XVI.<i>On musical air-bubbles and the sounds of running water</i>

Minnaert, M. G. J.

doi:10.1080/14786443309462277

Cited by 1,169 publications

(650 citation statements)

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“…(28) and (29). The resonant frequency ω 0 in Equation (33) is also known as the Minnaert frequency [51]. With the material properties summarized in Table 1, the relation ω 0 R E ≈ 20.1 m/s holds.…”

Section: The Linear Resonance Frequency Of the Bubblementioning

confidence: 99%

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Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia and his coworkers [1] revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that R E ω is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller-Miksis equation, are presented. It is shown that the validity range of Behnia's condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately 5 µm.

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Section: The Linear Resonance Frequency Of the Bubblementioning

confidence: 99%

“…When both the damping µ L and the surface tension σ are taken into account, its evolution is shown by the black line. The undamped eigenfrequency is shown by the blue line, and the red line shows when both µ L and σ is neglected (Minnaert frequency [51]). …”

Section: The Linear Resonance Frequency Of the Bubblementioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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“…Injected bubbles are also important in underwater sound absorption and scattering and in ambient sound production [Minnaert, 1933;Wenz, 1962;Kerman, 1984]. In addition, bubbles that burst at the ocean surface produce aerosol particles that are important for sea-to-air transport of salt, organic substances, microorganisms, and electric charge [e.g., Blanchard and Woodcock, 1957;Monahan, 1986;Blanchard and $yzdek, 1988].…”

Section: Introductionmentioning

confidence: 99%

Bubble shattering: Differences in bubble formation in fresh water and seawater

Slauenwhite¹,

Johnson²

1999

J. Geophys. Res.

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Abstract. Breaking waves result in very different populations of bubbles in fresh water and seawater. The differences in sizes and numbers of bubbles in the two media cause significant differences in many natural processes including gas transfer and generation of aerosols as well as affect sound and light propagation and ambient sound production. Observed differences in bubble populations in seawater and fresh water have in the past been attributed to coalescence inhibition in seawater, but bubble-shattering studies described here suggest that other factors may be important. When air bubbles are expanded through an orifice at constant pressure drop, they can be made to shatter into clouds of smaller bubbles. We report here measurements showing that the number and size distribution of resulting populations depend on the physical and chemical characteristics of the water samples. In particular, bubbles were found to break up into 4-5 times more small bubbles in seawater than in fresh water. The number of bubbles produced in shattering was found to be a function of salt concentration but was especially sensitive to the types of ions present. In addition, medium from the marine diatom Phaeodactylum tricornutum was found to further double production numbers, and a decrease in temperature from 20øC to 3øC was found to increase bubble production in seawater by nearly 50%. These effects appear to be separate from coalescence inhibition, the factor usually cited for differences in bubble populations in fresh water and seawater.

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“…The presence of gas complicates this relationship by introducing energy losses associated with resonance of interstitial gas bubbles Hampton, 1980a and1980b). The acoustic effects of gas bubbles in liquids was first addressed by Minnaert (1933), who developed a fundamental relationship describing bubble pulsation on the basis of energy considerations. Hampton (1980a and1980b) extended this theory by modifying the equations to fit a gassy, unconsolidated sediment case.…”

Section: Compressional Wave Dispersion and Attenuationmentioning

confidence: 99%

Compressional Wave Character in Gassy, Near‐Surface Sediments in Southern Louisiana Determined from Variable Frequency Cross‐Well, Borehole Logging, and Surface Seismic Measurements

Thompson¹,

McGinnis²,

Wilkey³

et al. 1995

Symposium on the Application of Geophysics to Engineering and Environmental Problems 1995

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DISCLAIMERThe submitted manuscript has been authored by a contractor of the U.S. Government under contract No. W-31-1WENG-38. Accordingly, the U. S. Government retains a nonexclusive, royalty.free licensn to pvblish or reproduce the published form of this contribution. or allow others to do so, for U. S. Government purposes.This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recorn- ABSTRACTVelocity and attenuation data were used to test theoretical equations describing the frequency dependence of compressional wave velocity and attenuation through gas-rich sediments in coastal Louisiana. The cross-well data (obtained from a variable-frequency, cross-well seismic experiment using source frequencies of 1, 3, 5, and 7 kHz) were augmented with velocities derived from a nearby seismic refraction station using a lowfrequency (QO Hz) source. Velocities obtained h m the borehole-sonic tool (18 kHz)were not used, because it is unclear at this time what signal phase was being detected. Energy at 1 and 3 kJ3z was successfully transmitted over distances from 3.69 to 30 m; the 5-and 7-lcHz data were obtained only at distances up to 20 m.Velocity tomograms were constructed for one borehole pair and covered a depth interval of 10-50 m. Results from the tomographic modeling indicate that gas-induced low velocities are present to depths of greater than 4-0 m. Analysis of the velocity dispersion suggests that gas-bubble resonance must be greater than 7 kHz, which is above the range of frequencies used in the experiment. Washout of the boreholes at depths above 15 m resulted in a degassed zone containing velocities higher than those indicated in both nearby reitaction and reflection surveys. Velocity and attenuation information were obtained for a low-velocity zone centered at a depth of approximately 18 m. Measured attenuations of 1.57,2.95, and 3.24 dB/m for the 3-, 5-, and 7-m~ signals, respectively, were modeled along with the velocity data using a silt-clay sediment type, Density and porosity data for the model were obtained from the geophysical logs; the bulk and shear moduli were estimated from published relationships. Modeling results indicate that gas bubbles measuring 1 mm in diameter occupy at least 25% to 35% of the pore space.

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XVI.On musical air-bubbles and the sounds of running water

Cited by 1,169 publications

References 2 publications

Classification of the bifurcation structure of a periodically driven gas bubble

Classification of the bifurcation structure of a periodically driven gas bubble

Bubble shattering: Differences in bubble formation in fresh water and seawater

Compressional Wave Character in Gassy, Near‐Surface Sediments in Southern Louisiana Determined from Variable Frequency Cross‐Well, Borehole Logging, and Surface Seismic Measurements

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