I. A. Soustova

Nonlinear acoustics of micro-inhomogeneous media

Abstract Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.

Application of three-dimensional resonant acoustic spectroscopy method to rock and building materials

This paper presents the experimental and theoretical results of applying resonant acoustic spectroscopy (RAS) to determine elastic parameters and losses in such consolidated granular materials as rock and building bricks. First, the theoretical aspects of the RAS method are outlined. A computer code for the rectangular and cylindrical samples was developed and tested. The results of experiments on specimens of rock and ceramic brick are then described. Finally, a modification of the previously published RUS algorithm is presented which permits a significant reduction in computing time for elongated samples.

Satellite altimetry of inland water bodies

An algorithm is proposed for determining water level in inland water bodies and coastal zones of seas and oceans. The algorithm was tested for the water area of the Gorki Reservoir, for which radioaltimeter databases show considerable data losses. A model was constructed, describing the shape of a mean impulse reflected from a statistically heterogeneous piecewise-constant underlying surface (topographic model). The model was used to substantiate criteria for data choice for the Gorki Reservoir and to construct a regional algorithm for estimating water level using data from Jason-1 satellite and based on the analysis of the shape of telemetric impulses (retracking). Water level was calculated with the use of an algorithm of regional adaptive retracking Sensor Geophysical Data Record databases for the Gorki and Rybinsk reservoirs. Algorithm application has been shown to considerably increase the amount of actual data and significantly improve the accuracy of water level evaluation. The general principles of retracking of a complex domain (a coastal zone, an inland water body, etc.) are discussed. The principles are based on the calculation of signal with allowance made for the roughness of the reflecting surface and they can be applied to different geographic regions.

Resonant acoustic spectroscopy at low Q factors

The application of resonant acoustic spectroscopy to rock, building materials, and materials with cracks is hindered by the substantial mechanical losses in these materials and by the overlapping of the individual resonance responses. The paper describes a method for the determination of the resonance frequencies in low-Q materials in the presence of a strong overlapping of resonances. The effect of cracks on the values of the resonance frequencies and Q factors is studied experimentally.

Effect of an Intense Sound Wave on the Acoustic Properties of a Sandstone Bar Resonator. Experiment

Experimental results and a theoretical description are presented for the effect of an intense pumping wave on a weak wave in a sandstone bar resonator. From the amplitude dependences of the resonance frequency shift and of the nonlinear loss, which are measured for the weak wave in the presence of the intense one, it is inferred that sandstone exhibits a dissipative acoustic nonlinearity.

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.

Nonlinear, low-frequency sound generation in a bubble layer: Theory and laboratory experiment

The difference-frequency sound generation as a result of interaction of two high-frequency harmonic waves in a bubble layer in water is investigated both theoretically and experimentally. Because the sound speed in the layer is less than that outside, the layer has resonance properties. As was shown before, this can considerably increase the efficiency of the nonlinear frequency transformation. However, unlike the cases considered before, the layer resonance is practically achievable only at the low (difference) frequency, whereas the high-frequency signal (pump) resonates at individual bubbles and then it strongly dissipates. Here the results of an experiment with a bubble layer with a thickness of about 10 cm in an anechoic tank are presented. One of the incident (primary) wave frequencies was 60 kHz, whereas the other could be varied, thus providing the low-frequency signal in the range of 0.8–14.8 kHz. Due to the first-mode layer resonance, this secondary signal had a pronounced maximum at a frequency...

Surface manifestations of internal waves investigated by a subsurface buoyant Jet: 1. The mechanism of internal-wave generation

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, we have performed a major laboratory simulation of the nonstationary dynamics of buoyant turbulent jets generated by wastewater flows from underwater collector diffusers. The interaction of buoyant jets with the pycnocline leads to an active generation of internal waves. An analysis of the dependence of wave amplitude on the control parameter proportional to the rate of liquid flow from the collector diffuser has indicated that this dependence is adequately described by a function that is characteristic for the presence in the Hopf bifurcation system, which occurs for a soft actuation mode of self-oscillations of the globally instable mode. To check the conditions for the actuation of the globally instable mode, we have performed an auxiliary experiment in a small reservoir with a salt stratification formulated similar to the experiment in the big reservoir. Using the particle image velocimetry (PIV) method, we have measured the velocity field in the buoyant jet and constructed the profiles of transverse velocity in several sections. When the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability by the Briggs criterion for axisymmetric jet oscillations is satisfied, which testifies to the fact that the globally instable mode is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations.

Surface manifestations of internal waves investigated by a subsurface buoyant jet: 3. Surface manifestations of internal waves

In a large test reservoir at the Institute of Applied Physics, Russian Academy of Sciences, a series of experiments were performed to investigate the surface manifestations of internal waves radiated by a subsurface buoyant jet. The field of currents on the water surface of the reservoir was studied through the distribution of temperature with shallow thermocline. Using Particle Tracking Velocimetry (PTV), the velocity field of surface currents was measured. A theoretical model was developed to calculate the rates of disturbances on the surface. A comparison with experimental data indicated that the calculated data of the surface rate value are overestimated. This discrepancy was explained by the presence of a film of surface-active substances (SASs) with experimentally obtained parameters. Using scale modeling coefficients, we estimated the parameters of internal waves radiated by the subsurface wastewater system and the values of their surface manifestations in field conditions. We estimated the hydrodynamic contrasts in the field of surface waves, which can be caused by these inhomogeneous currents on the surface. For a wind velocity of 5 m/s, the magnitude of the contrast in the field of short waves can reach up to 10–25%, which is detected with confidence by remote-sensing methods.