• Baschek, B., 2003: Air–sea gas exchange in tidal fronts. Ph.D. thesis, University of Victoria, 156 pp.

  • Baschek, B., 2005: Wave–current interaction in tidal fronts. Rogue Waves: Proc. 14th ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 131–138.

    • Search Google Scholar
    • Export Citation
  • Baschek, B., , Farmer D. M. , , and Garrett C. , 2006: Tidal fronts and their role in air–sea gas exchange. J. Mar. Res., 64 , 483515.

  • Fan, L-S., , and Tsuchiya K. , 1990: Bubble Wake Dynamics in Liquids and Liquid–Solid Suspensions. Butterworth-Heinemann, 384 pp.

  • Farmer, D. M., , and Li M. , 1995: Patterns of bubble clouds organized by Langmuir circulation. J. Phys. Oceanogr., 25 , 14261440.

  • Farmer, D. M., , Vagle S. , , and Booth A. D. , 1998: A free-flooding acoustical resonator for measurement of bubble size distributions. J. Atmos. Oceanic Technol., 15 , 11211146.

    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., , Pawlowicz R. , , and Jiang R. , 2002: Tilting separation flows: A mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans, 36 , 4358.

    • Search Google Scholar
    • Export Citation
  • Gargett, A., , and Moum J. , 1995: Mixing efficiencies in turbulent tidal fronts: Results from direct and indirect measurements of density flux. J. Phys. Oceanogr., 25 , 25832608.

    • Search Google Scholar
    • Export Citation
  • Hwang, P. A., , and Teague W. J. , 2000: Low-frequency resonant scattering of bubble clouds. J. Atmos. Oceanic Technol., 17 , 847853.

  • Medwin, H., 1977: In situ acoustic measurements of bubble populations in coastal ocean waters. J. Geophys. Res., 75 , 599611.

  • Minnaert, M., 1933: On musical air-bubbles and the sound of running water. Philos. Mag., 16 , 235248.

  • Thorpe, S. A., 1982: On the clouds of bubbles formed by breaking wind-waves in deep water, and their role in air–sea gas transfer. Philos. Trans. Roy. Soc. London, A304 , 155210.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , and Stubbs A. R. , 1979: Bubbles in a freshwater lake. Nature, 279 , 403405.

  • Woolf, D., , and Thorpe S. , 1991: Bubbles and the air–sea exchange of gases in near-saturation conditions. J. Mar. Res., 49 , 435466.

  • View in gallery

    The Fraser Estuary in British Columbia, Canada. The small map shows the location of the tidal front (dashed line) at Boundary Pass and the measurement transect across the sill (solid line).

  • View in gallery

    (a) Vertical current. (b) Acoustic backscatter intensity measured with a 100-kHz echo sounder at Boundary Pass on 24 Sep 2000. High intensity indicates seafloor (A) and gas bubbles (B). (c) The resonance radius of the sounder is marked by the thick black curve. The dashed lines show the “path” of the injected bubbles for w = −0.5 m s−1, as calculated with the bubble model.

  • View in gallery

    Wave breaking in the convergence zone of the tidal front at Boundary Pass.

  • View in gallery

    (a) Rise speed of dirty and clean gas bubbles in seawater (Fan and Tsuchiya 1990). (b) Resonance radius of a 100-kHz echo sounder (solid line) and “bubble paths” (dashed lines) for gas bubbles of different initial radii and corresponding vertical current speed wb0 = −w. (c) Relationship between bubble depth and the minimal vertical current that is required to explain the presence of bubbles at that depth.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 0 0 0
PDF Downloads 0 0 0

Gas Bubbles as Oceanographic Tracers

View More View Less
  • 1 University of California, Los Angeles, Los Angeles, California
  • 2 Graduate School of Oceanography, University of Rhode Island, Narragansett, Rhode Island
© Get Permissions
Full access

Abstract

Air bubbles can be used as oceanographic tracers that indicate the strength of a downwelling current by which they are subducted. In a tidal front in the Fraser Estuary, British Columbia, Canada, vertical currents of up to 0.70 m s−1 subduct bubbles to depths of more than 160 m. Echo sounder measurements are compared with simultaneous ADCP current measurements and are interpreted with a bubble model by S. A. Thorpe, yielding an estimate of the vertical current that carries the bubbles to the depth of measurement.

Corresponding author address: Burkard Baschek, Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, CA 90095. Email: baschek@atmos.ucla.edu

Abstract

Air bubbles can be used as oceanographic tracers that indicate the strength of a downwelling current by which they are subducted. In a tidal front in the Fraser Estuary, British Columbia, Canada, vertical currents of up to 0.70 m s−1 subduct bubbles to depths of more than 160 m. Echo sounder measurements are compared with simultaneous ADCP current measurements and are interpreted with a bubble model by S. A. Thorpe, yielding an estimate of the vertical current that carries the bubbles to the depth of measurement.

Corresponding author address: Burkard Baschek, Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, CA 90095. Email: baschek@atmos.ucla.edu

1. Introduction

Air bubbles are injected into the surface layer of the ocean by breaking waves. Vertical currents associated with wave motion or Langmuir cells can carry the bubbles to depths of more than twice the wave height, or 10–15 m (Thorpe and Stubbs 1979; Thorpe 1982; Farmer and Li 1995). A similar, but more extreme, phenomenon has been observed in tidal fronts, where gas bubbles can reach 160-m depth (Farmer et al. 2002; Baschek et al. 2006). Gas bubbles are active tracers with typical rise speeds of 0.001–0.3 m s−1 and can therefore be used as indicators of the strength of the vertical currents in these environments.

In this note, we present a new way of looking at bubbles by combining their physical and chemical properties with acoustical measurements to compute bubble behavior in this environment. Observations of gas bubbles in a tidal front in the Fraser Estuary, British Columbia, Canada (Fig. 1), are interpreted with a bubble model (Thorpe 1982) that includes dissolution and compression due to changes in hydrostatic pressure. The strength of the vertical current that carries the bubbles to the measurement depth is estimated. The results are compared with simultaneous acoustic Doppler current profiler (ADCP) measurements along cross-frontal transects.

2. Observations

Measurements of gas bubbles and currents were taken in a tidal front in the Fraser Estuary at Boundary Pass (48.78°N, 123.0°W) in September 2000 on research vessel CCGS Vector. A 100-kHz Biosonics echo sounder measured the acoustic backscatter intensity of the water column. The transducer was mounted at a depth of 2 m. The receiver bandwidth was set to 5 kHz, the transmission interval to 0.5 s, the pulse width to 0.3 ms, and the gain to 18 dB. A 150-kHz ADCP Workhorse from RDI was mounted on a strut at the side of the ship at a depth of 1 m. The instrument has a bandwidth of 39 kHz and a beam angle of 20°. Measurements were taken every 1 s, and the data were then averaged to create 10-s ensembles. The instrument operated in bottom-tracking mode, and the bin size was 4 m. The first useful measurement depth is at 5 m. The small surface wave motion in these protected waters and the high vertical current component allowed stable vertical current measurement using the standard ADCP four-beam solution. A comparison of both ADCP beam pairs showed that the results were accurate in spite of strong horizontal current gradients (Baschek 2003). The ship’s position and heading were provided by a differential GPS receiver and a flux gate compass.

An example of the flow field and acoustical backscatter intensity in the tidal front is shown in Fig. 2b. A sharp sill with a mean slope of 30° rises from 200- to 60-m water depth. An energetic tidal front is formed during flood tide over the sill crest by a hydraulically controlled sill flow (Baschek et al. 2006). Even at low wind speeds, the associated surface convergence zone causes wave breaking and the injection of gas bubbles due to wave–current interaction (Baschek 2005; Fig. 3). These bubbles are drawn down by a strong current with a vertical component in the range of w = −0.3 m s−1 to w = −0.7 m s−1 (Fig. 2a) and were detected by echo sounder measurements to depths of more than 160 m. The downwelling flow is subject to shear instability and overturning, and the measurements are sometimes blocked by dense bubble clouds.

The echo sounder image shows the acoustic backscatter intensity of the water column. Very strong backscatter indicates areas of bubble entrainment, since the acoustical cross section of a bubble is about 1000 times its geometrical one (Medwin 1977). We have verified the presence of bubbles in the downwelling regions of tidal fronts with independent acoustical resonator measurements (Farmer et al. 1998) within the upper 50 m of the water column (Baschek 2003). It can therefore be assumed that most of the high backscatter intensity in the water column is due to gas bubbles and not zooplankton, fish, or turbulence.

The echo sounder measures a signal that is the product of the bubble size distribution at a certain depth and the acoustic return of each bubble. Because this acoustic return is dominated by a very strong resonant peak of bubbles with a radius close to the resonance radius,
i1520-0426-27-1-241-e1
(Minnaert 1933), we can assume that the echo sounder primarily detects bubbles of that size; p is the hydrostatic pressure and f the transmitting frequency of the echo sounder. For our calculations we use a mean density of the subducting water mass of = 1024 kg m−3 and a polytropic coefficient of ν = 1.4 for air bubbles (Medwin 1977; Hwang and Teague 2000). The resonance radius rres is plotted in Fig. 2c for f = 100 kHz.

3. Results

After a bubble is injected into the ocean, it rises back to the sea surface because of its buoyancy or is drawn down by the vertical current. Its gas content and radius respond to the effect of hydrostatic pressure and dissolution. A model of this gas bubble behavior by Thorpe (1982) is used to interpret the bubble measurements (see also Baschek et al. 2006). It describes the temporal change of bubble radius r and number of moles n of the gases O2, N2, Ar, and CO2 along the “path” of a bubble, which is determined by its rise speed wb, the vertical velocity w, and the turbulent vertical velocity wturb:
i1520-0426-27-1-241-e2
i1520-0426-27-1-241-e3
i1520-0426-27-1-241-e4
Respectively, Dj, Sj, and Nuj are the diffusivity, solubility, and Nusselt number of a gas j (Woolf and Thorpe 1991); R, T, g, and γ are the universal gas constant, temperature, gravitational acceleration, and surface tension coefficient; P is the gas pressure inside the bubble and Pw the gas pressure in the water far away from the bubble, which is determined by the gas saturation. The three coupled ordinary differential equations [(2)(4)] were solved in MATLAB with an explicit Runge–Kutta formula.

The following calculations were carried out for different bubbles with initial radii r0 using a representative vertical velocity of w = −0.5 m s−1 below the injection depth of 0.1 m, a temperature of 10°C, and a gas saturation of 100% for all gases. The resulting bubble “paths” are shown in Fig. 2c (dashed lines). They intersect the resonant radius curve (solid line), which indicates the size of the bubbles that are detected by the echo sounder at a given depth. Subject to the limitations of our measurements, this allows the estimation of the radius r0 of these bubbles at the time of injection. The calculation is carried out backward in time, calculating the gas exchange across the bubble surface while considering the bubble’s rise speed (Fig. 4a) relative to the surrounding fluid at each step. The results of this calculation, shown in the figure as the intersection of the dashed curves with the surface, represents a conservative value, as the nominal vertical velocity of w = −0.5 m s−1 used in the calculations is closer to the upper bound of our measurements. The bubbles measured at 160-m depth would have had a radius of r0 = 1.7 mm at the sea surface. For a velocity of w = −0.4 m s−1, the initial radius would have been r0 = 2.3 mm, and for w = −0.3 m s−1 it would have been r0 = 4.4 mm.

To test the sensitivity of the model with respect to the parameters used we calculated the bubble radius r0 at the surface by changing one parameter at a time and comparing the results to the reference run with w = −0.5 m s−1, T = 10°C, and a gas saturation of 100%. A reduction of the diffusivities of all gases by 90%, as it may be caused by surfactants, would result in a decrease of r0 by 9%; a reduction of the diffusivities by 50% would reduce r0 by 32%. The effect of temperature variation is minimal. The temperature difference within the subducting water mass that carries the bubbles downward is <0.5°C, as indicated by the CTD measurements, which corresponds to a decrease of r0 by only 0.5%. A change of the polytropic coefficient (1) to the smallest possible value of ν = 1.0 causes a decrease of r0 by 6%. The effect of turbulence was estimated by multiplying a random walk function (normal distribution, mean = 0, standard deviation = 1) with the typical turbulent vertical velocity of 0.05 m s−1 and displacement of 3 m measured in tidal fronts (Gargett and Moum 1995) and adding it to the vertical velocity at each time step (2). The average of several model runs yields a reduction of r0 by 2%. Increasing the gas saturation by 2% to then 102% for all gases has an effect on r0 of <1%.

The model can also be used to estimate the minimal vertical velocity that is necessary to draw down a bubble from the sea surface to a certain depth where it is detected by the echo sounder. Bubbles that have a rise speed wb0 that is greater than the vertical current w return to the sea surface; bubbles with a rise speed of |wb0| ≤ |w| are drawn down by the current. The largest bubble that is drawn down reaches the greatest depth. Its radius corresponds to a rise speed of wb0 = −w since the rise speed of dirty bubbles steadily increases with radius (Fig. 4a). This means that the minimal vertical current required to explain the presence of a bubble of radius rres at the depth of measurement is equal to the initial rise speed wb0 of that bubble at its injection depth.

The path of this largest bubble is shown in Fig. 4b for different velocities and an injection depth of 0.1 m. The bubble rise speed is shown in Fig. 4a, and the relationship between minimal vertical current and depth is given in Fig. 4c, showing that bubbles at 160-m depth are drawn down by a vertical current of at least −0.27 m s−1. This is consistent with the current measurements in the tidal front showing values between −0.3 and −0.7 m s−1.

Although simplifying assumptions are required to overcome our measurement limitations in this complicated environment, our model analysis provides a first-order estimate of the bubble radius at the injection site that can be used to infer the vertical velocities of the front near the surface. Additional measurements of bubble size distribution and accurate vertical velocities from the sea surface downward would help to verify the model results.

Acknowledgments

We are grateful for the support of the officers and crew of research vessel CCGS Vector. Many thanks to the Ocean Acoustics Group at the Institute of Ocean Sciences, Canada, for their assistance during the experiments. The work formed a part of research projects carried out with the support of the Office of Naval Research.

REFERENCES

  • Baschek, B., 2003: Air–sea gas exchange in tidal fronts. Ph.D. thesis, University of Victoria, 156 pp.

  • Baschek, B., 2005: Wave–current interaction in tidal fronts. Rogue Waves: Proc. 14th ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 131–138.

    • Search Google Scholar
    • Export Citation
  • Baschek, B., , Farmer D. M. , , and Garrett C. , 2006: Tidal fronts and their role in air–sea gas exchange. J. Mar. Res., 64 , 483515.

  • Fan, L-S., , and Tsuchiya K. , 1990: Bubble Wake Dynamics in Liquids and Liquid–Solid Suspensions. Butterworth-Heinemann, 384 pp.

  • Farmer, D. M., , and Li M. , 1995: Patterns of bubble clouds organized by Langmuir circulation. J. Phys. Oceanogr., 25 , 14261440.

  • Farmer, D. M., , Vagle S. , , and Booth A. D. , 1998: A free-flooding acoustical resonator for measurement of bubble size distributions. J. Atmos. Oceanic Technol., 15 , 11211146.

    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., , Pawlowicz R. , , and Jiang R. , 2002: Tilting separation flows: A mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans, 36 , 4358.

    • Search Google Scholar
    • Export Citation
  • Gargett, A., , and Moum J. , 1995: Mixing efficiencies in turbulent tidal fronts: Results from direct and indirect measurements of density flux. J. Phys. Oceanogr., 25 , 25832608.

    • Search Google Scholar
    • Export Citation
  • Hwang, P. A., , and Teague W. J. , 2000: Low-frequency resonant scattering of bubble clouds. J. Atmos. Oceanic Technol., 17 , 847853.

  • Medwin, H., 1977: In situ acoustic measurements of bubble populations in coastal ocean waters. J. Geophys. Res., 75 , 599611.

  • Minnaert, M., 1933: On musical air-bubbles and the sound of running water. Philos. Mag., 16 , 235248.

  • Thorpe, S. A., 1982: On the clouds of bubbles formed by breaking wind-waves in deep water, and their role in air–sea gas transfer. Philos. Trans. Roy. Soc. London, A304 , 155210.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , and Stubbs A. R. , 1979: Bubbles in a freshwater lake. Nature, 279 , 403405.

  • Woolf, D., , and Thorpe S. , 1991: Bubbles and the air–sea exchange of gases in near-saturation conditions. J. Mar. Res., 49 , 435466.

Fig. 1.
Fig. 1.

The Fraser Estuary in British Columbia, Canada. The small map shows the location of the tidal front (dashed line) at Boundary Pass and the measurement transect across the sill (solid line).

Citation: Journal of Atmospheric and Oceanic Technology 27, 1; 10.1175/2009JTECHO688.1

Fig. 2.
Fig. 2.

(a) Vertical current. (b) Acoustic backscatter intensity measured with a 100-kHz echo sounder at Boundary Pass on 24 Sep 2000. High intensity indicates seafloor (A) and gas bubbles (B). (c) The resonance radius of the sounder is marked by the thick black curve. The dashed lines show the “path” of the injected bubbles for w = −0.5 m s−1, as calculated with the bubble model.

Citation: Journal of Atmospheric and Oceanic Technology 27, 1; 10.1175/2009JTECHO688.1

Fig. 3.
Fig. 3.

Wave breaking in the convergence zone of the tidal front at Boundary Pass.

Citation: Journal of Atmospheric and Oceanic Technology 27, 1; 10.1175/2009JTECHO688.1

Fig. 4.
Fig. 4.

(a) Rise speed of dirty and clean gas bubbles in seawater (Fan and Tsuchiya 1990). (b) Resonance radius of a 100-kHz echo sounder (solid line) and “bubble paths” (dashed lines) for gas bubbles of different initial radii and corresponding vertical current speed wb0 = −w. (c) Relationship between bubble depth and the minimal vertical current that is required to explain the presence of bubbles at that depth.

Citation: Journal of Atmospheric and Oceanic Technology 27, 1; 10.1175/2009JTECHO688.1

Save