On the correlation of moth flight to characteristics of aturbulent plumeTal Hadad1, Ally Harari2, Alex Liberzon3, Roi Gurka1 ∗

1 Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva,

Israel

2 Department of Entomology, The Volcani Center, Bet Dagan, Israel

3 School of Mechanical Engineering, Tel-Aviv University, Tel-Aviv, Israel

∗ E-mail: Corresponding gurka@bgu.ac.il

Abstract

Several mechanisms control male moth’s navigation towards a female releasing sex pheromone.

Optomotor anemotaxis is a visual mechanism for the moth flight direction relative to the

ground, mechanoreceptors are used for calculating its speed relative to the air current and

chemoreceptors on the antennae for sampling the pheromone concentration in the air. All

together result in a zigzagging flight pattern of the male moth that depends on the charac-

teristics of its encounters with the pheromone plume. The zigzagging flight pattern includes

constant counter-turnings across the wind line in an angle up to 90 degree (casting). In

this paper we address how air turbulence manifests the male flight behavior in respect to

the streamwise current that carries the pheromone, emphasizing a relationship between the

flight speed and the turbulent plume properties. The interaction between the moth flight

and the flow field characteristics was examined in a wind tunnel where moth trajectory

was recorded. Particle image velocimetry (PIV) and scalar imaging technique were utilized

for measuring velocities and scalar concentration distribution in the tunnel. The role of

turbulence in the moth navigation was evaluated by calculating the correlation function of

the moth trajectory path, the velocity fluctuation in the streamwise and normal directions

and the concentration fields. We have found that the moth navigates in a manner which

is directly correlated with the turbulent flow characteristics: the upwind motion is related

to the streamwise variations of the pheromone concentration while the zigzagging motion

is correlated with the cross-stream turbulent flow fluctuations. This finding can explain

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how the angle of the counter-turning flights, in respect to the main current, relates each

encounter with the pheromone patch to the zigzagging flight pattern

Introduction

Female moths release small amount of pheromone when are ready to mate. The physical

and chemical characteristics of these airborne stimuli are affected by wind velocity and

turbulence which causes various concentrations of the volatile materials along the flight

path (Murlis et al., 1992). Typically the air current contains bursts of pheromone filaments

alternated with gaps of "clean" air in which the pheromone is not detectable. The pattern

of the pheromone dispersal through time is rather constant within the first few meters from

the volatile source, but the concentration of the odor decreases (Murlis, 1986). Thus, spatial

pattern and the temporal occurrence of the pheromone plume affect the male flight path

(Baker et al., 1988; Rumbo and Kaissling, 1989; Christensen et al., 1996).

Two types of information are carried by the plume: the chemical content and its concen-

tration relative to its previous sample. The chemical content provides information about the

releaser, whereas the relative concentration may provide directional information. Nonethe-

less, due to the air turbulence, the sole gradient in pheromone concentration is not an

accurate indication for the direction of the pheromone source (Wright, 1958; Belanger and

Arbas, 1998) and the moth males must use additional cues to locate the "calling", pheromone

releasing, female.

Male moths can reach conspecific females from a long distance (Elkinton et al., 1987)

by following the plume of their pheromone. It was shown that the capacity to follow a

pheromone trail is innate and does not require learning (Willis and Arbas, 1991). Males

perceive information of the pheromone concentration (molecules/m3, through chemorecep-

tors on their antennae) and the rate of encounters with discrete pheromone patches (Vickers,

2000). During its flight the male intermittently encounters parcels of pheromone among gaps

of air with no traces of pheromone. It is known from both mathematical and physical mod-

eling studies that the transfer of odor molecules from fluid media to a sensillum can be

significantly affected by changes in velocity (of either the fluid or the sensillum) (Koehl,

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1995, 1996).

In general, the paradigm is that in its flight towards the odor source the male uses visual

cues from the flow field (optomotor anemotaxis) (Kennedy, 1939). When a male loses the

pheromone trail it zigzags perpendicularly across the wind line (casting), increasing ampli-

tudes with time, seeking a new patch of pheromone and regain the odor plume (Kennedy

and Marsh, 1974; David et al., 1983; Mafra-Neto and Cardé, 1994). The frequency of the

turnings is correlated to the male size; large males tend to zigzag less than small males.

In addition, fluctuations in the odor concentration are essential to elicit upwind flights.

In the presence of constant odor orientation, male moths do not orient upwind (Kaissling

et al., 1989; Kramer, 1992). Males experiencing patchy plumes with the same concentra-

tion demonstrated more zigzagging flight pattern (Vickers, 2006). Moth’s flight pattern

depends on its encounters with the pheromone plume (Preiss and Kramer, 1986; Kennedy,

1986; Baker, 1990; Willis and Arbas, 1991; Mafra-Neto and Cardé, 1994; Vickers and Baker,

1994). These counter-turns and surge flying along the current are suggested as sufficient to

understand the male flight behavior (Willis and Arbas, 1991; Mafra-Neto and Cardé, 1994;

Vickers and Baker, 1994b).

The significance of turbulence to the odor dispersal in respect to moth navigation was

acknowledged in previous papers (Kaissling, 1997), yet the mechanism by which male moths’

navigation is affected by turbulence is not fully understood. In particular, the assumptions

underline the understanding of male behavior is that the male knows its flight direction

relative to the ground (optomotor), its speed relative to the air current (through mechanore-

ceptors) and the concentration of the pheromone at time of sampling (chemoreceptors in

the antennae). The angles of the counter-turning flights relative to the main current was

proposed to be internally programmed at each encounter with the pheromone patch, result-

ing with the zigzagging flight pattern (Kennedy, 1983; Carde and Hagaman, 1984; Baker

et al., 1984). The angles between the counterturns is assumed to be related to upwind speed

(Ludlow, 1983; Willis and Arbas, 1998).

In this paper we study the way turbulence affects the male flight behavior in respect to

the streamwise current that carries the pheromone.

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Methods

Wind tunnel and measurement tools

The interaction between the moth flight and the turbulent flow field was examined in an

open-loop wind tunnel with optical access, as shown in figure 1, operated at 0.3 m/sec,

velocity, similar to male moth flying towards the female in natural environment. The female

moth was placed at the center of the up-wind section of the tunnel. Next to it, a rubber

septa loaded with the synthetic pheromone main component (E7,Z9-12:Ac) was located in

the synthetic pheromone experiment. The male moths began to fly towards the female from

the downstream section of the wind tunnel. Particle image velocimetry (PIV) (Raffel et al.,

2007), and scalar imaging (Hanson, 1988; Sarathi et al., 2010), measured the velocities and

scalar concentration distributions in the tunnel, respectively. The flow was seeded with two

types of tracers: oil smoke (0.5 µm) for scalar imaging and oil aerosol (1.2 µm) for PIV.

Measurements of the scalar and velocity fields were conducted in streamwise-vertical plane

at the mid-width of the wind tunnel as is shown in figure 2. Figure 2 shows an instantaneous

scalar image, whilst the dashed frame indicates the location of the PIV measurements and

the overlap region between PIV and scalar imaging.

For both PIV and scalar imaging techniques a dual-head pulsed Nd:YAG laser (NewWave

Solo 120 mJ/pulse, 532 nm) was used along with a laser sheet forming optics. High resolution

CCD camera (4008× 2672 pixels) operated at frame rate of 4 Hz and dynamic range of 12

bit was oriented perpendicular to the laser sheet imaged yielding a field of view of 21 × 27

cm2 (see figure 2). Standard FFT-based cross-correlation PIV analysis using 64× 64 pixels

correlation windows with 50% overlap was applied to 100 sequential images, resulting in

4760 velocity vectors for each velocity map (Taylor et al., 2010). Images of the smoke plume

were acquired at a frame rate of 4 frames per second for twenty seconds and a total of 38

frames were captured.

In addition, the male moth’s flight path along the wind tunnel was recorded using a

640×480 pixels video camera operated at the frame rate of 30 frames per second. The open

source particle tracking algorithm (www.openptv.net) was utilized to quantify the moth

location ~X(t) and flight speed ~vm(t) = d ~X/d t along its trajectory (Kreizer and Liberzon,

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Figure 1. The experimental setup of the open loop wind tunnel with theoptical access, dual head Nd:YAG laser and cameras.

2011).

Moth

Rearing protocol Lobesia botrana is routinely reared in the Entomology Department of the

Volcani Center, Bet Dagan on soy bean based diet, at 25oc, 60% humidity and 17:7 L:D

photoperiod. The moth colony is enriched yearly with field origin moth. Males and females

were separated to sexes at the pupa stage. The adult male and female moths were kept

separately in a 200 ml sealed plastic box and were supplied with 10% sugar solution as food.

In the experiments 1-2 days old virgin male and female moths were used.

Correlation analysis

Turbulence is traditionally described as a statistical phenomenon (Pope, 2000). In the

analysis we used a standard correlation function to characterize the effect of the turbulent

features on the moth’s flight path. The correlation function is given by:

Rij(~r, t) ≡ 〈ui(~x+ ~r, t), uj(~x, t)〉 (1)

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Figure 2. Scalar and velocity fields measurement areas.

where i and j, in given flow field are the velocity components and ~x denotes the distance

between two velocity components. In this case, ui,j is the turbulent velocity components at

locations ~x and ~x+~r at the same instant of time t (Pope, 2000). When the correlation func-

tion is applied to the same component of velocity, i = j, the result is called autocorrelation

function. Since at the origin, ~r = 0, the function is reduces to the variance of the investi-

gated field, R(0) = u2, it is presented usually in the normalized form of the autocorrelation

function, i.e. ρ(0) = 1. We applied the correlation function to the measured quantities in

our experiment: turbulent velocity, ~u(~x, t) and scalar, c(~x, t) fields and to the moth flight

speed along its trajectory, ~vm( ~X, t). It is noteworthy that the trend of these functions in re-

spect to turbulence content describes basic features in the flow, such as length and temporal

scales, as well as defining non-dimensional numbers associated with turbulence (Tennekes

and Lumley, 1971). For example, applying the correlation to the turbulent velocity com-

ponents in the streamwise or longitudinal direction ρ(~r ‖ ~u) is strikingly different from the

correlation function in the cross-stream or transverse direction, i.e. when ρ(~r ⊥ ~u) (Pope,

2000).

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Results

Turbulent flow and scalar dispersion

Typical instantaneous turbulent velocity and vorticity fields are shown in figure 3. The

arrows represent the velocity vectors and color scales are of the velocity and vorticity mag-

nitude, respectively.

(a) (b)

Figure 3. Instantaneous velocity field of a turbulent flow in the wind tunnel.The arrows represent the velocity vectors. Color scale represents the (a) velocitymagnitude,

√u2 + v2 (m/sec) and (b) vorticity magnitude, ω = ∇× u (1/sec). x and y are

normalized by the width of the wind tunnel, H.

Scalar imaging was utilized to characterize the dispersion of odor in the wind tunnel using

odor-mimicking material. The release of the odor-mimicking smoke was located next to the

location of the female moth. It is assumed that in the given turbulent flow the properly

chosen odor-mimicking smoke spreads by the same turbulent diffusion mechanism since its

Batchelor scale (Warhaft, 2000) is significantly smaller as compared to the measured scales

of the turbulent flow (Gurka et al., 2010). The patches of high concentration are stretched

and sheared in the turbulent flow in the region of interest, corresponding to the moths flight

paths. Figure 4 depicts the instantaneous concentration field of the odor-mimicking smoke.

Using the sequence of odor-mimicking scalar images we deduce the statistical distribution

of concentration in streamwise and cross-stream (vertical) directions (as shown in Figure 4).

The correlation analysis (Section ) was applied to the concentration fields, sampled along

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Figure 4. An instantaneous concentration field of the odor-mimicking smoke revealed bythe scalar imaging method. The bottom curve is the profile of the concentration sampledalong the streamwise direction c(x, y, t)

the streamwise and vertical axis, providing ρc(~r).

Moth flight tracking

The moth was released at the down-stream section of the wind tunnel and flew toward

the female. The flight paths towards the odor source (female or synthetic pheromone) were

recorded and analyzed using the open source particle tracking method (Kreizer and Liberzon,

2011). The moth’s trajectory was examined in the region of interest where the flow field and

scalar field are characterized. An example of a trajectory is shown in Figure 5a. In Figure 5b

the position of the moth is shown for one part of the trajectory. During the recording, the

male traveled a distance of approximately 80 cm in the up-wind direction, i.e. along the x

axis. The path in the cross-wind direction (i.e. the y axis) is shown to be zigzagging with

the maximal peak-to-peak amplitude of approximately 20 cm. This is the expected flight

pattern (e.g. (Balkovsky and Shraiman, 2002; Cardé et al., 2012), among others) for a moth

using a chemokinesis mechanism (Vickers, 2000).

Correlation analysis

In order to address the role of turbulence in the moth’s navigation plan, we have calculated

the correlation functions of the three measured compoenents: the moth’s trajectory path,

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Figure 5. The moth trajectory in the region of interest. (a) An example of a mothtrajectory. (b) Position of the moth ~x(t) along streamwise (x, blue) and vertical (y, red)directions

the velocity fluctuation in the streamwise and normal directions and the concentration field.

Figure 6 depicts the spatial correlation of the measured parameters in the tunnel during the

moth’s flight towards the odor source.

The correlation trends in figure 6 shows an exponential decrease in the correlation func-

tion with distance, which is the classical behavior of turbulent fluctuations for a given flow

field (Pope, 2000). Based on the correlation function of the turbulent fluctuations for the ve-

locity components, u and v, in the streamwise and cross-stream directions one can estimate

the integral length of the flow. These scales are characteristics of turbulent eddies which

govern the transport mechanisms (Tennekes and Lumley, 1971). For the flow in the wind

tunnel, the integral lengths in the x and y directions are about 300 and 200 mm, respectively,

for both velocity components. Yet, correlating the concentration field in the streamwise di-

rection shows that the convergence occurs on a greater distance, which presumably reflects

the nature of the odor field to concentrate in a so-called filament geometry strand along the

wind tunnel. Performing the spatial correlation on the moth’s trajectory in both direction

shows remarkable similarity to the flow field features.

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Figure 6. Streamwise and cross-wind correlations of moth’s velocity with theflow and concentration fields.

Discussion and conclusions

Male moth’s flight when searching for a mate is guided mainly by the dispersing plume of

the female pheromone. It was also confirmed, in our wind tunnel experiments, that the moth

reached its destination, the female moth, under varying wind conditions. We have utilized

the correlation analysis on the turbulent flow field and concentration of the odor mimicking

smoke, complemented with the tracking of moth flying upwind to a pheromone source.

Our major result, shown in figure 6, reveals that the correlation curve of the upwind com-

ponent of the moth’s flying speed, ρV (x) overlaps the curve of the streamwise fluctuations

of the odor-mimicking smoke plume, ρc(x), whilst the zigzagging motion (ρV (y)) resembles

the correlation curve of the cross-stream fluctuations of the turbulent velocity, ρv(y). It

means the moth navigates in a manner which is directly correlated with the turbulent flow

characteristics: the upwind motion is related to the streamwise variations of the pheromone

concentration, while the zigzagging motion is correlated with the cross-stream turbulent flow

fluctuations.

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It is plausible to assume that the moth uses flow field information of two quantities for

its navigation: concentration and velocity. However, the notion that the moth correlates its

transverse trajectory with the turbulent fluctuations leads to a new paradigm: the moth,

samples both velocity and concentration during flight. To reach its destination, it follows

the odor trail marked via the filaments strand along the plume, whilst the zigzagging motion

is controlled by adjusting its path to the transverse turbulent scales. Essentially, the moth,

while performing the zigzag motion, follows the integral scales of the flow. This is however,

not surprising from the fluid mechanics point of view, since the integral scales of the flow

dominants both the velocity fluctuations and the dispersion of concentration in a given

turbulent flow (Warhaft, 2000). This finding can explain how the angle of the counter-

turning flights, in respect to the main current, relates each encounter with the pheromone

patch to the zigzagging flight pattern (Kennedy, 1983; Carde and Hagaman, 1984; Baker

et al., 1984).

The correlation distributions hint that the moth’s path follows both the mean flow (up-

wind) using optomotor reaction, supplemented by some additional sensing capabilities to

the turbulent scales. The way the moth senses the flow could be through the velocity fluctu-

ations gradients (e.g.: vorticity) or through some other related fluctuation properties, such

as the Reynolds stress and this remained to be explored by additional set of experiments.

The combination of the wind speed and the turbulent intensity level in the flow can serve

as two quantities that a robot would need to sense in order to navigate.

Acknowledgments

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