1. Background
Extremely high winds and heavy rain associated with tropical cyclones (hurricanes and typhoons) may cause devastating disasters at landfall. Thus, successful forecasting is of paramount importance to save people’s lives and billions of dollars in property. Since the intensity of tropical cyclones is significantly affected by the air–sea interaction between the cyclones and the underlying ocean (Emanuel 2003), an understanding of air–sea processes at the extreme winds of tropical cyclones may be important in formulating accurate coupled cyclone models (Chen et al. 2007; Xie et al. 2010; Wu et al. 2012). In recent years, several field experiments addressing these issues have been conducted (Black et al. 2007; D’Asaro et al. 2011; Pun et al. 2011). In this paper, we report on underwater ambient sound measurements made as part of one of these projects: Impact of Typhoons on the Ocean in the Pacific (ITOP) (D’Asaro et al. 2014).
Bubbles are generated in the ocean by both wind and rain (Medwin et al. 1990), with rain tending to dominate over wind when it is present (Nystuen 2001). It has long been known that a layer of small bubbles exists at the surface when the wind speed exceeds about 7 m s−1 (Thorpe 1982; Crawford and Farmer 1987; Thorpe 1992; Lamarre and Melville 1994) with the layer thickness increasing with wind speed (Thorpe 1992; Wang et al. 2011). Extremely heavy rainfall (above 150 mm h−1) may also generate a subsurface bubble layer (Nystuen et al. 1993). Wind speed and rainfall rate can be estimated from the underwater ambient sound (e.g., Shaw et al. 1978; Nystuen and Farmer 1989; Vagle et al. 1990; Nystuen et al. 1993; Ma and Nystuen 2005). Visual observations of the sea surface at high winds suggest nearly complete coverage of the ocean surface by bubbles and spray, perhaps due to the instability of the surface itself (Holthuijsen et al. 2012; Soloviev and Lukas 2014).
Bubbles can act as tracers of vertical exchange as they are advected by vertical velocities into the ocean interior (Farmer et al. 2001; Vagle et al. 2010; Liang et al. 2011). At depth, the bubbles dissolve, thereby enhancing air–sea gas exchange (D’Asaro and McNeil 2007). However, because bubbles are buoyant, they rise relative to the water. Larger bubbles rise faster; a bubble with a radius of 100 μm rises at about 1.5 cm s−1, while a 1-mm bubble rises at 20 cm s−1 (G. B. Deane 2013, personal communication). Thus, small bubbles are more accurate tracers than large ones.
In recent years, sound measurements beneath tropical cyclones have been reported. Wilson and Makris (2006, 2008) suggest that low-frequency sound, which is unaffected by bubble attenuation, may be used to monitor the wind speed and show supporting measurements from a single hydrophone at 800-m depth measuring 10–50-Hz sound beneath Hurricane Gert (1999). Wang et al. (2011) measure bubble layer depth under Hurricane Ivan (2004) using a bottom-mounted 300-kHz ADCP.
Here, we report broadband (40 Hz–50 kHz) sound measurements from seven Lagrangian floats deployed beneath three different tropical cyclones with wind speeds up to 45 m s−1 and use this information to infer some properties of subsurface bubble clouds under these conditions. The paper is arranged as follows: Section 2 describes the field experiments, Lagrangian floats, and the acquisition and processing of sound measurements. Section 3 describes the observations of breaking waves. Section 4 presents the statistical features of the underwater ambient sound field. Sections 5 and 6 contain a discussion and summary, respectively.
2. Measurements
a. Tropical cyclones
Measurements of underwater ambient sound were made in three tropical cyclones: Hurricane Gustav (2008) in the Gulf of Mexico and Typhoons Fanapi (September 2010) and Megi (October 2010) in the western Pacific Ocean. Table 1 and Fig. 1 provide basic information about these storms and the measurement locations.
A list of tropical cyclones and Lagrangian floats.
Measurements. (a) Hurricane Gustav in the Gulf of Mexico. Colors indicate the wind field at 0730 UTC 1 Sep 2008, obtained from the HWIND-analyzed aircraft measurements. The gray line shows the Louisiana coast. The magenta curve shows Gustav’s track. The black curve shows the trajectory of Lagrangian float 50; the blue section indicates the float location at the time of the wind field. (b) As in (a), but for Typhoon Fanapi and Lagrangian floats 60–62. The time of the wind field is 0015 UTC 18 Sep 2010. (c) As in (a), but for Typhoon Megi and Lagrangian floats 66–68. The time of the wind field is 2330 UTC 16 Oct 2010.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
b. Lagrangian floats
Sound measurements were made from hydrophones mounted on custom-built Lagrangian floats (model MLFII), similar to those described by D’Asaro (2003) and D’Asaro and McNeil (2007), but with somewhat different instrument payloads. Floats were air launched ahead of each storm from WC-130J aircraft operated by the 53rd Air Force Reserve squadron “Hurricane Hunters” and recovered by research vessels after the storm passage. During the peak winds, the floats were repeatedly carried across the upper, well-mixed layers by turbulence in these layers, thereby sampling this layer nearly uniformly, if irregularly. Before and after the peak winds, each float profiled vertically, surfaced, and obtained GPS positions. Float trajectories (Fig. 1, black curves) were estimated by interpolating between these GPS fixes guided by time-integrated velocity measurements from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats deployed nearby (Sanford et al. 2005, 2011).
c. Vertical velocity
The Lagrangian floats follow the vertical motion of the water so that their vertical motion measures the vertical velocity of the surrounding water (D’Asaro et al. 1996; Harcourt and D’Asaro 2010). Float depth was measured from pressure sampled at 1 Hz; vertical velocity was computed from the centered difference of pressure. Instrumental noise was suppressed with a 5-point running median filter. The pressure fluctuations due to surface waves are naturally filtered because pressure is constant along the Lagrangian trajectories of surface waves to second order in wave height. These are further filtered by a second-order Butterworth filter with a cutoff frequency of 0.1 rad s−1 (63-s period) applied forward and backward across each Lagrangian drift. This removes both residual surface wave pressure signals and, more importantly, pressure sensor noise. The resulting spectra show negligible variance past the cutoff.
d. Wind fields
For the two typhoons, wind fields were measured using Vaisala RS92 dropsondes deployed by the WC-130Js and the Taiwanese Dropwindsonde Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) aircraft (Wu et al. 2005) and a nadir-looking stepped-frequency microwave radiometer (SFMR) (Uhlhorn and Black 2003) on the WC-130Js. Winds at 10-m height (U10) were computed directly from the dropsonde profiles; most of the RS92 dropsondes gave good data at this height. Winds from the SFMR measurements were matched to nearby dropsondes, and a cubic polynomial was used to correct the SFMR to the wind. Corrections are small, 2 m s−1 or less for 20 < U10 < 50 m s−1, but rise rapidly below this; the SFMR winds were not used below 20 m s−1. For Typhoon Fanapi, aircraft surveys near 0000 UTC on 17 and 18 September were used. The storm passed closest to the float at about 0000 UTC on 18 September (Fig. 1b). The 18 September survey included 651 data points (11 dropsondes) within 100 km of the storm center at six different azimuths. For Typhoon Megi, surveys near 0000 UTC on 16, 17, and 18 October were used; the storm passed closest to the floats at about 0000 UTC on 17 October. The 17 October survey included 744 data points (13 dropsondes) within 100 km of the storm center at six different azimuths (Fig. 1c).
For each survey, a continuous wind field was created as follows: First, a radially symmetric wind field was fit to the observations. For radii r > Rmax, the form Vmax(Rmax/r)n was used. For r < Rmax, the form Vmax(r/Rmax) was used. The parameter n had values from 0.4 to 0.7. A map of the deviations from this form was constructed by smoothing the observations in polar coordinates with smoothing scales of 0.1 in log10(r) and π/4 in azimuth. The deviations were about 5 m s−1 for both storms at the peak winds. This map was added to the radially symmetric model to form the final wind field. The standard deviation of the maps from the data is 1.8 and 3.0 m s−1 for Fanapi and Megi, respectively, well within the expected uncertainty in the SFMR data; deviations at the peak winds were less than 1 m s−1 for both storms.
For Hurricane Gustav, wind fields from the operational HWIND product (Powell et al. 1998, 2010), created approximately eight times per day from all available observations, were used.
For all three storms, a continuously varying surface wind field was formed by linearly interpolating the wind maps with time in storm coordinates and then advecting the storm along its track. Winds at the floats were found by interpolating this field to the float locations. The winds at the floats have the least sampling error near the time of maximum winds; we estimate less than 2 m s−1, since the maps were made as the storm passed over the floats. The winds have low accuracy in the outer parts of the storm, that is, below 15 m s−1, which are not radially symmetric and not as well sampled.
e. Underwater sound
The float generated significant noise from four sources: the ballasting piston motor, the drogue control motor, the CTD pump, and the gas tension device (GTD) pump. Removal of this noise was essential to obtaining high-quality data. The Lagrangian float adjusted its volume and thus its buoyancy by moving a piston in and out of the bottom of the float at least once every 30 s, with the duration of this motion varying (Fig. 2b). The times of these motions were logged and the data flagged and removed. The float carried a cloth drogue to increase its vertical drag, which was occasionally folded to allow profiling. The folding/unfolding process usually lasted about 30 s (Fig. 2b). These events were logged, flagged, and removed.
Sample spectrograms showing float noise sources and their removal. (a) Float with a GTD. (b) Float without a GTD. (top) Complete spectrogram; (bottom) exclusion of times where float noise dominates the spectrum. Various sources of noise from the ballasting piston motor, the drogue control motor, the CTD pump, and the GTD pump are labeled. Note that the CTD and GTD noises are periodic.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
All floats measured temperature and salinity using a Sea-Bird Electronics SBE-41 CTD sensor mounted on the bottom of the float; this made negligible noise. Floats 60–62 also included a SBE-41 CTD sensor at the top of the float, only a few inches from the hydrophone, which generated noise for about 3 s for each 30-s sampling cycle (Fig. 2b). These were detected using the 5-kHz sound level, exploiting the exactly 30-s separation and constant duration of this noise, and removed.
Floats 50 and 66–68 each carried a GTD with a pump that ran nearly continuously (McNeil et al. 2006), leaving only 2 s of quiet time during each 30-s repeating cycle (Fig. 2a). These times were logged and flagged. The noise spectrum of the GTD dominates the ambient sound only for frequencies between 100 Hz and 8 kHz (Fig. 3), although the ambient sound appears to reach the noise level at the highest wind speeds and frequencies. Thus, sound levels in the rest of the frequency domain can be used to study rainfall and breaking waves even in the presence of the GTD noise.
Sound spectra at various wind speeds compared to GTD and instrumental noise. Shown here are representative measurements by float 50. The GTD noise is mainly between 100 Hz and 8 kHz (shaded). The sound measurements out of this frequency range are not significantly contaminated by the GTD noise. The thick gray line indicates the background instrumental sound level recorded by a hydrophone in air in a quiet laboratory.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
f. Data
For both floats with and without a GTD, the cleaned sound measurements were resampled onto 1-min grids. For every minute, the median sound spectrum was computed from all individual sound spectra; a median was used instead of a mean to further filter float noises.
The resultant spectrograms from all seven floats are shown in Fig. 4. The 30-min data gaps every 30 min as well as other missing data are shown by the white regions. Wind speed (green) and float depth (blue) are shown on the bottom panel for each float. Note that the floats repeatedly move between the surface and about 50 m, allowing measurement of both the depth and time variations in sound level.
Lagrangian float measurements. For each float, (top) the sound measurements and (bottom) the float depth (blue) and the 10-m height wind speed (green). The sound measurements have been cleaned and resampled onto 1-min grids. The hydrophones were alternatively on and off every 30 min, causing gaps in the sound measurements (white bands). Note that the y axis for float depth is scaled differently above and below (a) 30- or (b)–(g) 60-m depth.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
3. Breaking waves
The analysis of these data will assume a near-surface source of sound generated by breaking waves. Figures 5a–c show evidence of the intermittent sound bursts characteristic of wave breaking as seen by floats a few meters below the surface. Each burst lasts 2–4 s, consistent with previous acoustic observations of breaking waves (Farmer and Ding 1992). Deeper floats in Figs. 5d and 5e show much less variability but similar average sound levels. This is consistent with previous observations (Farmer and Vagle 1988) and attributed to the larger area of the surface and the larger number of breaking events heard by deeper floats. These observations support our assumption that breaking waves are a dominant source of noise in these data. They also suggest that the rate and intensity of wave breaking could be measured by counting and analyzing these events. Such an analysis is beyond the scope of this paper.
Five 20-s-long sound samples recorded under different wind speeds and float depths as noted in each title. In each, (top) the sound spectrogram and (bottom) the time series of sound levels at four frequencies. (a)–(c) We interpret the bursts as signatures of breaking waves. (d),(e) No such signatures are heard when the floats are at depth at similar wind speeds.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
4. Sound level variations
a. Wind speed dependence for different frequencies
Figure 6 shows sound levels at six selected frequencies as a function of wind speed. Each panel shows the measurements from one float (Figs. 6a–g), with the last panel combining measurements from all seven floats (Fig. 6h). Three different wind speed dependencies are seen:
The low-frequency sound (100 Hz) monotonically increases with wind speed over the entire wind speed range.
The intermediate frequencies (1, 5, and 8 kHz) first increase and then decrease with wind speed. The increase at low wind speeds is qualitatively consistent with the observations of Vagle et al. (1990).
The high frequencies (15 and 33 kHz) increase slightly at low winds and then decrease with increasing wind speed. This is consistent with Farmer and Lemon’s (1984) measurements in Queen Charlotte Sound, British Columbia at 14.5 and 25 kHz.
Sound level vs wind speed at six selected frequencies. (a)–(g) Sound measurements from one float as labeled. See colors in the legend for different frequencies. For (e)–(g), the data points are further discriminated by rising wind (ahead of cyclone arrival; circles) and falling wind (after cyclone passage; crosses). (h) Sound measurements from all seven floats except for those recorded in falling wind by floats 60–62. A larger version of (h) is given in Fig. 11.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
Although all floats show the same features, the measurements from floats 60–62 show a wider scatter (Figs. 6e–g). For these floats, the sound levels on a rising wind (dots) are higher than those on a falling wind (crosses). This appears to indicate a decoupling of waves and wind in these storms with the sound levels following the waves rather than the wind. This will be examined in more detail in future studies. In this paper, the sound measurements during the falling wind period measured by floats 60–62 are excluded from further analysis.
b. Spectra for different wind speeds
Figure 7 shows sound level spectra in 5 m s−1 wind speed bins (color coded). Multiple curves of the same color are from different floats in the same wind range. At high frequencies, the spectra from the different floats agree within 2 dB, comparable to the uncertainty in the calibration (appendix A). At low frequencies, differences of up to 5 dB are found. Figure 7 again shows low frequencies increasing with increasing wind speed (blue to red) and high frequencies decreasing with increasing wind speed (red to blue), with a more complex pattern at intermediate frequencies.
Spectra colored by wind speed. Each curve averages all spectra in 5 m s−1 wind speed bins from measurements at depth > 2 m of a single float. Multiple curves of the same color denote observations from multiple floats. Four lines show representative spectral slopes at low (α) and high (β) frequency. Gray box shows the transition frequency (2–4 kHz) between the two slope regions. The dip in sound level near 3 kHz may be an instrumental effect.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
All spectra show a break in slope at ≈3 kHz (bubble radii of ≈1 mm) with higher frequencies having steeper slopes. Surprisingly perhaps, these spectral shapes are similar to those found in Deane and Stokes’s (2002) laboratory observations of breaking waves, and we follow their notation by using α and β for the low- and high-frequency slopes, respectively. Both steepen with increasing wind speed, α from −5 to −10 dB decade−1 and β from −20 to −40 dB decade−1. The breakpoint between these two regimes does not appear to vary with wind speed and is very similar to that found by Deane and Stokes (2002). Deane and Stokes (2002) associate this breakpoint with the Hinze scale, the size of the largest bubbles that can exist in a turbulent flow without being fragmented by the turbulence. This scale is set by the turbulent kinetic energy dissipation rate and the water properties. If this interpretation holds in our data, it implies that Deane and Stokes’s (2002) 10-cm high laboratory breaking waves have the same turbulence levels as the 10-m high breaking waves observed in tropical cyclones. A more direct measurement of the turbulence levels would be necessary to confirm such a remarkable similarity.
c. Low frequencies
Wilson and Makris (2006, 2008) report the 10–40-Hz sound level increasing monotonically with increasing wind speed up to 50 m s−1. Figure 8 shows linear fits to sound levels at 40, 160, 200, and 400 Hz. The fit slopes at all frequencies are similar. However, the sound levels roll off above 30–40 m s−1 at 200 and 400 Hz and above 40 m s−1 at 160 Hz. At 40 Hz our data are in agreement with Wilson and Makris’s (2008) relationship above 30 m s−1. Below 20 m s−1, our measurements are strongly affected by noise. This correspondence supports the validity of both of our datasets and the idea that low-frequency sound levels could be used to estimate the wind speed of tropical cyclones (Wilson and Makris 2008).
Low-frequency sound level vs wind speed. The gray dots show measurements at depth > 2 m from all seven floats. The gray circles and bars indicate the mean and standard deviation of data points in 2 m s−1 wind speed bins. The horizontal lines show the background noise levels as in Fig. 3. The thick black lines are the linear fits; the solid sections indicate the wind range used in the fits, and the dashed sections indicate extrapolation. The thin black line in (a) shows the sound–wind relation obtained by Wilson and Makris (2008).
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
d. Multifrequency variations
Scatterplots of sound levels between two frequencies show the wind and frequency dependencies in a different way (Farmer and Lemon 1984). Figure 9 compares the 5- and 20-kHz sound frequencies. Both frequencies first increase and then decrease but with a rolloff that peaks at different wind speeds, about 25 m s−1 at 20 kHz and 30 m s−1 at 5 kHz. The resulting scatterplot has a “snail” shape with the wind speed increasing monotonically along the spiral path. This suggests that a multifrequency analysis could be used to determine wind speed using sound level from these frequencies.
Scatterplot of sound levels at 5 and 20 kHz. The measurements are 1-min gridded measurements from all seven floats. The dots are color coded using wind speed (see colorbar). A snail shape is formed as the sound levels at both frequencies first increase and then decrease with increasing wind speed. Outliners (data points in the circle) are likely due to rainfall events. The dashed line is from the empirically fitted curves at 5 and 20 kHz as shown in Fig. 11.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
The outliers in Fig. 9 (circled) have low wind speed but high noise levels at both 5 and 20 kHz. These are the signatures of rainfall events (Nystuen 2001; Ma and Nystuen 2005). It suggests that broadband sound measurements could distinguish wind and rainfall signatures within tropical storms. At high winds, it is possible that spray droplets, generated by wind and waves, could have an acoustic signature similar to that of rain, further complicating this issue. Nevertheless, wind speed appears to be the dominant factor and we do not address the issue of rainfall further here.
e. Vertical variations
Figure 10 shows the variation in 0.1-, 2-, 8-, and 25-kHz sound levels with depth for six wind speed bins. Because the float is about 1.4 m long with the hydrophone mounted about 0.5 m above its center, some of the increase in sound in the upper meter could be due to the hydrophone breaching the ocean surface, making the interpretation of the sound levels above 1-m depth difficult. From 1 to 2 m, the limited data suggest an increase of about 5 dB for wind speeds above 35 m s−1. At deeper depths and/or lower wind speeds, there is no attenuation of sound with depth. The near lack of depth dependence justifies the compositing of all data independent of depth in the previous analyses and has important implications for the distribution of bubble clouds (section 5).
Vertical variation of sound levels at four selected frequencies. Each panel shows measurements from all floats falling into 5 m s−1 wind speed bins as noted in each title. Multiple depth scales, separated by horizontal gray lines, are used to highlight the near-surface region. Vertical lines and bars show the average and one standard deviation in each depth range.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
f. Empirical wind–sound relationships
Sound level vs wind speed at nine selected frequencies. Data points are the combined measurements of all seven floats (as in Fig. 6h). For each frequency, an empirically fitted curve is obtained following the description in appendix B. The empirical relation between wind speed and the 8-kHz sound level is shown as a solid bold curve (Vagle et al. 1990) and extrapolated to the high wind domain (dashed line).
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
Wilson and Makris (2006) model the sound level as due to a surface source attenuated by a bubble layer of specified absorption and thickness. As discussed below, their model is simplified, making physical interpretation of such parameters difficult. Furthermore, without additional measurements it is nearly impossible for us to separate the expected strong wind dependences of both generation and absorption. Instead, we present empirical fits to our sound measurements (appendix B; Fig. 11) in the hope that other researchers may find the method useful to interpret ocean acoustic data.
5. Discussion
These data show both the spectrum of underwater ambient sound at very high wind speeds and its distribution with depth. An understanding of the spectrum requires detailed modeling of wave breaking, bubbles, and acoustics, for example, Deane and Stokes (2010), which is beyond the scope of this paper. However, the lack of depth dependence in the observed sound fields and the measured vertical velocities has important consequences for the distribution of bubbles. Figure 12a shows a simple model of bubble and sound distribution near the ocean surface (Farmer and Lemon 1984; Wilson and Makris 2006). Sound is generated at the ocean surface and attenuated in an underlying layer of bubbles. Below this layer, the sound level is uniform. Using this model, our observations imply that the layer of bubbles affecting our range of frequencies measured is less than 2 m thick even under hurricane winds. This contrasts with the upward-looking ADCP measurements (Wang et al. 2011) of bubble clouds extending to greater than 20 m at wind speeds of 41 m s−1 in Hurricane Ivan, as well as oxygen and conductivity measurements implying gas injection by bubbles (D’Asaro and McNeil 2007) at 10 m in Hurricane Frances.
Conceptual models of the upper-ocean bubble and sound distribution. (a) A uniform surface sound source is attenuated by a near-surface layer of bubbles. Below this layer, the sound level is uniform. (b) Sound is generated by newly created bubbles on the surface of bubble clouds. Buoyant big bubbles (gray) are trapped near the surface, attenuating the sound at their resonant frequencies very close to the source. Neutrally buoyant small bubbles (red) form a more uniform surface layer and are carried downward in downwelling plumes where they dissolve. Sound at the resonant frequencies for these bubbles attenuates more slowly with depth as shown in the insert.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
The geometry of sound generation is more complex than in Fig. 12a. Even at our highest wind speeds, sound generation is highly intermittent, apparently generated by breaking waves. Deane and Stokes (2010) suggest that only a small region of the wave actively radiates to the underlying ocean, with much of the sound produced during breaking being absorbed close to the source. These highly localized sources are illustrated (sources) in Fig. 12b. The geometry of bubble clouds is also more complex than in Fig. 12a. Bubble clouds are shaped by the combination of ocean velocities and the upward buoyant motion of the bubbles and thus vary greatly depending on the size of bubble. “Big” bubbles (gray in Fig. 12b) have rise velocities much larger than those of the water and eventually rise to the surface and burst. “Small” bubbles (red in Fig. 12b) have rise velocities much smaller than those of the water and can be carried away from the surface by downward-going currents, forming plumes of bubbles extending from the surface as sketched in Fig. 12b. Such plumes, observed in numerous sonar measurements (Thorpe 1992; Vagle et al. 2010), commonly extend to 10-m depth for 10 m s−1 winds. These bubbles compress and are absorbed at depth and therefore only exist in regions of active downwelling. Thus, although small bubbles exist at depth, many regions at the same depth do not have any bubbles. Sound absorption by the big bubbles is certainly limited to the surface, while that by small bubbles should extend more deeply (Fig. 12b, right). However, the concentration of small bubbles into plumes could allow sound to travel from the surface sources to depth without being absorbed by the bubbles, for example, downward and to the left in Fig. 12b. Thus, the amount of absorption depends both on the average bubble profile and its geometry.
We explore the transition between big and small bubble behavior for winds greater than 35 m s−1, using a simple Lagrangian model of the bubble depth distribution and G. B. Deane's (2013, personal communication) compilation of bubble rise velocities as a function of bubble size (Fig. 13 and appendix C). Since our floats are Lagrangian, their trajectories directly measure the exchange between the near surface and any other depth. We synthesize buoyant bubble trajectories by adding a fixed upward velocity to the measured float trajectories. We choose all float trajectory segments (26) that start at 1-m depth and end at 1-m depth; trajectories longer than 1000 s are cut off at 1000-s length (Fig. 14a, black). We create 26 bubble trajectories from these, starting them at 1 m (a reasonable guess of the bubble injection depth) and ending them at the end of the float trajectory or when the bubble hits the surface (Fig. 14a, green and red). The float trajectories are nearly uniformly distributed in the upper 15 m (Fig. 14b), as is expected if the floats are Lagrangian. The bubble trajectories are increasingly concentrated toward the surface with increasing upward velocity. Bubbles with vertical velocities less than 0.01 m s−1 (radius < 80 μm, resonant at 40 kHz) are distributed similarly to the floats; these are small bubbles. Bubbles with vertical velocities greater than 0.12 m s−1 (radius > 400 μm, resonant at 8 kHz) are shallower than 3 m more than 90% of the time; these are big bubbles. These values are similar to those expected by comparing the bubble rise velocity to the statistics of measured vertical velocity (Fig. 13).
Bubbles and water vertical velocities. Rise velocity (Deane 2013) for a spherical bubble as a function of radius (black line, bottom axis) and resonant frequency of the bubble (top axis). Shading indicates the frequency range (40 Hz–50 kHz) of our measurements. The green lines indicate the frequencies (200 and 300 kHz) used to study the bubble layer depth by Vagle et al. (2010) and Wang et al. (2011). Probability distribution of vertical velocities in the upper 10 m (red lines) with steps in line thickness indicating selected percentiles, for example, 90% of the velocity measurements are smaller than W90. Blue line indicates the bubble size with a rising velocity larger than any measured vertical velocity.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
Results of a simple bubble trajectory model. (a) All float trajectories for winds greater than 35 m s−1 starting at 1-m depth and ending at 1-m depth (black). Synthetic bubble trajectories created by adding a 0.1 m s−1 upward velocity to the float trajectories, terminating them when the bubble hits the surface (red), and all the same, but for 0.03 m s−1 (green). (b) Cumulative probability distributions of float (black) and bubble (colored) trajectories for various upward velocities as labeled.
Citation: Journal of Physical Oceanography 44, 10; 10.1175/JPO-D-14-0040.1
We explore the geometry of the bubble clouds using a similar model. We classify all float trajectories passing through 5-m depth into those that have come downward from shallower than 2 m (bubble), those that have come upward from deeper than 10 m (clear), and those that have remained between 2 and 10 m (weak). For winds greater than 35 m s−1, these groups contain 34%, 38%, and 32% of the trajectories, respectively, implying that about ⅓ of the water is bubble free, ⅓ contains fresh bubbles, and ⅓ is intermediate. This is probably an overestimate of the bubble case; D’Asaro and McNeil (2007) find that not all downward-going trajectories result in gas injection. Nevertheless, these estimates confirm that the bubble layer at 5 m is likely to be highly intermittent, with a significant fraction of its area bubble free.
We now address the differences in various observations of bubble cloud depth at wind speeds greater than 35 m s−1. Wang et al. (2011), using 300-kHz backscatter, observed small bubbles extending to 20 m, consistent with the bubble rise rate and our measured vertical velocity. D’Asaro and McNeil (2007) find gas injection at 10-m depth; this must be mostly due to small bubbles. The acoustic frequencies measured here have resonant bubbles that are big or intermediate in size. At frequencies below 8 kHz, the resonant bubbles are all big and should be confined to the upper few meters. This is consistent with the lack of acoustic attenuation below a few meters. However, attenuation by nonresonant small bubbles is also possible (Commander and Prosperetti 1989). The lack of attenuation clearly constrains the number of such bubbles, but a detailed evaluation of this effect is beyond the scope of this paper. At higher frequencies, our analysis is inconclusive. For 25 kHz (yellow in Fig. 10), the upward bubble velocity of 0.02 m s−1 results in 50% of the modeled bubbles shallower than 6 m and 98% shallower than 17 m in our bubble model. This alone does not exclude sound absorption by the resonant ≈100 μm bubbles; it is likely that our bubble model, which ignores bubble dissolution, is insufficient. Quantitative and geometrically realistic modeling of the interaction of bubbles, turbulence, and sound, perhaps following the detailed simulations of Liang et al. (2011), will be necessary to address these issues.
6. Summary
Underwater ambient sound levels were measured at seven locations in three tropical cyclones for frequencies 40 Hz–50 kHz and from the sea surface to 50-m depth for wind speeds up to 45 m s−1. Measurements were made on water-following Lagrangian floats that also measured the vertical velocities of the water.
Our major results are as follows:
Low frequency (<200 Hz) sound increases with wind speed. Higher-frequency sound increases at low wind speeds, but decreases at higher wind speeds. The wind speed of maximum sound level (the rolloff point on the sound–wind curves) increases with decreasing frequency.
Spectra of sound level show a break in slope at 2–3 kHz at all wind speeds, with flatter slopes at −5 to −10 dB decade−1 with increasing wind speed for lower frequencies, and −20 to −40 dB decade−1 with increasing wind speed for higher frequencies.
Empirical fits to the dependence of sound on wind speed and frequency are found. These may be useful for measuring high wind speeds from sound levels.
The sound levels are nearly constant with depth from 2 to 10 m at all frequencies, with some increase between 1 and 2 m at the highest frequencies and wind speeds that may represent the hydrophone breaching the surface.
The weak vertical variation in sound level implies that the bubble clouds that both generate and absorb sound in this frequency range are mostly confined to the upper 1–2 m even at the highest wind speeds. At wind speeds greater than 35 m s−1, a simple model of bubble trajectories based on the measured float trajectories finds that bubbles larger than 400 μm (rise velocity 0.12 m s−1, resonant at 8 kHz) are confined to the top few meters of the ocean by their rise velocity alone. The rise velocity of bubbles smaller than 80 μm (rise velocity 0.01 m s−1, resonant at 40 kHz) has only a small effect on their distribution in the upper 10 m. Bubbles resonant at 25 kHz can easily be advected into the upper 10 m; this alone cannot explain the observed lack of acoustic attenuation at this frequency.
Acknowledgments
This work was supported by National Science Foundation (OCE0549887) and the Office of Naval Research through the Impact of Typhoons on the Ocean in the Pacific (ITOP) project (N00014-08-1-0577). We are grateful to the people and aircraft of the 53rd Air Force Reserve squadron, Hurricane Hunters. Discussions with R. Harcourt and J. H. Liang were very helpful. Two anonymous reviewers significantly focused and clarified the manuscript.
APPENDIX A
Hydrophone Intercalibration
Seven Lagrangian floats with hydrophones were mounted on a rigid stand and lowered into the water off the University of Washington Applied Physics Laboratory (APL-UW) research vessel (R/V) Robertson on 13 July 2009. An acoustic rain gauge (ARG) (Ma et al. 2005) was mounted on the same cluster to serve as an additional reference. Sound levels were varied by up to 20 dB by moving the floats vertically from 1 to 25 m and by spraying water on the surface above the floats using the boat’s fire hose. Additional ambient noise was generated by the boat and nearby shipping traffic. The sound levels at the different instruments differed by 1–2-dB RMS over the entire frequency range.
A dip in spectral level of about 2 dB near 3 kHz appears both in these calibration data and in the tropical cyclone data (Fig. 6). We suspect that this represents a variation in the sensitivity of the combined float/hydrophone system of unknown origin.
APPENDIX B
Empirical Relation between Wind and Sound
Parameters in the empirical relation between sound and wind [Eq. (B1)] by frequency (kHz). These parameters are determined by optimized least squares fitting.
APPENDIX C
Bubble Rise Speed
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