Nonlinear Interaction Of Surface Waves Research Articles

Using Axial Base cabled array sensor data to study the prediction of second-order pressures from nonlinear surface wave interactions associated with microseisms

There are currently no published experimental measurements of second-order pressures in the water column from nonlinear surface wave interactions. Microseism researchers have focused on predicting and measuring microseisms directly without measuring second-order pressures in the water column. We considered several Ocean Observatory regional cabled arrays as sources for water column measurements to compare with analytical model second-order pressure predictions based on hindcast directional wave spectra. We selected the Axial Base cabled array for its location and suite of instruments including two hydrophones, 3D velocity sensor, and seismometer near the seafloor. Here we present results for predicted second-order pressures along with hydrophone measurements at the Axial Base site over different times of a year (2019–2020) to demonstrate a correlation. Validating a prediction model for second-order pressures based on directional surface wave spectra using the OOI cabled array sensor data could spur development of wave energy harvesting devices in the deep ocean and other applications.

Analysis of the conditions for the occurrence of "the voice of the sea" using infrasound observations in marine waters

We study the conditions for the occurrence of "the voice of the sea" in the infrasound range can occur and determine its parameters from infrasound measurements in the Black Sea water area conducted in 2011 and 2016 and in the water area of the Sea of Okhotsk in 2017. To this end, we compared the observations of different parameters (mean correlation, spectra of acoustic arrivals, direction and phase velocity) of the high-frequency infrasound (1–10 Hz), recorded in Katsiveli (Crimea) in 2011 and 2016. We performed a detailed study of the wind conditions in the Black Sea water area during the measurement period, as well as the conditions for the propagation of acoustic waves along the direction of their arrivals.
 In both cases the atmospheric vortices in the direction of the arrival of infrasound were detected, which caused changes in wind velocity vector above the sea surface. The infrasound recorded in 2011 was caused by the interaction of two differently rotating atmospheric vortices over the sea. In 2016, a vortex was observed to the West from the registration point. The possibility of generating "the voice of the sea" due to the rotation of the wind velocity, which causes a nonlinear interaction of surface waves propagating in opposite directions to each other, and the formation of their 2nd harmonic in the form of a standing surface wave is discussed.
 From the analysis of the wind speed and wind direction profiles along the infrasound arrival path, as well as the acoustic pressure fields calculated by the parabolic equation method for the effective sound speed profiles in the direction of infrasound propagation, the most probable areas of infrasound generation were determined. In both cases these areas coincided with the zones in which the wind speed drops to zero, and the direction of the wind changes to the opposite.
 An example of simultaneous detection from one direction of the microbaroms with frequencies 0.2–0.3 Hz and "the voice of the sea" with a higher frequency of 5.5 Hz is given.

Analyzing Conditions for the Occurrence of the Voice of the Sea on the Basis of Infrasound Measurements

Conditions for the occurrence of the “voice of the sea” within the infrasonic range are studied and its parameters are determined from measurements performed in the waters of the Black Sea (2011 and 2016) and the Sea of Okhotsk (2017). Different parameters (mean correlations, acoustic-arrival spectra, directions, and phase velocities) of high-frequency infrasounds (1–10 Hz) recorded during the 2011 and 2016 experiments carried out in Katsiveli (Crimea) are compared. Wind conditions over the Black Sea waters and the conditions of propagation of acoustic waves along the direction of their arrivals during these measurements have been studied in detail. In both cases, atmospheric vortices are observed in the direction of infrasound arrivals, which cause the wind to change its direction over the sea surface. The interaction between two oppositely directed atmospheric vortices (according to data obtained in 2011) and a vortex observed to the west of the recording point (according to data obtained in 2016) result in the generation of infrasounds. The generation of microbaroms and the voice of the sea due to wind-direction variations, which cause the nonlinear interaction of surface waves propagating in opposite directions and the formation of their 2nd harmonics in the form of standing surface waves, is discussed. The most probable regions of infrasound generation are determined from an analysis of the profiles of wind velocity and direction along the path of infrasound arrivals and acoustic-pressure fields calculated using the parabolic-equation method according to the $${{C}_{{{\text{eff}}}}}$$ profiles in the direction of infrasound propagation. In both cases, these regions coincide with zones in which the wind velocity had dropped to zero and the wind direction had reversed. The infrasound within a microbarom frequency range of 0.2–0.3 Hz and the (higher frequency) sea voice with a mean frequency of 5.5 Hz, which were simultaneously recorded from the same direction, are given as an example.

A wind-driven noise model in deep water

Surface processes, including non-linear surface wave interactions and bubble oscillations, dominate the deep water ambient noise in the absence of shipping and wildlife. A single-parameter noise model, determined by the wind speed above the ocean surface, is proposed to interpret the deep ocean acoustics from 1 Hz to 4 kHz. Below hundreds of hertz, the sound is primarily generated by surface wave interactions, which is the function of surface wave spectrum. A theoretical expression of wave spectrum is proposed to contain the gravity and capillary waves, which is in accord with the features of measured wave spectra. The noise spectrum for frequency above hundreds of hertz due to the effective bubble oscillation within the bubble cloud is proposed. The noise spectrum has been estimated as a function of frequency and wind speed based on available information of the bubble distribution. The model/data comparison shows that the proposed single-parameter noise model are in reasonable agreement with the data. [Work supported by National Natural Science Foundation of China, Grant No. 11125420.]

On experience in recording the voice of the sea in the water area of the Black Sea

Some data on a high-frequency infrasound recorded within a range of 2–16 Hz (voice of the sea) in the water area of the Black Sea are given. Different parameters of the recorded infrasonic signal—the direction and phase velocity of arriving infrasonic waves, spectral composition, and coherence—have been studied. In the course of measurements, both wind and wave conditions in the water area of the Black Sea have been studied in detail. The collision of two atmospheric vortices was observed a few hours before the first arrivals of infrasonic waves, and the collision of differently directed sea waves was observed during infrasound recording. The direction of the arrivals of infrasonic waves coincides with the direction between the zone of collision of sea waves and the point of infrasound recording. The assumption was made that, in order to explain the observed infrasonic waves, it is necessary to use the mechanism responsible for the emission of infrasound into the atmosphere by standing surface waves formed due to the nonlinear interaction of surface waves propagating in opposite directions and to take into account the frequency-filtering properties of both wind-velocity and temperature stratifications of the atmosphere itself along the path of infrasound propagation. This assumption calls for additional verification.

Correlation matrices as a method of source function isolation and classification in ambient noise

At low frequencies (1–100 Hz), the deep-ocean ambient noise field is a mixture of many source types, including seismic activity, marine life, ship traffic, seismic airgun surveys, and nonlinear surface wave interactions. The location of the sensors used to monitor these types of noise typically result in an extremely dynamic recorded ambient noise field. This study proposes the use of correlation matrices as a tool for identifying the predominant noise sources present in samples of ambient noise. These correlation matrices work by identifying frequency ranges in which the noise levels tend to change at the same time, thus identifying frequency ranges where noise is driven by one particular source mechanism. The effectiveness of this strategy will be demonstrated using low-frequency deep-ocean ambient noise recorded in the Pacific, Atlantic, and Indian Oceans by the Comprehensive Nuclear-Test Ban Treaty Organization (CTBTO) hydroacoustic monitoring system.

Wave–wave interactions and deep ocean acoustics

Deep ocean acoustics, in the absence of shipping and wildlife, is driven by surface processes. Best understood is the signal generated by non-linear surface wave interactions, the Longuet-Higgins mechanism, which dominates from 0.1 to 10 Hz, and may be significant for another octave. For this source, the spectral matrix of pressure and vector velocity is derived for points near the bottom of a deep ocean resting on an elastic half-space. In the absence of a bottom, the ratios of matrix elements are universal constants. Bottom effects vitiate the usual "standing wave approximation," but a weaker form of the approximation is shown to hold, and this is used for numerical calculations. In the weak standing wave approximation, the ratios of matrix elements are independent of the surface wave spectrum, but depend on frequency and the propagation environment. Data from the Hawaii-2 Observatory are in excellent accord with the theory for frequencies between 0.1 and 1 Hz, less so at higher frequencies. Insensitivity of the spectral ratios to wind, and presumably waves, is indeed observed in the data.

Distribution of wave packet sizes in microbarom wave trains observed in Alaska

This work reports on a study of the distribution of wave packet sizes contained in intervals of continuous microbarom activity. Microbaroms are a class of atmospheric infrasound that is characterized by narrow-band, nearly sinusoidal, waveforms with periods near 5 s. They are known to be generated by marine storms, presumably through a nonlinear interaction of surface waves, however the detailed analysis of the process is still incomplete. The data analyzed were obtained using the University of Alaska infrasound array of four microphones located in central Alaska. Because of the narrow-band feature of the microbarom signals, the Hilbert transform is applicable as a method for finding phase breaks in the signal. The phase breaks are interpreted as the demarcation of the boundaries of wave packets. When applied to long sequences of microbaroms a broad distribution of packet lengths is found that diminishes monotonically with length and has a mean near 10 cycles and a variance nearly as large. The distribution function decreases exponentially with packet length. The distribution of packet sizes is influenced by the presence of multiple sources and multiple propagation paths between the sources and the sensor array. Identification of individual packets should open the way to a more detailed analysis of microbarom wave trains. After separating the wave train into individual wavelets the intermicrophone correlation is estimated as a function of microphone separation. As has been observed in earlier microbarom studies, a decrease in correlation was observed for microphone pairs orthogonal to the direction of propagation when compared to correlations between microphones spaced along the direction of wave propagation.

MULTI-ANGULAR MEASUREMENTS OF SEA-SURFACE POLARIZED MICROWAVE EMISSION CARRIED OUT DURING A SERIES OF GROUND-BASED EXPERIMENTS

The results of sea-surface microwave brightness measurements carried out from a pier in 1999-2002 are presented. The measurements were performed by W-band microwave radiometer (wavelengths of 0.3 cm), and Ka-band radiometer-polarimeter (wavelength of 0.8 cm). All equipment was installed on a pier (200 meters long) at 3 meters over the surface; the sea depth at the site was approximately 8 meters. The microwave instruments were mounted on a rotating/scanning platform, which permitted measurements at angles from 10 up to 170 degrees off nadir over 300 degrees range of azimuthal angles. The measurements were carried out 24 hours a day under various meteorological conditions. Microwave brightness dependence on surface wind was studied over wide range of incidence angles. The modulus of brightness contrasts caused by the wind was shown to increase with wind speed increasing. Also, the brightness contrast at both polarizations changes its sign as the viewing angle increases. Under variable wind conditions, the delay of brightness variation relative to wind speed as large as 1-2 hours was found. This effect may be treated as an evidence of non-linear interaction of surface waves in coastal area

Measurement and prediction of ultralow frequency ocean ambient noise off the eastern U.S. coast.

Ultralow frequency (0.02-2 Hz) acoustic ambient noise was monitored from January to April 1991 at six ocean bottom stations off the eastern U.S. coast. The depths of the stations ranged from about 100 m to 2500 m. The measured spectra are in good agreement with predictions made using Cato's theory [J. Acoust. Soc. Am. 89, 1076-1095 (1991)] for noise generation by surface-wave orbital motion after extending the calculations to incorporate horizontally stratified environments. Contributions from both the linear, single-frequency (virtual monopole) and the nonlinear, double-frequency (dipole) mechanisms are clearly recognizable in the data. The predictions make use of directional wave data obtained from surface buoys deployed during the SWADE experiment and an ocean bottom model derived from compressional wave speed data measured during the EDGE deep seismic reflection survey. The results demonstrate conclusively that nonlinear surface-wave interactions are the dominant mechanism for generating deep-ocean ULF noise in the band 0.2-0.7 Hz.

Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method

Linear and second-order surface wave interactions with floating and bottom-mounted bodies of realistic geometry are simulated in the time domain by a three-dimensional Rankine panel method. The fundamental stability analysis governing the propagation of transient wave disturbances on a panel mesh distributed on the free surface is carried out from first principles. The radiation condition is enforced by a dissipative beach selected to coincide with an outer annulus of panels. The fundamental physics governing the wave energy absorption is presented and the beach attributes are selected and validated for the linear and second-order problems. Computations are presented of the linear and sum-frequency second-order forces on a single and multiple truncated circular cylinders, and very good agreement is found with benchmark computations. The accuracy and efficiency of this method render it a promising candidate for the study of complex nonlinear wave induced phenomena upon offshore platforms, like springing and ringing.

Nonlinear interaction of surface waves in a basin covered with broken ice

The nonlinear interaction of periodic traveling waves of the first and second harmonics in a constant-depth uniform fluid covered with broken ice is considered. Uniform asymptotic expansions up to third-order values for the velocity potential of the fluid and the elevation of the basin surface are found by means of the multivariable expansion procedure. The dependence of the wave perturbations on the thickness of the ice and the interacting-harmonic characteristics is analyzed.

Boundary effects on the nonlinear interactions of surface waves

A traditional cold-plasma boundary model is revised to allow for proper description of nonlinear effects in surface wave propagation. It is shown that induced nonlinear surface currents can exist at the boundary. As an example, the third-order ponderomotive phenomena are considered, and the effect of the boundary condition on these nonlinear interactions is examined.

Theoretical and measured underwater noise from surface wave orbital motion

This paper develops a theory of sound generation by orbital motion of sea surface waves (as distinct from motion directly resulting from wave breaking such as bubble oscillation) and compares the noise predictions with measurements in a carefully controlled experiment. Theory and measurement were found to agree within the experimental errors. The mechanism is also known as the nonlinear interaction of surface waves and has been addressed by a number of authors. The approach of this paper differs from other models in that it avoids the use of the commonly applied perturbation expansion, and calculates the total noise field whereas others have limited their estimates to sound production from standing waves and waves that closely approximate standing waves. It is shown that while standing waves result in distributed dipoles with vertical axes, other wave interactions result in dipoles with axes inclined to the vertical so that there are components with both horizontal and vertical axes. The relative contribution of the horizontal dipole components to the noise field is of the same order of magnitude as that of the vertical dipole components. This paper therefore predicts higher noise levels and different directionalities, and also determines the contribution from the evanescent or near field that dominates for receiver depths less than several hundred meters (depending on frequency) resulting in substantially higher noise levels at shallow receivers. On the basis of this and previous work there seems little doubt that this mechanism is a significant source of noise in the ocean, usually dominant from about 0.2 to 5 Hz.

The nature of the inhomogeneous component of the wave‐induced microseismic noise field

Spectra of the near‐field microseismic noise induced by nonlinear surface wave interactions are calculated to examine the influence of the inhomogeneous component of the wave‐induced pressure field. The contribution of this component appears to be critically dependent on the thickness of the water column, the properties of the bottom structure, and the position of the observation point. Calculation for a typical six‐layered bottom with an overlying unconsolidated sediment on top of a solid half‐space, in a shallow‐water environment (100‐m water layer), shows that the microseismic spectrum inside the active wave region is dominated by the inhomogeneous component that is some 40 dB higher than the homogeneous component. However, when the bottom is a single solid basement, this component reduces by about 30 dB. Further, when the observation point moves beyond the boundary of the active region, the spectral level drops dramatically and finally approaches the level of the Rayleigh mode of the basement. Applications of these results to the estimation of the ULF noise spectra from microseismic data recorded on shore are discussed. Variation of the spectra with distance from the active region is also examined. [Work supported by ONR.]

Sound‐channel effects on ambient noise spectra

Possible causes of the observed site dependence of deep ocean noise spectra below 100 Hz are examined through a coherent ambient noise prediction scheme due to Ingentio and Kuperman. The model accounts for propagation from a random distribution of surface dipoles in a range‐independent, compressional sound‐velocity structure; hence data‐theory comparisons were limited to deep ocean abyssal plain environments. A variety of environments from open ocean (with varying wind speeds) to noisy ice‐edge configurations were considered. Results below 100 Hz reveal a frequency‐dependent, sound‐channel‐controlled amplification of the noise‐source spectra which is sensitive to bottom sound‐speed profile/attenuation coefficient and sea‐surface scattering loss. Below 5 Hz the computed amplification accurately accounts for the apparent discrepancy between theoretical and measured noise due to nonlinear interaction of surface waves. Above about 50 Hz the computed noise‐source spectral shapes in the open ocean and at the ic...

Waves generation due to nonlinear interaction of S-surface waves at the plasma boundary

Nonlinear interaction of surface waves in a homogeneous, unbounded, weakly nonlinear medium, takes place at the following decay rules: Σi ωi=0, Σ iKi=0 where, ω i and Ki are the frequencies and wave vectors of the interacting waves. Dologopolov et al. (1976) already investigated the interaction of P-surface waves where the amplitudes of magnetic field of waves with combination frequencies, radiating into the plasma and vacuum, was obtained in terms of the amplitudes of the magnetic field of the surface waves. The authors consider the nonlinear interaction of S-surface waves at the boundary of a semi-bounded plasma by solving accurately the equations for the fields at combination frequencies in a 'homogeneous plasma-vacuum transition layer'. They also consider that the tangential components of the electric field of waves with combination frequencies are discontinuous at the plasma boundary as proved by Barakat et al. (1975).

Infrasonic ambient ocean noise measurements: Eleuthera

Measurements of ambient ocean noise in the frequency range 0.02 to 20 Hz were made with three hydrophones bottomed off Eleuthera Island, at depths of 13, 300, and 1200 m, respectively, over a period of about six weeks in June, July, and August. The results are compared with reported results of other experimenters and with results of some published theories of infrasonic noise generation in the ocean. Comparisons with published data in the frequency range from 0.1 to 20 Hz show reasonable agreement. There do not appear to be published data in the region below 0.1 Hz for comparison. Comparisons with theories do not allow conclusive identification of generating mechanisms, but it appears that nonlinear interaction of surface waves and/or ocean turbulence are likely candidates in the frequency range 0.1 to 10 Hz. Below 0.1 Hz no specific mechanism is postulated to account for the steep rise in noise level with decreasing frequency observed in the Eleuthera data.

Dependence of infrasonic ambient noise levels on wind speed and surface wave properties

Near‐coincident ambient noise and wind speed measurements were made over a frequency range 2–20 Hz on a 3400‐m‐deep bottom‐mounted hydrophone in the North Atlantic for wind speeds between 5 and 50 knots. Above about 5 Hz, spectrum levels were dependent on wind speed, w, and frequency, f, approximately as w4/f2. The wind speed dependence is in reasonable agreement with the theory of noise generation through near‐surface atmospheric turbulent pressure fluctuations. The observed spectral shape differs from previous measurements and may be site‐dependent. Below about 5 Hz, the measured wind‐dependence of spectrum levels was consistent with computations based on (1) the theory of noise generation by nonlinear interaction of surface waves propagating in opposite directions, (2) Hasselman's prescription for the wind dependence of the surface wave spectrum [J. Phys. Ocean. 6, 200–228 (1976)], and (3) Tyler's characterization of the directionality of the sea surface wave field [Deep Sea Res. 21, 989–1016 (1974)]. ...

Nonlinear interactions of surface waves with incident radiation at a narrow inhomogeneous plasma layer

The amplitudes of the waves radiating at combination frequencies from the plasma boundary due to nonlinear interaction of surface waves with radiation incident on a narrow inhomogeneous plasma layer, are determined. The method used allows for the discontinuity at the plasma boundary of the tangential components of the electric field of the wave at the combination frequencies.