misalignment is rare, even during the passage of a dust devil over the sensors, as is shown here. The difference between directional measurements (blue) remains below 30° for all but the most extreme wind shifts in the dust devil. Static pressure readings (green) as the dust devil passes the sensor are shown as a reference.

Citation: Journal of Atmospheric and Oceanic Technology 30, 10; 10.1175/JTECH-D-12-00246.1

6. Conclusions

The instrument described in this article makes high-frequency measurements of the 3D wind vector as well as static and total pressures in a wind of changing direction, such as those expected in dust devils. The difference between the static and total pressures measured by the MPS has an average error of less than 7.7% for flow speeds up to 35 m s−1. The MPS is also able to maintain alignment between its pressure measuring system and the wind direction to within 30° for nearly all of the severe wind shifts expected in strong dust devils and within 12° for the majority of the dust devil wind measurements in general. This results in measurement errors caused by misalignment to be less than +4% in most cases. The fact that the error shown in Fig. 6 is always positive indicates that misalignments always produce an increase in the static pressure measurement.

The MPS is readily deployable as an accurate stand-alone system, providing static and total pressure data as well as wind direction in a convective vortex.

Acknowledgments

The authors thank Steve Musko, Robb Gillespie, and Fernando Saca for their contributions to this study, as well as Frank Marsik for his guidance in the technical writing. This research was supported by NSF Award AGS 1118467.

REFERENCES

  • Campbell Scientific Inc., 2012: CSAT3 three-dimensional sonic anemometer. Campbell Scientific Instrument Manual, 72 pp.

  • Kravchenko, A. G., and Moin P. , 2000: Numerical studies of flow over a circular cylinder at ReD = 3900. Phys. Fluids, 12, 403417.

  • Marks, L. S., 1934: The determination of the direction and velocity of flow of fluids. J. Franklin Inst., 217, 201212.

  • Moller, A. R., 1978: The improved NWS storm spotters' training program at Ft. Worth, Tex. Bull. Amer. Meteor. Soc., 59, 15741582.

  • Prandtl, L., 1952: Essentials of Fluid Dynamics: With Applications to Hydraulics Aeronautics, Meteorology, and Other Subjects. Hafner, 452 pp.

  • Rennó, N. O., 2008: A thermodynamically general theory for convective vortices. Tellus,60A, 688–699.

  • Rennó, N. O., Burkett M. L. , and Larkin M. P. , 1998: A simple thermodynamical theory for dust devils. J. Atmos. Sci., 55, 32443252.

  • Rennó, N. O., Halleaux D. G. , Saca F. , Rogacki S. , Gillespie R. , and Musko S. , 2010: A generalization of Bernoulli's equation to convective vortices. Extended Abstracts, 41st Lunar and Planetary Science Conf., The Woodlands, TX, Lunar Planetary Institute, 1745.

  • Saca, F. A., Rennó N. O. , Halleaux D. G. , Rogacki S. , Gillespie R. , and Musko S. , 2010: A portable instrument for atmospheric measurements. Extended Abstracts, 41st Lunar and Planetary Science Conf., The Woodlands, TX, Lunar Planetary Institute, 1767.

  • Wieringa, J., 1967: Evaluation and design of wind vanes. J. Appl. Meteor., 6, 11141122.

  • Zucrow, M. J., and Hoffman J. D. , 1976: Gas Dynamics. Wiley, 772 pp.

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