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How Snapping Shrimp Snap: Through Cavitating Bubbles

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Science  22 Sep 2000:
Vol. 289, Issue 5487, pp. 2114-2117
DOI: 10.1126/science.289.5487.2114

Abstract

The snapping shrimp (Alpheus heterochaelis) produces a loud snapping sound by an extremely rapid closure of its snapper claw. One of the effects of the snapping is to stun or kill prey animals. During the rapid snapper claw closure, a high-velocity water jet is emitted from the claw with a speed exceeding cavitation conditions. Hydrophone measurements in conjunction with time-controlled high-speed imaging of the claw closure demonstrate that the sound is emitted at the cavitation bubble collapse and not on claw closure. A model for the bubble dynamics based on a Rayleigh-Plesset–type equation quantitatively accounts for the time dependence of the bubble radius and for the emitted sound.

The oceans may be deep, but they are not at all quiet (1). Sounds in the oceans include those of waves; rain, hail, and snow; and the biological sounds of fish, dolphins, whales, and snapping shrimp. The latter, in particular, produce the dominant level of ambient noise in (sub)tropical shallow waters throughout the world (2). These shrimp usually occur in such large numbers that there is a permanent crackling background noise, similar to the sound of burning dry twigs (3). The snapping sound can be heard day and night (4), with source levels as high as 190 (5) to 210 dB (6) (peak to peak) referenced to 1 μPa at a distance of 1 m. This severely limits the use of underwater acoustics for active and passive sonar, both in scientific and naval applications. The frequency spectrum of a snap is broad, ranging from tens of hertz to >200 kHz (5). The noise of snapping shrimp is therefore also used as a source for creating pictorial images of objects in the ocean through ensonification (7).

A snapping shrimp of the species Alpheus heterochaelis(∼5.5 cm in size) is shown in Fig. 1A. The shrimp produces the snapping sound by an extremely rapid closure of its large snapper claw, which may reach 2.8 cm in length, about half of its body size. The claw (Fig. 1B) has a protruding plunger on the dactyl and a matching socket in the propus. Before snapping, the claw is cocked open by co-contraction of an opener and a closer muscle, building up tension until a second closer muscle contracts (8). This results in an extremely rapid closure of the claw (9). A high-velocity water jet (10, 11) is formed when the dactyl plunger is driven into the propus socket, displacing water. The water jet is received and analyzed by sensory hairs on the snapper claw of conspecific snapping shrimp. Therefore, the snapping plays an important role in intraspecific communication (12). In addition, it is used to defend a shelter or territory and to stun and even kill prey animals (10, 13).

Figure 1

(A) Alpheus heterochaelis, one of the largest snapping shrimp. The large snapper claw may be either on the right or the left in both sexes. Modified after (30). (B) Close-up of the snapper claw in its cocked position. The claw is made transparent by the use of methyl salicylate. The claw has a protruding plunger (pl) on the dactyl (d) and a matching socket (s) in the immobile propus (p) (photograph by B. Seibel). During the extremely rapid closure of the snapper claw, a high-velocity water jet is formed when the plunger displaces the water from the propus socket.

The loud snap has been attributed to the mechanical contact made when the dactyl and the propus edges hit each other as the claw closes (6, 14). Here, we show that the sound originates solely from the collapse of a cavitation bubble that is generated by the fast water jet resulting from the rapid claw closure. The water jet velocity is so high that the corresponding pressure drops below the vapor pressure of water. Seawater contains tiny air bubbles, called nuclei (15). Such a microbubble, if located between the dactyl and the propus of the snapper claw, will grow in size when it is entrained in the region of low pressure generated through the water jet. Subsequently, it collapses violently when the pressure rises again.

The experiments were performed with seven individuals of A. heterochaelis. Each shrimp was positioned on a small textile platform in a seawater aquarium and tethered to a vertical holder by a plastic nut glued to its back. The snap was evoked by gently touching the freely movable snapper claw with a soft paintbrush. A hydrophone with an upper frequency limit of 100 kHz was positioned at a small distance from the shrimp. Simultaneously, high-speed images were recorded with a digital monochrome video camera at a frame rate of 40,500 frames per second (fps) with a resolution of 64 by 64 pixels. The image acquisition was triggered by the sound of the snap. A typical hydrophone signal is shown in Fig. 2A (16). The main peak at time t = 0 is followed by a very broadband signal, which is partly due to the reflections of the main signal at the aquarium walls located at a minimum distance of 15 cm. Therefore, the first reflections start after 200 μs. The hydrophone signal shows a precursor signal before the main peak, similar to that previously observed in recordings of the smaller Synalpheus paraneomeris snapping shrimp (5).

Figure 2

(A) Hydrophone signal of a snap by an A. heterochaelis female measured at a distancer = 4 cm. The numbered points correspond to the respective frames in (B). The precursor signal is before and the broadband signal is after the main peak at t = 0. The broadband signal is partly due to the reflections of the main signal at the aquarium walls. The small peak att = –425 μs coincides with the collapse of a small cavitation bubble under the claw (29). (B) A sequence of high-speed images in top view showing the closure of the snapper claw taken at 25-μs intervals (40,500 fps). Each tick mark on the time axis of the hydrophone signal (A) indicates an image recording. The dactyl rotation starts at frame 1 at t = –1250 μs. The main peak of the sound emission is at t = 0 (frame 3) and coincides with the collapse of the cavitation bubble. Full closure of the claw was already achieved at frame 2, 650 μs before bubble collapse.

A sequence of high-speed images, showing the snapper claw from the top, is shown in Fig. 2B. The snapper claw is in its cocked position in frame 1. Full closure of the claw is achieved at frame 2 (600 μs later), followed by bubble growth (within 375 μs, although the onset of bubble growth is not visible in this view) and bubble collapse (in <300 μs) at t = 0 in frame 3. The images show that the cavitation bubble, which was recorded in each of our 108 experiments, is nonspherical and elongated in the direction of the water jet. The bubble grows to a maximum equivalent radius of 3.5 mm on average. At collapse (frame 3), the transparent single cavitation bubble breaks apart, and an opaque cloud of small bubbles is formed, which finally dissolves.

The temporal correlation between the snapping sound and the bubble dynamics was determined from these high-speed video recordings. The hydrophone signal and the exposure timing of the high-speed camera were measured simultaneously, referenced to a trigger signal. The main peak of the snapping sound and the collapse of the cavitation bubble always coincide. An analysis of 19 different experiments showed that the temporal correlation of sound and bubble collapse is achieved with a standard deviation of 0.86 frames, i.e., accurate to within 25 μs. The claw is closed in frame 2 of Fig. 2, 650 μs (or 26 frames at 40,500 fps) before bubble collapse.

The angular velocity of dactyl rotation was determined from the position of the tips of the dactyl and propus in relation to the position of the pivot point. Claw closure begins with moderate angular velocities (on the order of 100 rad/s) for large opening angles. In the final stage of claw closure, the dactyl rotates with an impressive 3500 rad/s. Angular velocities of this order were previously measured with a thin laser-coupled optical fiber glued to the distal tip of the dactyl (9).

The occurrence of cavitation bubbles explains why the snaps are harmful to prey animals: It is cavitation damage, known to damage ship propellers and centrifugal pumps. The destructive force of a collapsing cavitation bubble can be seen during interspecific encounters. Small prey (e.g., worms, goby fish, or other shrimp) can be stunned or killed (13), and small crabs (Eurypanopeus depressus) are injured by the snap of snapping shrimp (17). The interaction distance, defined as the distance from the tip of the snapper claw to the nearest body part of the opponent measured along the long axis of the snapper claw, was reported to be 3 mm on average. In our experiments, it is shown that the cavitation bubble collapses 3 mm in front of the tip of the snapper claw (Fig. 2). In intraspecific encounters, the snap does not injure the opponent; the interaction distance is 9 mm on average (12), far enough to avoid implosion danger.

The velocity of the water jet was estimated from the speed of the cavitation bubble. High-speed video close-ups of the cavitation bubble indicate velocities of the front end of the bubble as high as 32 m/s, whereas the bubble expands longitudinally with a speed of 9 m/s. This indicates a flow with a speed v max on the order of 25 m/s. This high water jet velocity implies a pressure drop from the ambient pressure P 0 = 105Pa, which can, in principle, be modeled through Bernoulli's law. However, there is limited information on the actual temporal and spatial shape of the velocity field and, consequently, also on the pressure field. Nevertheless, the unsteady term in Bernoulli's law, ρ∂tφ (where ρ represents the density of water, ∂t is the partial derivative with respect to time, and φ is the velocity potential), can be estimated by dimensional arguments and is smaller than or, at most, of the same order of magnitude as the kinetic energy term. Therefore, we estimate the magnitude of the pressure drop as P a ∼ (1/2)ρv max 2. With the above water jet velocity, P a ∼ 3 × 105 Pa. Moreover, we assume a Gaussian pressure distribution in timeEmbedded Image(1)where σ represents the width of the Gaussian pulse. As the pressure P(t) drops below the vapor pressure of water (P vap = 2 × 103 Pa), cavitation occurs.

The bubble that arises at the tip of the snapper claw is not spherical. Modeling the dynamics of nonspherical bubbles is nontrivial (18), requiring that all parameters, such as the water jet velocity and width and the size and shape of the bubble nucleus, be precisely known. However, to get at least a semiquantitative statement, we can assume a spherical bubble, whose dynamics is well described by Rayleigh-Plesset–type equations (15).

Typical bubble nuclei in seawater are between 1 and 50 μm in radius (15, 19). We assume a nucleus initially filled with air and of the initial radius R 0 = 10 μm under normal conditions. The results hardly depend on the choice ofR 0. The response of the bubble nucleus on the pressure reduction (Eq. 1) is described by the (modified) Keller equation (20), which is of Rayleigh-Plesset typeEmbedded Image Embedded Image Embedded Image(2)The parameters for an air bubble in water are the viscosity of water ν, its density ρ, the speed of soundc, and the surface tension of the air-water systemS. The terms proportional to /ctake into account the effects of liquid compressibility.p(R, t) is the pressure inside the bubble and can be modeled by a van der Waals equation of state. From an estimation of the Peclét number, we find that we can assume adiabatic behavior (15, 21, 22), and because the amount of water vapor inside the bubble is diffusion-controlled (23), we couple an additional equation for the water vapor concentration inside the bubble to the Keller equation (24). For given bubble dynamics R(t), the emitted sound wave at distance r from the bubble simply follows from (25, 26)Embedded Image(3)In Fig. 3, the modeled pressure reduction (Eq. 1) and the calculated bubble radius resulting from Eq. 2 are plotted. As the pressure decreases, the bubble begins to grow up to a maximum radius of ∼3.6 mm. There is a time delay through inertia: At maximum bubble radius, the pressure has already risen again to the ambient pressure P 0. Subsequently, the bubble collapses rapidly within ∼300 μs. After the bubble collapse, the numerical solution of Eq. 2 shows some afterbounces. These are not observed in the experiment, as the bubble is destroyed upon collapse. Indeed, if we perform a linear stability analysis of the spherical bubble (22,27), we find exactly the same feature at bubble collapse: The bubble is destroyed through a Rayleigh-Taylor–type instability.

Figure 3

The calculated bubble radiusR(t) as a function of time (solid line). The temporal change of the pressure fieldP(t) that was modeled for this calculation is also given (dashed line). The model parameters (P a = 2.2 × 105 Pa and σ = 360 μs) were fitted to match the theoretical radius with the experimentally determined equivalent bubble radius of the ellipsoidal cavitation bubble (indicated by solid circles).

The model parameters P a and σ were fitted to match the theoretical radius with the experimentally determined equivalent bubble radius of the ellipsoidal cavitation bubble (solid circles in Fig. 3). With these model parameters, the calculated sound pressure curve (from Eq. 3) is in good agreement with the experimental sound signal (Fig. 4). The main acoustical signal is preceded by a small sinusoidal precursor, caused by the bubble expansion and contraction. At collapse (t = 0), the main acoustical signal is emitted. The narrow peaks in the calculated sound signal after the main pressure peak are produced by the aforementioned afterbounces and should not be considered here, as the bubble is destroyed on collapse. Quantitatively, the model overestimates the measured sound pressure, especially the maximum pressure, for three reasons: (i) The nonspherical shape of the real bubble reduces the strength of the collapse and therefore the intensity of the emitted sound, (ii) thermal damping effects (28) are not included in the model, and (iii) on the experimental side, the limited bandwidth of the hydrophone underestimates the peak value of the sound pressure.

Figure 4

(A) The calculated sound pressureP s(r, t) forr = 4 cm with P a = 3.0 × 105 Pa and σ = 210 μs. The main peak att = 0 (Ps = 2 × 108 Pa) is drawn off-scale to emphasize the precursor signal. (B) An enlarged view of the experimental sound pressure curve of Fig. 2.

The calculated width of the main acoustical peak for the modeled spherical bubble is very small, on the order of 100 ps. This δ-like pulse corresponds to a white noise spectrum, consistent with the wide frequency range of the sound of the snapping shrimp. A more quantitative comparison of the theoretical and experimental spectrum must include the asphericity of the collapse, the acoustical emission of the bubble fragments, and the sound reflections from the walls into the model.

The variation in claw size, claw shape, cocking duration, applied closer muscle force, and claw closure speeds of snapping shrimp all lead to slightly different sound signals and have different water jet characteristics. By adjusting the parameters P aand σ in our model, we are able to account for the variety of precursor signals measured in our experiments (29).

  • * To whom correspondence should be addressed. E-mail: lohse{at}tn.utwente.nl

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