On the Use of Hot-Wire Anemometers for Turbulence

On the Use of Hot-Wire Anemometers for Turbulence Measurements in Clouds

HOLGER SIEBERT AND KATRIN LEHMANN

Leibniz Institute for Tropospheric Research, Leipzig, Germany

RAYMOND A. SHAW

Department of Physics, Michigan Technological University, Houghton, Michigan

(Manuscript received 7 February 2006, in final form 18 September 2006)

ABSTRACT

The use of a hot-wire anemometer for high-resolution turbulence measurements in a two-phase flow (e.g.,atmospheric clouds) is discussed. Experiments in a small wind tunnel (diameter of 0.2 and 2 m in length)with a mean flow velocity in the range between 5 and 16 m s�1 are performed. In the wind tunnel a spraywith a liquid water content of 0.5 and 2.5 g m�3 is generated. After applying a simple despiking algorithm,power spectral analysis shows the same results as spectra observed without spray under similar flowconditions. The flattening of the spectrum at higher frequencies due to impacting droplets could be reducedsignificantly. The time of the signal response of the hot wire to impacting droplets is theoretically estimatedand compared with observations. Estimating the fraction of time during which the velocity signal is influ-enced by droplet spikes, it turns out that the product of liquid water content and mean flow velocity shouldbe minimized. This implies that for turbulence measurements in atmospheric clouds, a slowly flying plat-form such as a balloon or helicopter is the appropriate instrumental carrier. Examples of hot-wire anemom-eter measurements with the helicopter-borne Airborne Cloud Turbulence Observation System (ACTOS)are presented.

1. Introduction

Atmospheric turbulence is characterized by ex-tremely large Reynolds numbers. This means that theturbulent cascade extends over a large range of spatialscales and that the turbulence at the smallest scalestends to be highly intermittent (e.g., Wyngaard 1992).These general features are thought to hold true for tur-bulence in clouds also, but there the problem becomesmore complex. It is suggested, for example, that thepresence of droplets in a turbulent flow can modify theenergy dissipation rate and, when gravitational sedi-mentation is significant, can introduce anisotropy atsmall spatial scales and lead to a reverse energy cascade(Elghobashi and Truesdell 1993; Ferrante and Elg-hobashi 2003). Furthermore, growth and evaporation ofcloud droplets is associated with a large phase-changeenthalpy and it is therefore possible to inject energy at

small scales, also modifying the dynamics of the turbu-lent cascade near the dissipation scale (Andrejczuk etal. 2004). Unfortunately, however, it has not been pos-sible to study these processes in natural clouds becauseof the difficulty of making finescale turbulence mea-surements in a two-phase system. Quantifying the richinteractions thought to occur in clouds at centimeterscales remains an experimental challenge.

The fundamental measurement challenge is to obtaina high-spatial-resolution measurement of turbulence inthe presence of cloud droplets (and possibly ice crystalsand precipitation). Most aircraft-based flow measure-ments are made with five-hole probes, yielding spatialresolutions on the order of several meters. Much of ourexperimental understanding of the turbulent structureof clouds, therefore, is based on measurements that areonly able to resolve the largest eddies of the turbulentflows. Higher-resolution measurements with ultrasonicanemometers in clouds have been made (Cruette et al.2000; Siebert et al. 2006) but are limited in general to aresolution of around 10 cm because of line averagingover the pathlength (Kaimal et al. 1968). To obtainlocal statistical parameters, such as local energy dissi-

Corresponding author address: Holger Siebert, Leibniz Institutefor Tropospheric Research, Permoserstr. 15, 04318 Leipzig, Ger-many.E-mail: [email protected]

980 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24

DOI: 10.1175/JTECH2018.1

© 2007 American Meteorological Society

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pation rates ��, a record of at least 100 samples isneeded for a statistically stable estimation (Frehlich etal. 2004). With ultrasonic anemometer data, a spatialresolution for �� of only �10 m is possible, which isoften too low to resolve the turbulent cloud structure.Therefore, turbulence probes with much higher sam-pling frequencies are needed to obtain �� with higherspatial resolution. Furthermore, spectral deviationsfrom classical Kolmogorov turbulence resulting fromdroplet growth/evaporation and sedimentation are ex-pected to be present at centimeter scales (e.g., Korczyket al. 2006) and therefore cannot be observed directly incloud with the current instrumentation.

The sensor of choice for many decades in wind tunnelexperiments and atmospheric boundary layer studies isthe hot-wire anemometer (HWA). State-of-the-art sen-sors for high-resolution turbulence measurements havea bandwidth up to 100 kHz and are, therefore, suitablefor turbulence measurements well within the dissipa-tion range. High-resolution measurements with hotwires in the atmosphere have been made, for example,with a sensor package carried by a tethered balloon(Muschinski et al. 2001) or based on a tower (Shaw andOncley 2001). However, even though the application ofhot wires for measurements in two-phase flows is dis-cussed in textbooks (e.g., Bruun 1995; Goldstein 1996),measurements with HWA in the cloudy atmosphere arerare.

A few measurements in clear air with HWAs fixed ona slow-flying research aircraft were reported by Len-schow et al. (1978), but on fast-flying aircraft with typi-cal high true airspeed (TAS) on the order of 100 m s�1,hot wires with a diameter of several micrometers likelyare too fragile. Merceret (1976) showed that hot-filmprobes are useful for airborne small-scale turbulencemeasurements with better than centimeter resolution.Measurements were suggested for clear-air turbulencebut also in the presence of rain (Merceret 1970). It wasfound that ice would damage the hot-film probes andthat flights in clouds were harmless, but the true veloc-ity signal cannot be recovered in clouds because of thelarge numbers of droplet impacts. More recently,Henze and Bragg (1999) made flow measurements in awind tunnel with spray generators using hot-wire an-emometers. They developed a digital accelerationthreshold filter to remove distinct spikes from the hot-wire data caused by droplet impaction. Given this ex-perience over the last decades, it seems worthwhile toexplore the possible use of hot-wire anemometry inclouds in greater detail.

The aim of this paper is to investigate the feasibilityof using hot-wire anemometers for finescale turbulencemeasurements in clouds or other two-phase flows. To

extend previous work (e.g., Henze and Bragg 1999), theinfluence of the droplet spikes on the signal statisticsand the efficiency of the despiking filter have to beanalyzed in more detail. To accomplish this we havetested a hot-wire anemometer under various flow con-ditions in a controlled laboratory setting, which are rep-resentative of typical cloud conditions. The laboratoryexperiments are described in section 2. Specifically, wediscuss the wind tunnel setup (section 2a), the nature ofdroplet–hot-wire interactions and the implications forthe quality of the turbulence measurements (section2b), the hot-wire signal (HW) despiking filter (section2c), and examples of data for three different flow con-ditions (section 2d). In section 3 we present results fromhot-wire measurements made in an atmospheric cloud,using a helicopter-borne payload Airborne Cloud Tur-bulence Observation System (ACTOS). In this configu-ration, hot-wire measurements were possible in naturalclouds because true airspeeds were sufficiently low. Fi-nally, our findings are summarized and discussed in sec-tion 4.

2. Wind tunnel experiments

a. Wind tunnel and experimental setup

The wind tunnel consists of a horizontal Plexiglastube that is 2 m long and 0.2 m in diameter. A sketch ofthe setup is shown in Fig. 1, in which the flow directionis from right to left. The ratio between tube length l andtube diameter d that is necessary for fully developedturbulence can be approximated by l/d � (A)ReB, withthe flow Reynolds number Re � ud/� and two con-stants A � 0.6 and B � 0.25 for turbulent flows (Bohl1998). Here u is the mean flow velocity, � � �/a � 1.5 10�5 m2 s�1 is the kinematic viscosity of air, � is thedynamic viscosity of air (1.81 10�5 kg m�1 s�1), a isthe air density, and d is the tube diameter. With u � 10m s�1, it follows that Re � 105 and (A)ReB � 11.Therefore, l2/d � 8 and the conditions for fully developedturbulence are nearly met. This conclusion is also sup-ported by power spectral analysis (discussed in Fig. 8).

The spray in the wind tunnel is created by an injectornozzle. The basic operating principle and location ofthis nozzle is shown in Fig. 1. The injector nozzle isdesigned to create a spray with a median droplet diam-eter of 10 �m. Purified water was used to protect thewire of the HWA from any further material remainingat the surface. The tube to the water reservoir can beclosed by a manual valve and since no additional com-pressed air passes through this tube, this valve has noinfluence on the flow speed. Thus, identical flow situa-tions with or without spray can be established. To in-crease the flow speed, two additional nozzles consisting

JUNE 2007 S I E B E R T E T A L . 981


of 1/4-in. tubes are placed side by side with the mixingnozzle. The maximum pressure for the nozzles is 5 barseach. For the 1/4-in. tubes the pressure can be roughlyadjusted to vary the flow speed. However, it was foundthat stable flow conditions exist only for completelyopened valves; that is, experiments with three differentstable flows could be performed. The three differentflow cases are denoted in the text by subscripts describ-ing the valve settings (cf. Table 1).

b. Hot-wire anemometer

Turbulence was measured with a one-dimensionalHWA (Dantec Dynamics A/S, Denmark, type 54T30)that was located about l2 � 160 cm behind the inlet ofthe wind tunnel (cf. Fig. 1). The HWA system is a con-stant temperature anemometer with a platinum-platedtungsten wire (type 55P01) with a diameter of 5 �m andan overall length of around 3 mm, whereas the sensing

part is only 1.25 mm long. Essentially, an HWA mea-sures the convective heat transfer between the heatedwire and the flow that is described by the Nusselt num-ber Nu � C � (D)Re1/2 (King’s law) with the Reynoldsnumber Re � udHW/� (Goldstein 1996; Bruun 1995).Here, C and D are empirical constants and dHW is thediameter of the hot wire. The electrical power input Pis �V2

p � Nu; therefore, the output voltage Vp of theHWA is �Re1/4 � u1/4. The bandwidth of the system is10 kHz.

To calibrate the HWA over the range of the threedifferent flow speeds, a few measurements for varyingspeeds were made simultaneously with a Pitot tubeplaced slightly behind the hot wire, so as not to disturbthe turbulence measurements. The sampling frequencyfs was set at 1 kHz for all devices. A correlation plot ofthe flow velocity uPitot measured with the Pitot tube andthe HWA output VHW is shown in Fig. 2. To reduce thescatter, the hot-wire signal was averaged over nonover-

TABLE 1. Mean parameters for the three datasets: mean flow speed u with standard deviation �u, energy dissipation rate �, andKolmogorov microscale K. The LWC was measured with the PVM-100A at the end of the wind tunnel. Furthermore, the thresholdat for the despiking filter, the total number Ntot of observed spikes, the integration time Ti with spray, and the droplet numberconcentrations NHW and NFSSP are summarized. The ratio �� is an approximation of Eq. (4) and �m � Ntot Tm/Ti is the observed ratiobetween the total time affected by droplet strikes and the integration time.

Datasetu

(m s�1)�u

(m s�1)� � �3

u /d(m2 s�3)

�K � ��3

��1�4

(10�4 m)LWC

(g m�3)at

(104 m s�2) Ntot

Ti

(s)NHW

(c m�3)NFSSP

(c m�3)��

(10�2)��m

(10�2)

010 4.9 0.8 3 1.9 2.50 0.12 5880 15 8211 1500 2.2 20110 8.8 1.3 11 1.3 0.78 1.5 170 18 511 675 1.3 0.5111 16.5 2.8 110 0.7 0.47 3.3 66 13 268 330 1.4 0.3

FIG. 1. Sketch of the wind tunnel and the location of the (left) turbulence probes and (right)nozzles. The upper and lower nozzle (P1 and P3) create the major part of the flow, the nozzlebetween (P2) is a mixing nozzle that creates a small flow speed but is responsible for the spray.The principle of the mixing nozzle is illustrated in the enlarged sketch. The flow of water forthe spray (W) can be turned off without influencing the flow. The length l of the tube is 2 m,l1 � 0.2 m, and l2 � 1.6 m. The liquid water content is measured at the end of the tube witha PVM.



lapping flow velocity ranges of 1 m s�1. A fit with athird-order polynomial was made to estimate the cali-bration coefficients.

c. Characterization of the spray

To study the effects of droplets on the HWA signal itwas necessary to characterize the spray under the threeflow conditions. A particle volume monitor (PVM-100A) was placed at the end of the wind tunnel tomeasure the liquid water content (LWC) of the spray(cf. Fig. 1). An internal low-pass filter for antialiasingwas set at around 100 Hz. Details of this optical probecan be found in Gerber et al. (1994).

The droplet size distribution �N/�dd is derived frommeasurements performed with an M-Fast ForwardScattering Spectrometer Probe (FSSP; Schmidt et al.2004), which was located at the end of the tube (insteadof the PVM). The integral over �N/�dd gives the drop-let number concentration N. Figure 3 depicts the sizedistributions for the three different flow states. For thetwo situations with the highest flow velocities (110 and111), both distributions have nearly the same shape

with a mean diameter around 9 �m and a long tailtoward large droplet sizes. The ratio of both distribu-tions and number concentrations (�2) is similar to theratio of the flow velocities. For the third case with lowflow velocities, the number concentration reaches veryhigh values and the M-Fast FSSP is near saturation.Thus, the M-Fast FSSP measurements for this caseshould be interpreted with caution.

d. Influence of droplet–hot-wire collisions on thevelocity signal

When a droplet impacts the hot wire, the system re-acts so as to evaporate the water and maintain the wireat a constant temperature. As a result a sudden spike inthe voltage is observed. This spike must be distin-guished from voltage variations due to turbulent veloc-ity fluctuations. Essentially, the result is a continuouslysampled signal interrupted by random spikes. The use-fulness of the velocity signal is inversely related to thefraction of signal lost because of droplet–hot-wire col-lisions. In the following we attempt to estimate thatfraction.

FIG. 2. (a) The correlation between the raw hot-wire signal VHW and the flow velocity uPitot measured with the Pitot tube. A fit witha third-order polynomial is included. (b) A time series of the flow velocity measured with the Pitot tube and the signal of the calibratedhot wire.



1) IMPACT RATE OF DROPLETS ON THE HOT WIRE

The particle Stokes number for a 10-�m droplet in-teracting with a hot wire is

St �dd

2�wu

9�gdHW� 1200, �1�

where w is the density of liquid water. This Stokesnumber is much higher than the critical Stokes numberrequired for impaction (St � 0.3); therefore, we cansafely use the geometric cross section in determiningthe droplet–hot-wire collision rate.

The hot wire has a cross section � for a typical clouddroplet with an average diameter of dd � 10 �m of � �L(dHW � dd) � 1.25 mm (5 �m � 10 �m) � 1.9 10�8 m2. With a droplet number concentration of N �675 cm�3, the mean free path is 1/(N�) � 8 cm. Fur-thermore, with a mean flow velocity of u � 10 m s–1 weobtain an average arrival time of � � 1/(N�u) � 8 ms.In fact, if the droplets are randomly distributed in theturbulent flow, we expect that the probability densityfunction for the (random) droplet interarrival time t isexponential, p(t) � ��1 exp(�t/�). This is observed tobe a reasonable approximation, as illustrated in Fig. 4,which shows the probability density function (PDF) ofinterarrival times under flow conditions 110. As a resultof the skewness of the exponential function, we expectthere will be a significant number of velocity data seg-ments that remain uninterrupted for times several timeslarger than � (e.g., see Fig. 4 where it can be seen that

approximately 1% of the interarrival times are �5�.).Thus, the natural tendency of random droplet arrivalsto be clustered improves the ability to extract meaning-ful data.

2) DURATION OF A DROPLET IMPACT IN THE

HOT-WIRE SIGNAL

If we wish to know the fraction of useable signal wemust estimate the typical duration of a voltage spike inthe hot-wire signal due to a droplet impact. We proceedby considering the time required for a spherical dropletto evaporate after coming into contact with the hot

FIG. 4. PDF for droplet interarrival time (points), as determinedfrom the hot-wire voltage spikes for flow state 110. The interar-rival time is plotted relative to the mean interarrival time, � � 108ms. An exponential curve (solid line) is shown for comparison.

FIG. 3. Droplet size distribution for three flow states. The drop number concentration isgiven as the integral over the size distribution.



wire. Of course, after a collision the droplet may nolonger be a sphere, but we expect the analysis to give asatisfactory estimate for the purpose of a scale analysis.

The ratio of energy required to evaporate a dropletwith radius rd and the energy required to increase thedroplet temperature by approximately �T � 80 K (e.g.,from a laboratory temperature around 20°C to Tw �100°C) is � � L� /(cp�T) � 2.2 106 J kg�1 (4200 Jkg�1 K�1 80 K) �1 � 7, where L� is the latent heat ofvaporization for water and cp is the specific heat capac-ity at constant pressure for water. Therefore, as a first-order approximation we consider only the evaporationtime scale of a droplet with a uniform, constant tem-perature of 100°C. The evaporation of a droplet is de-scribed by (e.g., Pruppacher and Klett 1997)

rd

drd

dt� �

MwD�

�wR �E�Tw�

Tw�

e

T�, �2�

with the diffusivity for water vapor D� � 0.211(T/T0)1.94(p0/p) 10�4 � 3.6 10�5 m2 s�1 (with T0 � 273K, T � 373 K, and p0 /p � 1), the universal gas constantR � 8.31 J mol�1 K�1, the molecular weight of waterMw � 18 10�3 kg mol�1, the saturation water vaporpressure at droplet temperature E(TW � 100°C) � 105

Pa, and the ambient water vapor pressure e� at ambienttemperature T�. The ambient temperature is muchlower than the droplet temperature and, therefore, e�

(T�) � E(Tw), such that the second term in the bracketsof Eq. (2) is negligible. Since the right-hand side of Eq.(2) is constant {C � [MwD� /wR][E(Tw)/Tw] � 2.1 10�8 m2 s�1}, the integration reveals the time T neces-sary for the complete evaporation of the droplet of ini-tial radius �d:

T �rd

2

2C. �3�

Because of the large relative speeds between the airand the hot wire, the evaporation time is slightlysmaller because of “ventilation,” or advection of thevapor field away from the droplet by the flow. TheReynolds number–dependent ventilation coefficient(e.g., Pruppacher and Klett 1997) does not exceed 1.5for our flow conditions. For droplet sizes commonlyobserved in this experiment (e.g., 1–10 �m) our analysissuggests that evaporation times are approximately inthe range 1 T 10 ms. Actual voltage spikes result-ing from droplet impact are observed to be on the orderof 0.5 ms (cf. Fig. 6). We speculate that the difference isdue to enhanced evaporation due to the increase insurface area when droplets wet the hot wire. Neverthe-less, the analysis provides an upper bound for the du-ration of voltage spikes resulting from droplet–hot-wirecollisions.

This section may be summarized by specifying thefraction of time during which the velocity signal is in-fluenced by droplet evaporation. The fraction can beestimated as the ratio of the droplet evaporation time Tand the mean interarrival time � :

� �T

��

Ndd2�dHW � dd�lu

8C. �4�

From Eq. (4) it can be seen that for a constant u, �varies approximately as Nd3

d, which is proportional tothe liquid water content. It follows, therefore, that inorder to maximize the fraction of useful turbulent ve-locity signal from a given hot-wire system, the productLWC u should be minimized.

e. Hot-wire measurements and despiking method

To describe and test the despiking method, wechoose flow and cloud conditions similar to those thatwould likely be encountered with low-true-airspeedcloud research platforms (see section 3). Specifically,we begin with flow conditions for state 110, with a meanflow of u � 9 m s�1 and a mean LWC � 0.8 g m�3. Thecomplete time series is 30 s long. The first 12 s werewithout droplets; for the last 18 s the spray was added.Figures 5a–c show the time series of the calibrated hot-wire signal uHW, the LWC, and the first time derivativeaHW � �tuHW, respectively. Two subsequences labeled“Part I” and “Part II” are used for further comparisonof drop-free and cloudy conditions. The spikes of theimpacting droplets are most evident in the time seriesof aHW (cf. Fig. 5c).

A typical signal of a droplet spike (cf. spike in thedashed box in Fig. 5c) is enlarged in Fig. 6. The signalhas a duration of approximately 0.5 ms (five samples);the amplitude change of �u � 20 m s�1 corresponds toan acceleration of nearly 105 m s�2, which is about oneorder of magnitude higher than the maximum valuesobserved for the drop-free flow. Therefore, the spikescan be clearly distinguished from natural turbulenceand a threshold can be defined. The signal during thedroplet impact is then linearly interpolated for a dura-tion of five samples (cf. dashed line in Fig. 6).

To derive a criterion for the threshold, PDFs of uHW

and aHW are calculated and depicted in a semilogarith-mic plot in Fig. 7. For smaller values, uHW can be wellapproximated with a Gaussian fit whereas the wings ofaHW are closer to an exponential curve, in agreementwith theory (Frisch 1995). For positive velocities largerthan around 6 m s�1 an increased probability of uHW isfound because of the spikes. For the derivative aHW thiseffect is symmetric (cf. Fig. 6), and the influence of thespikes appears as a sharp change in the slope, which is



clarified by the dashed lines. This slope change is usedto define the threshold �at for the despiking algorithm.For this case, at � 1.5 104 m s�2 is chosen.

To illustrate the effectiveness of this simple despikingalgorithm, power spectra F(k ) are calculated as afunction of the nondimensional parameter k andshown in Fig. 8, where k is the wavenumber and is theKolmogorov microscale. The spectra are calculated forPart I (drop free) and Part II (raw signal and despikedsignal) individually. In general all three spectra follow a�5/3 slope and drop off at around k � 0.05, wheredissipation becomes effective. However, it can beclearly seen that the spectrum of the data including thespikes drops off much less rapidly than for the drop-free case (Part I). This effect is significantly decreasedby the despiking algorithm. For k � 0.03, there is nodifference between the spectra including drops and thedespiked spectra.

f. Hot-wire measurements for three different flowstates

To confirm the utility of the despiking algorithm overa broad range of cloud conditions, it is tested for thetwo additional wind tunnel flow states described in sec-

tion 2a. The mean parameters for all three flow casesare summarized in Table 1. For this investigation thesetup was slightly changed, resulting in 20% increasedmean flow velocities compared with the calibration (cf.Fig. 2). With the total number of detected spikes Ntot

and the total integration time Ti, the droplet numberconcentration NHW � Ntot�uTi can be estimated andcompared with the concentration derived from FSSPdata (NFSSP). The results are also included in Table 1.For the two cases with higher flow rates (110 and 111),the NHW is about 20%–25% lower than the concentra-tion observed from FSSP measurements. There are twopossible explanations for this disagreement. First, thecollision efficiency between the hot wire and droplets issmaller than one and, second, the signal of small drop-lets is too low and therefore is interpreted as naturalturbulence. The latter argument is supported by thefact that the spectrum of the despiked data lies abovethe spectrum of the drop-free data. For the low flowcase (010), the hot wire “detected” 5 times more drop-lets than counted with the M-Fast FSSP. In this case,the definition of the threshold was difficult and alsohigh accelerations in the drop-free part were inter-preted as droplet spikes. Here, the despiking algorithmreduces natural variance and consequently the spec-

FIG. 5. Time series of the (a) calibrated hot-wire signal uHW, (b) LWC, and (c) first derivative aHW. The meanflow speed was at 9 m s�1 and the mean LWC for the cloud part of the record was 0.8 g m�3. Two subsequencesmarked with Part I and Part II are defined for further analysis.



trum of the despiked data is below the spectrum of thedrop-free data over a wide frequency range. On the onehand, a lot of droplet spikes would remain in the timeseries when increasing the threshold; therefore, a com-

promise had to be found. On the other hand, as de-scribed in section 2c, the M-Fast FSSP was near satu-ration and coincidence counts led to an underestima-tion of NFSSP.

FIG. 6. A 3-ms-long subsequence of the data shown in Fig. 5 (cf. dashed box) indicating thesignature (a) of a striking droplet and (b) in the first derivative. A typical spike due to dropletimpact lasted 4–5 samples (0.4–0.5 ms).

FIG. 7. PDFs of uHW and aHW. In the PDF, the threshold for the despiking algorithm �at

is included.



The ratio �� in Table 1 is equal to Eq. (4), but thefactor N d2

d(dHW � dd) is approximated by (LWC) (4/3�w)�1. The direct measured ratio �m � NtotTm/Ti isthe ratio between the total time affected by dropletstrikes and the integration time with T m � 0.5 ms as the

mean observed evaporation time (e.g., the observedlength of the voltage spikes due to droplet impact).

In Fig. 9, the power spectral densities (PSDs) F(k )(hereafter called “spectra”) for all three datasets areshown as a function of k . The spectra of the three

FIG. 9. PSD functions of all three flow cases. A (k )�2/3 fit is included as a reference forinertial subrange behavior. The PSD of set 111 is shifted by a factor of 100, whereas the PSDof set 010 is shifted by a factor of 0.01 for better presentation.

FIG. 8. PSD functions. A (k )�2/3 fit is included as a reference for inertial subrangebehavior.



cases are vertically shifted for clearer presentation. Forthe high flow case (111), nearly no differences can befound between the spectrum of the data including drop-lets and the despiked data. The spectrum follows a �5/3slope for inertial subrange behavior over a range ofnearly 2 decades and starts to drop off at k � 10�1

because of the influence of dissipation. Most obvious isthe effect of despiking for the low flow case (010) wherethe spectrum of the droplet-free part drops off signifi-cantly at k � 10�1, whereas the spectrum of the dataincluding droplets is contaminated at dissipation scales.However, for this case all 3 spectra exhibit much morescatter than observed for the other 2 cases, and theslope in the inertial subrange is slightly steeper than�5/3. The spectra of the despiked and drop-free dataagree at least qualitatively.

The first 4 statistical moments are calculated for thehot-wire signal and the central difference �HW �(HWi�1 � HWi�1)/2 before and after the despiking al-gorithm was applied. All moments are summarized forall three datasets in Table 2. The first moment (e.g., themean value �) is not influenced by droplet impacts. Themean values differ slightly from the values given inTable 1 since the moments are estimated from the sec-ond part (including droplets) of the record only. Forhigher moments the influence of the despiking algo-rithm becomes more obvious. In particular, for the kur-tosis of the hot-wire signal of set “010,” the despikingleads to a reduction from K � 8 to K � 3, which is thetheoretical value for a Gaussian distribution, which il-lustrates the efficiency of the despiking algorithm.

Figure 10 shows the time series of the despiked dataand the removed spikes (shifted for a better presenta-tion). For set 010, the despiked data still include a fewspikes due to coincidences. If the time between twospikes is too short, the linear interpolation fails andends within the following spike. Since the LWC and the

droplet number concentration for set 010 are quite un-realistic for most atmospheric cloud types, we use thedespiking algorithm without taking coincidence into ac-count. Compared to Fig. 5 for set “110,” the onset of thespray can hardly be detected in the despiked data inFig. 10.

3. First field data

An HWA of the same type as used for the windtunnel investigations was attached to the outrigger ofthe helicopter-borne version of ACTOS. ACTOS is anautonomous payload with turbulence sensors and sev-eral devices that measure cloud microphysical andaerosol properties. The payload is additionallyequipped with a navigation unit, a real-time data acqui-sition system, and a power supply. An overview of aformer version of ACTOS can be found in Siebert et al.(2003, 2006b), where ACTOS was carried by a tetheredballoon. During a field experiment in April 2005,ACTOS was deployed beneath a helicopter, carried asexternal cargo from a 140-m-long rope (Siebert et al.2006a). ACTOS was dipped into cumulus clouds whilethe helicopter remained outside. The true airspeed wasaround 15 m s�1 (similar to the high flow conditions inthe wind tunnel), which is sufficient to avoid the influ-ence of the helicopter downwash. The low TAS of ahelicopter compared to the high TAS of typical re-search aircraft protects the hot wire from being de-stroyed by impacting droplets, and also reduces � bynearly a factor of 10 [see Eq. (4)].

Unfortunately, electronic noise reduced the amountof useful HWA data from this experiment. Further-more, most flights were performed at cloud tops of con-tinental clouds with high LWC and high droplet con-centrations. According to the discussion at the end ofsection 2a, these conditions are more difficult for thedespiking analysis. A short sample of 35-s duration

TABLE 2. First four statistical moments (mean �, variance �2, skewness S, and kurtosis K ) of the calibrated hot-wire signal HW, thecentral difference �HW, the despiked hot-wire signal HWdes, and the central difference of the despiked signal �HWdes.

Dataset Parameter � �2 S K

010 HW 5.5 100 9.6 10�1 8.1 10�1 8.4 100

010 HWdes 5.5 100 8.8 10�1 4.0 10�1 2.9 100

010 �HW 3.5 10�6 2.9 10�2 3.5 100 4.9 102

010 �HWdes 3.5 10�6 5.7 10�3 �5.7 10�1 2.1 102

110 HW 9.7 100 2.6 100 2.5 10�1 3.3 100

110 HWdes 9.7 100 2.5 100 1.7 10�1 2.8 100

110 �HW 1.5 10�5 7.3 10�2 8.8 10�1 5.1 101

110 �HWdes 1.5 10�5 5.6 10�2 2.6 10�1 8.3 100

111 HW 1.7 101 9.2 100 2.1 10�1 3.1 100

111 HWdes 1.7 101 9.2 100 2.0 10�1 3.1 100

111 �HW �1.7 10�6 3.6 10�1 3.0 10�1 7.3 100

111 �HWdes �1.7 10�6 3.5 10�1 3.0 10�1 5.6 100



from a flight conducted on 24 April 2005 was chosen toinvestigate the capabilities of an HWA in atmosphericclouds. The sample was taken at a height of around1700 m with a mean static temperature of 7°C and amean TAS of 16 m s�1. The time series of the LWC ascloud indicator, the horizontal wind velocity measuredwith an ultrasonic anemometer (Gill Solent HS; seeSiebert and Muschinski 2001), and the horizontal windvelocity measured with the HWA are shown in Fig. 11.For this experiment the sampling frequency of theHWA was 2 kHz. The HWA was calibrated against thesonic measurements (here a polynomial of second or-der was used). The 17-s-long cloud penetration is char-acterized by a low but variable LWC with a maximumof 0.2 g m�3. The wind velocity data from the sonicanemometer and hot wire were not corrected for atti-tude or motion of the ACTOS payload since in thisstudy only small-scale features are of interest. In Fig. 11the time series of the velocity data are shifted relativeto each other by �1 m s�1. In the upper curve thespikes due to droplets can be clearly seen. A few spikesin the despiked data (lower panel) result from coinci-dences; that is, the time between two droplets wasshorter than the time of a typical droplet spike. For thiscase the interpolation creates a new spike even if bothdroplets have been correctly detected. However, thisproblem occurred much more often in real clouds than

in the wind tunnel, even with similar droplet numberconcentrations and LWC, indicating that droplet clus-tering is more pronounced in natural clouds.

In Fig. 12 the spectra of the horizontal velocity mea-sured with the sonic anemometer (sampling frequencyfs � 100 Hz) and the hot wire are shown. The temporalresolution of the hot-wire data was reduced from 2 kHzto 400 Hz by calculating nonoverlapping block averagesto reduce high-frequency noise (after applying the de-spiking algorithm). The spectra were calculated overthe complete 35-s-long record, including the cloud data.For frequencies below 10 Hz, all 3 spectra agree wellbut have a slope slightly below �5/3. For higher fre-quencies, the raw hot-wire spectrum begins to flattenwhereas the sonic and despiked data show a similarbehavior. Between 10 and 40 Hz both spectra begin toflatten but the despiked hot-wire spectrum decreasesagain with a nearly constant slope.

4. Discussion and summary

We have described HWA measurements made in asmall wind tunnel at maximum flow speeds rangingfrom 4.2 to 13.3 m s�1 and 0.47 LWC 2.50 g m�3.The resolution was close to the Kolmogorov dissipationscale. At these flow speeds, an HWA with a wire di-ameter of 5 �m was not destroyed by the impacting

FIG. 10. Time series of the despiked hot-wire signal and the removed spikes.



droplets. For LWC � 1 g m�3, the fraction of the hot-wire signal influenced by spikes due to droplet impactswas small (� � 0.01). The power spectrum of a 10-s-long record including the spikes compared well with the

spectrum of a drop-free record with the same flow char-acteristics. Removing the spikes did not change thespectral behavior significantly. At lower flow speed andtherefore increased droplet number concentration (and

FIG. 12. Power spectra of sonic and hot-wire data as presented in Fig. 11. Nonoverlappingblock averages were used to reduce the frequency of the hot-wire data from 2 kHz to 400 Hz.A �5/3 slope is included as a reference for inertial subrange behavior.

FIG. 11. (top) Time series of LWC and (bottom) velocity fluctuations measured with thesonic and hot wire. The sonic measurements are used as a reference; the raw and despikedhot-wire measurements are shifted vertically �1 m s�1 for better presentation.



increased LWC), the power spectrum begins to flattenat wavelengths about 10 times the Kolmogorov scale.This flattening could be reduced after despiking. Athigh LWC of about 2.5 g m�3, the despiking algorithmbecomes less effective since coincidence becomes morepronounced. Furthermore, the ratio of the time that isaffected by spikes and the total integration time in-creases to � � 0.2 (the “010” case). However, evenunder these conditions, the despiking algorithm is ef-fective and the flattening of the spectrum could be re-duced significantly.

Initial validation of the technique was accomplishedby flying an HWA on the helicopter-borne ACTOS incumulus clouds. The despiked spectra compare reason-ably well with the lower-resolution data from the sonicanemometer. Future measurements can be improvedby sampling at a higher rate and by improving the noiseshielding in the data acquisition system.

The experiments confirm that hot-wire anemometryis most useful when the fraction � of signal contami-nated by droplets is minimized. This fraction varies ap-proximately as � � LWC u, making it clear that thetrue airspeed of the measurement platform is an impor-tant consideration. We have confirmed that speedstypical for a helicopter system (�20 m s�1) are accept-able, given realistic cloud liquid water contents. Itseems unlikely, however, that the technique wouldwork reliably on a high-speed aircraft platform.

Besides the density of droplet spikes, it is also nec-essary to consider the amplitude of the spikes so as todetermine whether they can be distinguished from theturbulence itself. For the velocity derivative methoddescribed here it is necessary to compare the “accelera-tion” due to a droplet impact to the typical acceleration(velocity increment) measured by the hot wire. Empiri-cally, we found the droplet acceleration spikes to be onthe order of 104 m s�2; presumably, this depends on theexact configuration of the chosen hot-wire system.

Within the inertial subrange, the second-order struc-ture function D(t�) � �[u(t � t�) � u(t�)]2� with a giventime increment t� is related to the energy dissipationrate as (Kaimal and Finnigan 1994)

� ��1

2D�t ��3�2

t u. �5�

With calculating a critical Dt(t�) at the time increment�t � 1/fs � 10�4 s, we get Dt(�t) � (at�t)2, where at �104 m2 s�3 is the critical acceleration for the case withhigh flow velocity (u � 16.5 m s�1). Therefore, we mayestimate that for

� �

�12�3�2

at3�t2

u� 102 m2 s�3 �6�

droplet spikes would no longer be distinguishable fromturbulent accelerations, making the despiking algo-rithm unusable. This high critical value for � is quiteunrealistic even for local areas of deep convective cu-mulus clouds. In this case, however, we would speculatethat the droplet spikes have little influence on the tur-bulence statistics and energy spectra.

Acknowledgments. We thank T. Conrath for techni-cal help with the wind tunnel setup and E. W. Saw, M.Wendisch, and F. Stratmann for many helpful discus-sions on this manuscript. R. Shaw acknowledges sup-port from U.S. National Science Foundation GrantATM0320953.

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On the Use of Hot-Wire Anemometers for Turbulence