Subsurface Bubble Layer Research Articles

Interaction of a subsurface bubble layer with long internal waves

A two-layer model describing the interaction of a shear bubble layer formed by breaking waves and an underlying potential layer is derived in shallow water approximation. A non-hydrostatic formulation taking into account the entrainment effects in shear flows is proposed. Time and space periodic solutions are found, and some basic problems (the formation of bores and periodic structures from a uniform flow) are numerically solved.

Influence of Internal Wave on the Sound Propagation in the Subsurface Bubble Layer

In the paper the influence of non-linear internal wave on the propagation of acoustic signal in the subsurface ocean layer containing gas bubbles is considered. During interaction with surface waves the internal wave causes its collapse and influences the structure of bubble layer. Inhomogeneous structure of the layer promotes the local speed of sound and intensity of scattering near the ocean surface to modulate by internal wave with slight shift in phase in the direction of its propagation, which agree with recent experimental observations made on the shelf of Japan Sea.

Structure formation in the oceanic subsurface bubble layer by an internal wave field

We model the effects of an internal wave on the structure of the oceanic subsurface bubble layer, generated by breaking surface waves. We consider two situations: when breaking is caused either by a strong sustained wind or by the direct interaction of surface waves with an internal wave. We find that the effects are twofold; bubbles are driven by the internal wave field and the injection of bubbles into the water is enhanced in downwelling areas behind the crests of the internal wave. We use an uncoupled problem formulation, substituting the solution for an internal wave in a two-layer fluid model into the equations describing the bubble dynamics. The latter equations are solved numerically, showing structure formation in the bubble layer for each of the two cases, when one of the aforementioned mechanisms dominates the other.

A hybrid model for the acoustic response of a two-dimensional rough surface to an impulse incident from a refracting medium

A numerical model to calculate the impulse response of a two-dimensional, impenetrable, rough surface directly in the time domain has been recently introduced [J. Acoust. Soc. Am. (2000) 107, 27]. This model is based on wedge diffraction theory and assumes that the half-space containing the source and receiver is homogeneous. In this work, the model is extended to handle media where the index of refraction varies with the distance to the surface by merging the scattering model with a ray-based propagation model. The resulting hybrid model is tested against a Finite-Difference Time-Domain (FDTD) method for the problem of backscattering from a corrugated surface in the presence of a refractive layer. This new model can be applied, for example, to calculate acoustic reverberation from the sea surface in cases where the water mass is inhomogeneous and in the presence of a subsurface bubble layer at low frequencies where dispersion is negligible. It can also be used for atmospheric propagation problems where there is a sound speed gradient overlying rough terrain.

Nonlinear scattering of acoustic waves by natural and artificially generated subsurface bubble layers in sea.

The paper describes nonlinear effects due to a biharmonic acoustic signal scattering from air bubbles in the sea. The results of field experiments in a shallow sea are presented. Two waves radiated at frequencies 30 and 31-37 kHz generated backscattered signals at sum and difference frequencies in a bubble layer. A motorboat propeller was used to generate bubbles with different concentrations at different times, up to the return to the natural subsurface layer. Theoretical consideration is given for these effects. The experimental data are in a reasonably good agreement with theoretical predictions.

On the relative role of sea-surface roughness and bubble plumes in shallow-water propagation in the low-kilohertz region

In the low-kilohertz frequency range, acoustic transmission in shallow water deteriorates as wind speed increases. Although the losses can be attributed to two environmental factors, the rough sea surface and the bubbles produced when breaking- or spilling waves are present, the relative role of each is still uncertain. For simplicity, in terms of an average bubble population, the time- and space-varying assemblage of microbubbles is usually assumed to be uniform in range and referred to as “the subsurface bubble layer.” However the bubble population is range- and depth-dependent. In this article, results of an experiment [Weston et al., Philos. Trans. R. Soc. London, Ser. A 265, 507–606 (1969)] involving fixed source and receivers, and observations during an extended period of time under varying weather conditions are re-examined by exercising a numerical model that allows for the dissection of the problem. Calculations are made at 2- and 4-kHz. It is shown that at these frequencies and at wind speeds capable of generating breaking waves the main mechanism responsible for the excess loss in the shallow-water waveguide is the patchy nature of the subsurface bubble field. Refraction and attenuation within the pockets of high void fraction are minor contributors to the losses.

Enhancement of the total acoustic field due to the coupling effects from a rough sea surface and a bubble layer

At wind speeds higher than a few meters per second, when breaking waves are present, the sea surface roughness is accompanied by an assemblage of microbubbles forming different structures or clouds, varying in range and in time. For simplicity, in terms of an average bubble population, the time and space varying assemblage of microbubbles is often assumed to be uniform and referred to as the subsurface bubble layer. Of fundamental importance is the role that this subsurface bubble layer may play in connection with scattering from a rough air/sea interface. The purpose of this paper is to determine the effect that the rough surface in the presence of this subsurface bubble layer has on the total field at low frequencies. Numerical calculations indicate that at low frequencies the bubble layer shifts the incident angle on the surface to steeper angles. In addition it was found that the enhancement of the total field is a consequence of scattering at the rough surface in the presence of the upper refracting bubble layer. An enhancement of approximately 40 dB with respect to the bubble-free medium was obtained very near the surface for a frequency of 400 Hz, with a nominal grazing angle of 20 deg, and a void fraction at the surface of 3.2×10−5. The enhancement decreases to about 10–15 dB at 10 m below the surface, but is still significant at depth exceeding the bubbly region. For a void fraction at the surface of 3.1×10−6 the enhancement is approximately 5 dB.

Nonlinear acoustic scattering from a gassy poroelastic seabed

A model for difference frequency backscatter from trapped bubbles in sandy sediments was developed. A nonlinear volume scattering coefficient was computed via a technique similar to that of Ostrovsky and Sutin [“Nonlinear sound scattering from subsurface bubble layers,” in Natural Physical Sources of Underwater Sound, edited by B. R. Kerman (Kluwer, Dordrecht, 1993), pp. 363–373], which treats the case of bubbles surrounded by water. Biot’s poroelastic theory is incorporated to model the acoustics of the sediment. Biot fast and slow waves are included by modeling the pore fluid as a superposition of two acoustic fluids with effective densities that differ from the pore fluid’s actual density and account for its confinement within sediment pores. The principle of acoustic reciprocity is employed to develop an expression for the backscattering strength. Model behavior is consistent with expectations, based on the known behavior of bubbles in simpler fluid media.

Nonlinear acoustic interactions in liquids with bubbles and their applications for bubble measurements at sea

It is known that, in comparison with homogeneous media (e.g., water, air), acoustical nonlinearity of a liquid with a small concentration of bubbles can be anomalously high. The influence of bubbles upon nonlinear properties of the medium is often much more significant than the simultaneous change of linear characteristics, such as sound speed. This paper presents a brief review of our investigations of nonlinear acoustic phenomena in bubble clouds, and some results concerning nonlinear acoustic methods of measurements of bubble radii and their distribution in water. (1) The theory of the bubble medium is based on summation of the fields scattered by separate bubbles. The scattered field consists of coherent and noncoherent parts, and the latter can be treated as a nonlinear reverberation signal which takes place at frequencies different from those of the incident acoustic wave: second harmonics in the case of a harmonic primary radiator, and sum- and difference-frequency signals for a bifrequency radiator. The formulas relating these signals to the bubble distribution in the layer have been obtained. (2) To observe nonlinear acoustic effects in a subsurface bubble layer and in sea sediments, two echosounders working at different frequencies were used. The sum- and difference-frequency components were observed in the signals scattered from sediments with bubbles and from the subsurface bubble layer. The theory of such nonlinear scattering is in good agreement with experimental data.

Subsurface bubble layers generated by extremely heavy rainfall

Acoustical evidence for the formation of subsurface bubble layers generated by extremely heavy rainfall will be presented. These bubble layers are associated with the presence of very large raindrops (over 3.4 mm diameter) within the rain, which in turn, tend to be associated with extremely heavy rainfall. The splash physics of very large raindrops include a turbulent downward propagating jet which has been shown to carry bubbles into the underlying water. These raindrops have also been shown to rapidly deepen a rain-induced mixed layer, suggesting that rain can generate a subsurface bubble layer. The bubble populations are measured by predicting the sound field generated at the surface and then measuring the acoustic extinction well below the surface. Vertically integrated bubble population densities equivalent to the bubble field generated by 10-m/s winds are observed. These bubble populations quickly dissipate when the very large raindrops are no longer present in the rain, suggesting that the bubble layer generated by extremely heavy rain is very thin (tens of centimeters at most). [Work sponsored by NSF and ONR.]

Inversion of the underwater sound field to quantify the formation of a subsurface bubble layer.

The underwater sound field can be used to quantify oceanic processes that actively produce sound, including, for example, wind/wave breaking (wind speed) and rainfall. These ‘‘active’’ sound sources are subsequently modified by the acoustic environment. In the case of wave breaking or rainfall, the sound source is located at the ocean surface. One of the principal features of the near‐surface zone in the ocean capable of modifying the sound field is the ambient bubble field. Frequency‐dependent modifications of the underwater sound field during heavy rainfall are observed. Using a rainfall generated sound field as an example, the change in the spectral character of the sound field will be used to quantify the formation and decay of an ambient bubble field. Documentation of the formation of a bubble layer has implications for gas and momentum exchange at the ocean surface by rainfall.

Observation of nonlinear scattering of acoustical waves at a subsurface bubble layer

To observe nonlinear acoustic effects in a subsurface bubble layer, two echo sounders working at different frequencies were used. The experiments were performed in the shallow area of the southern part of the Baltic Sea aboard the research vessel ‘‘Oceania.’’ Two echo sounders were run at 30 and 37 kHz; each had a power of about 0.3 kW. The depth of the echo sounders was about 15 m and the intensity of the acoustic signal in the subsurface bubble layer was enough to observe nonlinear effects. The sum and difference frequency components in the spectra of the scattered signal were determined. A theory of such a nonlinear scattering, based on summarizing the signals scattered by separate bubbles, was developed. It was shown that the sum frequency component was due to a noncoherent reverberation in the bubble layer and the difference frequency component was coherent. This component was generated in the process of primary wave propagation and can be received after sea surface reflection. Experimental and theoretical results have shown that the nonlinear scattering can be used to determine bubble density at sea. [Work was supported by ONR.]

Coherent and incoherent scattering by oceanic bubbles

A substantial amount of research on acoustic scattering by underwater bubbles is based on the theory of incoherent scattering. More recent work, devoted to much denser bubble assemblies, has instead used effective-media formulations that presuppose coherent effects. Here the mutual relationship between the two approaches is elucidated. It is shown that, underlying the incoherent results, is a WKB approximate solution of the effective equations. As an application, the scattering by tenuous subsurface bubble layers and acoustical bubble counting techniques are examined. Significant differences with previous results are found.

The underwater sound generated by heavy rainfall

The underwater acoustic signature of heavy rainfall is very different from that of light rainfall. During heavy rainfall sound levels are observed to rise with increasing rainfall rate at all frequencies monitored (4–21 kHz) and the 15-kHz spectral peak observed during light rainfall is absent. The sound levels are most highly correlated (r≊0.8) with heavy rainfall rate for frequencies less than 10 kHz. Lower correlations between sound levels and heavy rainfall rate were observed for frequencies above 10 kHz under several different conditions. When wind speed exceeds 10 m/s, wave breaking mixes bubbles downward and creates a layer of bubbles. This bubble layer attenuates subsequent surface-generated sound (from the raindrop splashes) for frequencies above 10 kHz. Extremely heavy rainfall (total rainfall above 150 mm/h) also generates a subsurface bubble layer. This rainfall-generated bubble layer is evidence of rainfall-induced turbulent mixing of the ocean surface layer and has implications for air/sea exchange processes (momentum, heat, and gas exchange). Finally, previous studies have shown that light rain generates acoustic energy above 10 kHz and that this sound is poorly correlated with total rainfall rate. A simple empirical acoustic rainfall rate algorithm for heavy rain is offered. This algorithm may be site specific. Furthermore, it overestimates rainfall rate early in the rain events examined here (convective rain events), and then underestimates rainfall rate later in the same events. This observation is shown to be consistent with likely changes in the drop size distribution during the lifetime of the rain event. The sound produced by large drops within heavy rain (drop diameter greater than 2.2 mm) is shown to dominate the underwater sound field. The empirical acoustic rainfall rate algorithm is therefore more correctly a measure of the rainfall rate from large raindrops. Fortunately, the rainfall rate from large raindrops is highly correlated with the total rainfall rate, making acoustic monitoring of underwater sound an effective measure of rainfall rate in oceanic regions.

A stochastic model for scattering from the near-surface oceanic bubble layer.

A stochastic scattering model has been developed that allows the backscatter from a subsurface bubble layer to be written as the product of a geometric factor times the horizontal wave-number (‘‘power’’) spectrum of the bubble layer. By dividing the measured backscatter versus frequency data by the geometric factor, one can ‘‘invert’’ the backscatter data and directly infer the horizontal wave-number spectrum of the bubble layer. Three different data sets give power-law wave-number spectra: P(K)≊A‖K‖−β, where β≊4 for two of the data sets and β≊3 for the third data set. The factor A is a constant that is different for each data set. When the inferred wave-number spectrum is used to predict backscatter versus angle, good agreement is obtained with the data at low frequencies and low grazing angles. The consistency in the inferred wave-number spectrum strongly suggests that a systematic power-law spectrum exists for the near-surface oceanic bubble layer. A time-dependent bubble plume model is discussed that shows how a power-law wave-number spectrum can arise in the bubble layer. [Work supported by ONR.]

Optimum SNR enhancement of narrow‐band signals in surface reverberation

Theoretical performance capabilities of the optimum filter for maximization of signal‐to‐noise ratio (SNR) and a suboptimum approximation, easy to realize in practice, are compared to the conventional matched filter (designed for white noise only) in the case of low Doppler signals masked by surface reverberation. Spectrum models for surface backscattering as a function of local environmental parameters are based on recent results describing scattering from a subsurface bubble layer. Significant improvements in SNR in the low Doppler region as well as a dramatic dependence of performance on windspeed and direction, and the ratio of reverberation to uncorrelated noise power are predicted. Results serve as average performance limits to be compared to those obtained by algorithmic implementations of optimum and adaptive filters.

Effects of the sub-surface bubble layer on sound propagation

Based on photographic data of bubble populations and theoretical considerations, a formula for the spectrum of wind-generated bubbles in the open sea is derived. This formula is used in a computer study to calculate the full effect of bubbles on refraction and attenuation in sound propagation both in the surface duct and in vertical paths. The study is carried out for frequencies in the range 8–60 kHz, and wind speeds to 30 kn. Attenuation is found to be very significant in this range. For practical purposes formulae for the loss per limiting ray cycle and for the two-way attenuation in a vertical path are obtained by fitting the numerical results. These formulae can be easily implemented on hand-held calculators.