Nonlinear Interaction of Infragravity and Wind Sea Waves

Abstract

In this paper, the authors analyze data obtained from a supersensitive detector of hydrosphere pressure variations which was positioned on the shelf of the Sea of Japan at a depth of 25 m for several months. When processing this data, the main attention was paid to studying nonlinear hydrophysical disturbances of “rogue waves” type: “one sister”, “two sisters”, “three sisters”, and “potential well”, the origin of which is associated, apparently, with the interaction of the hydrophysical wave field in gravity range and disturbances in the infragravity range. Analysis of synchronous data of the laser strainmeter and laser nanobarograph, installed at Shultz Cape, with synchronous records of the supersensitive detector of hydrosphere pressure variations confirmed these conclusions.

1. Introduction

In a recently published paper [1], we discussed the results obtained from a laser meter of hydrosphere pressure variations during registration of anomalous nonlinear hydrosphere disturbances of the “rogue waves” type of various origins. In addition to single large-amplitude nonlinear disturbances, classical nonlinear disturbances related to the “one sister”, “two sisters”, and “three sisters” “rogue waves” were found. In the above-mentioned paper, the authors assumed that their occurrence is associated with the interaction of gravity and infragravity sea waves in the area where the recording equipment is located during intermode energy transfer, similar to the energy transfer of the modified Fermi–Pasta–Ulam recurrence. The mechanism of formation of these anomalous hydrophysical disturbances is associated with the interaction of wave hydrophysical fields of different frequency ranges, gravity and infragravity. The correctness of this explanation is confirmed by the conclusions in [2], where it was established that, for the origin of the Fermi–Pasta–Ulam recurrence, the presence of a medium with high frequency (for example, gravity waves) and low frequency (for example, infragravity disturbances) fluctuations is a necessary condition. This behavior is typical for deep water, in which anomalous nonlinear disturbances originate in the presence of two fields of different frequency ranges.

In the field of one frequency range, for example, gravity sea waves, formation of various nonlinear hydrophysical disturbances is also possible. The papers [3,4,5] describe in detail the mechanisms of formation of various “rogue waves”. For formation of anomalous nonlinear hydrophysical disturbances of the “rogue waves” type, special mechanisms of energy concentration in a specific space–time region are required, i.e., there should be transfer of energy from various spectral maxima to specific spectral maxima. This can also occur during interaction of waves of the gravity range, but of different origin, for example, during interaction of swell waves (“free” wind waves, i.e., wind waves that have left the zone of the driving force influence) with wind waves of local origin. In theoretical descriptions of “rogue waves”, researchers resort to various methods that give an approximate formation of the observed nonlinear disturbances. We understand that it depends on the personal “taste” of a theorist. In [6], the final solution is sought based on application of the dispersion focusing method in the framework of the Korteweg–de Vries equation and, of course, wave front reversal [6,7,8], which allow for an abrupt increase in wave energy in a certain point in space. Another approach is based on the application of the Schrodinger equation, but, again, with an additional mechanism, leading to the intended goal: modulation instability [9]. In addition, it is impossible to do without the sine-Gordon equation in mathematical description of “rogue waves” [10], which have different properties of modulation instability. We should note that we also are not indifferent to this equation, since it allows us to understand the breather behavior of short-term tsunami precursors [11].

However, in this paper, we will again turn to the nature of the origin of various non-linear hydrophysical formations of anomalous amplitude (“rogue waves”), occurring from the interaction of gravity waves and infragravity disturbances. Only in this case, in an attempt to explain the nature of their occurrence, we will also use data from other measuring systems that work simultaneously with the laser meter of hydrosphere pressure variations and practically in the same measuring area. When interpreting the data obtained from the supersensitive laser meter of hydrosphere pressure variations, we will also use the data from the laser nanobarograph, and data from the laser strainmeter.

The importance of conducting these studies is related to the necessity of creating a unified theory of occurrence of the nonlinear hydrophysical disturbances described above (“rogue waves”). After all, it is evident that various theoretical approaches, described also in [3,4,5,6,7,8,9,10], merely indicate that the physics of occurrence of these nonlinear hydrophysical disturbances has not yet been established. We believe that the obtained in-situ data, and the results of their processing and preliminary interpretation, will help in solving the most important task of determining the physics of their occurrence. The importance of conducting these studies is also connected with the urgent practical need to predict the appearance of these nonlinear hydrophysical disturbances in the areas of human marine activity. If twenty years ago there were only individual reports about “rogue waves”, which we perceived as fables, in subsequent years, according to [3,4,12,13], “rogue waves” started to appear in abundance. This is due not only to scientific work, but also to the expansion of human marine activity and attention to these nonlinear hydrophysical disturbances. We hope that our results will allow theorists to take yet another right step towards constructing the physics of occurrence of these nonlinear hydrophysical disturbances.

2. Laser Interference Measuring Complex

In-situ data, analyzed in the paper, were obtained during synchronous measurements of variations in microdeformations of the Earth’s crust with the 52.5-m laser strainmeter [14], microfluctuations of atmospheric and hydrosphere pressure with the laser nanobarograph [15], and the supersensitive detector of hydrosphere pressure variations [16], respectively. Figure 1 shows the layout of measuring systems at Shultz Cape and on the shelf of the Sea of Japan. The laser nanobarograph is located in one of the laboratory units close to the laser strainmeter.

The optical scheme of the laser strainmeter was based on an unequal-arm Michelson interferometer using a frequency-stabilized helium-neon laser with long-term stability from the ninth to the eleventh decimal place as a light source. The length of the measuring arm of the laser strainmeter was 52.5 m. The reference arm had a length of 0.4 m. All structural elements of the laser strainmeter were underground in hydrothermally insulated rooms at a depth of 3–5 m from the ground surface. The laser beam propagated in a vacuum-processed sealed stainless steel light guide. The applied interferometry methods allowed to measure displacement of two abutments of the laser strainmeter relative to each other with an accuracy of 10 pm. The operating range of the laser strainmeter was from 0 (conditionally) to 100 Hz.

The optical scheme of the laser nanobarograph was assembled according to the scheme of the equal-arm type Michelson interferometer using a frequency-stabilized helium-neon laser with long-term stability in the ninth decimal place as a light source. The measuring and reference arms were 0.2 m long. The sensitive element of the laser nanobarograph was an aneroid box with mirror coating. The modified laser nanobarograph used in the experiment had the following characteristics: operating frequency range from 0 (conditionally) to 1000 Hz, measurement accuracy of hydrosphere pressure variations of 1 MPa.

The supersensitive detector of hydrosphere pressure variations was created on the basis of a modified homodyne-type Michelson interferometer and a frequency-stabilized helium-neon laser, providing radiation frequency stability in the ninth decimal place. It was placed in a cylindrical stainless-steel case, which was fixed in a protective grating, designed to protect the instrument in severe operating conditions (rocky or slimy bottom). One side had a cable entry hole. The other side was hermetically sealed with a lid. Besides the protective grating, outside the device there was an elastic container with air, the outlet of which was connected by means of a tube to a compensation chamber located in a removable cover. Inside the case were a Michelson interferometer, a compensation chamber, an electromagnetic valve, and a digital registration system. The sensitive element of the supersensitive detector was a round membrane, which was fixed at the end of the device. Outside, the membrane interacted with water. A mirror, fixed on the inner side of the membrane, was a part of the “cat’s eye” system, consisting of a biconvex lens with an appropriate focal length and this mirror. The mirror with the lens was a part of the interferometer’s measuring arm. It was rigidly fixed in the center of the membrane and shifted along the axis of the interferometer under the influence of pressure variations in the hydrosphere. A change in the length of the measuring arm led to a change in the intensity of the interference pattern, which was recorded by a digital registration system. The output signals of the supersensitive detector, after pre-processing by the digital registration system, were hydrosphere pressure variations. The main technical characteristics of the detector were: operating range from 0 (conditionally) to 1000 Hz, measurement accuracy of hydrosphere pressure variations of 0.24 MPa, operating depths up to 50 m. It was possible to obtain the best technical characteristics by reducing the noise of photoelectronic equipment, compensating for temperature noise, and more accurately equalizing the difference in the lengths of the measuring and reference arms of the interferometer, which corresponded to the following design parameters: operating range from 0 (conditionally) to 10,000 Hz, measurement accuracy of hydrosphere pressure variations of 1.8 μPa.

All in-situ data, obtained from all measuring systems in real time, was placed on hard media of a writing computer after pre-processing (filtering, decimation), with creation of an experimental database with reference to the exact time system via GPS Trimble 5700 with 1 µs accuracy.

3. Processing and Analysis of Obtained In-Situ Data

In this paper, we mainly analyze in-situ data obtained on the supersensitive detector of hydrosphere pressure variations, installed at the depth of 25 m on the bottom of the Sea of Japan, to the south of Shultz Cape, which worked there from 1 August to 15 November 2022. Before analyzing the obtained data in the gravity and infragravity ranges, we first filtered them with a Hamming bandpass filter in the 0.0004–2 Hz band (periods from 42 min to 1 s). Then, the series, filtered with the bandpass filter, was processed with a high-frequency Hamming filter at the cutoff frequency of 0.002 Hz, which allowed us to analyze the data in the band of periods from 8 min to 1 s. Surface wind waves in the range of periods from 2 to 20 s, and infragravity waves observed earlier in this water area, fit into this band [17]. Figure 2 shows the spectrogram of the filtered series for the entire observation period, where the range of gravity sea waves (surface wind waves and swell waves), and the less energy-intensive range of infragravity sea waves are distinguished. In the infragravity range, oscillations in the range of periods of 31–33 s are almost always observed, which are characteristic of high-frequency infragravity waves, and which, apparently, are defined by the bathymetry of a particular area of the shelf.

Next, we analyzed the records of the supersensitive detector of hydrosphere pressure variations for the presence of anomalous signals in them, the amplitudes of which differ greatly from the amplitudes of neighboring signals. The simplest example of solitary nonlinear hydrophysical disturbances is the perturbation shown in Figure 3. As we can see in this figure, the nature and amplitude of this anomaly differ greatly from the neighboring instrument record. Spectral processing of equal size records (1024 points at sampling rate of 2 Hz) before the anomalous signal, during the anomalous signal, and after the anomalous signal showed that the spectra of the records before and after the anomalous signal are approximately the same in terms of total power, and the total power during the anomalous signal is 2–2.5 times greater. This happens due to the appearance in the spectrum of infragravity signals with periods of about 3 min 39.8 s (amplitude is 1686.7 Pa) and 1 min 18.4 s (amplitude is 1676.7 Pa). In the gravity range, there is a peak with period of 6.4 s (amplitude is 722.9 Pa). Figure 4 shows the spectrum obtained when processing this section of the recording. The signal processing was carried out using the maximum likelihood spectral method with 20 harmonics. When processing the section of the instrument record before the anomalous signal, the maxima with periods of 6.2 s (amplitude is 1688.7 Pa), 3 min 56.8 s (amplitude is 1219.7 Pa), and 5.7 s (amplitude is 1076.4 Pa) are observed, Figure 5. When processing the section of the instrument record after the anomalous signal, maxima are observed with periods of 5.7 s (amplitude is 1127.7 Pa), 5.2 s (amplitude is 999.2 Pa), 7.4 s (amplitude is 617.6 Pa), and 8.0 s (amplitude is 560.9 Pa), Figure 6.

From the above, we can note that during the anomalous signal, the maximum amplitude is observed for the harmonic of the infragravity range, and before and after the anomalous signal, the harmonic of the gravity range has the maximum.

The spectral processing of the records of laser-interference devices was almost everywhere carried out using the maximum likelihood method. The number of fundamental harmonics was chosen depending on the set tasks; it could be 20, 40, or 60. With a large number of harmonics, the calculations took a very long time, which was not always justified. The main criterion for choosing the number of harmonics was a good similarity of the constructed model (in terms of the number of harmonics) with the original series. In our case, we believe that the number of harmonics equal to 20 was sufficient to meet this condition. For example, Figure 7 shows the original series (green, a part of the graph shown in Figure 3) and the model (red), from which we can see that the model matches the original series almost perfectly.

Now, let us briefly discuss the nature of occurrence of the anomalous signal shown in Figure 3. It can originate in one of the geospheres; the atmosphere, the hydrosphere, or in the Earth’s crust. In order to clarify the nature of these signals’ presence in the Earth’s crust or atmosphere, we analyzed the records of the laser strainmeter and laser nanobarograph of the same time period. Figure 8 shows a section of the laser strainmeter record synchronous with Figure 3, and Figure 9 shows a section of the laser nanobarograph record.

As we can see in Figure 4 and Figure 5 in the records of the laser strainmeter and laser nanobarograph there are no signals of anomalous amplitude similar to the anomalous signal shown in Figure 3. This only indicates that the primary source of this disturbance is the hydrosphere. That is, the nonlinear hydrophysical disturbance shown in Figure 3 appears as a result of nonlinear interaction of gravity sea waves with a train of high-amplitude infragravity sea waves. It is interesting, of course, to understand the nature of occurrence of this train, but this is the subject of the other, more thorough studies. We can only assume that the mechanism of formation of these trains in the spatiotemporal domain of the sea can be associated with/described by the Fermi–Pasta–Ulam recurrence of the field of infragravity sea waves.

A more complex example of solitary nonlinear hydrophysical disturbances is the perturbation shown in Figure 10. Spectral processing of records sections of equal size (1024 points at sampling rate of 2 Hz) before the anomalous signal, during the anomalous signal, and after the anomalous signal showed that the spectra of the record before and after the anomalous signal have approximately the same total power; and the total power during the anomalous signal is 5 times greater. This happens due to the appearance of a signal with a period of about 4 min 40.4 s (amplitude is 5353.8 Pa) in the infragravity range. In the gravity range, there is a peak with period of 8.0 s (amplitude is 999.4 Pa). The signal processing was carried out using the maximum likelihood spectral method with 20 harmonics. During processing the section of the instrument record before the anomalous signal, maxima are observed with periods of 7.8 s (amplitude is 1412.9 Pa), 8.7 s (amplitude is 939.2 Pa), 7.0 s (amplitude is 427.4 Pa), and 2 min 57.4 s (the amplitude is 425.2 Pa). During processing the section of the instrument record after the anomalous signal, maxima are observed with periods of 8.4 s (amplitude is 3423.2 Pa) and 7.0 s (amplitude is 1331.9 Pa). From the paragraph above, we can note that during the anomalous signal, the maximum amplitude is observed for the harmonic of the infragravity range, and before and after the anomalous signal, the harmonic of the gravity range has the maximum.

To clarify the nature of presence of anomalous signals, similar to those registered by the supersensitive detector of hydrosphere pressure variations, in the Earth’s crust or in the atmosphere, we analyzed the laser strainmeter and laser nanobarograph records in the same time period. Figure 11 shows a section of the laser strainmeter record and Figure 12 shows a section of the laser nanobarograph record, both synchronous with Figure 10.

As we can see from Figure 11 and Figure 12, there are no anomalous amplitude signals similar to the anomalous signal shown in Figure 10 in the records of the laser strainmeter and laser nanobarograph.

In the records of the supersensitive detector of hydrosphere pressure variations, classical examples of a solitary “potential well” perturbation are observed; an example of one of them is shown in Figure 13. Spectral processing of record sections of the same size (1024 points at sampling frequency of 2 Hz) before the anomalous signal, during the anomalous signal, and after the anomalous signal showed that the records spectra before and after the anomalous signal are approximately the same in terms of total power, and the total power during the anomalous signal is 2.5–3 times greater. This happens due to appearance of infragravity signals with periods of about 4 min 28.6 s (amplitude is 2685.1 Pa) and 2 min 31.9 s (amplitude is 2266.8 Pa) in the spectrum. In the gravity range, peaks with periods of 6.4 s (the amplitude is 1159.2 Pa) and 8.6 s (the amplitude is 701.7 Pa) are distinguished. The signal processing was carried out using the maximum likelihood spectral method with 20 harmonics. During processing the section of the instrument record before the anomalous signal, maxima are observed with periods of 8.8 s (amplitude is 611.2 Pa), 6.1 s (amplitude is 573.6 Pa), and 9.5 s (amplitude is 428.4 Pa). During processing the section of the instrument record after the anomalous signal, maxima are observed with periods of 6.0 s (amplitude is 438.2 Pa), 7.5 s (amplitude is 391.7 Pa), 8.0 s (amplitude is 392.1 Pa), and 6.8 s (384.8 Pa). From the above paragraph, we can note that during the anomalous signal, the maximum amplitude is observed for the harmonic of the infragravity range, and before and after the anomalous signal, the harmonic of the gravity range has the maximum.

To clarify the nature of presence of anomalous signals, similar to those registered by the supersensitive detector of hydrosphere pressure variations in the Earth’s crust or in the atmosphere, we analyzed the laser strainmeter and laser nanobarograph records in the same time period. Figure 14 shows a section of the laser strainmeter record and Figure 15 shows a section of the laser nanobarograph record, both synchronous with Figure 13.

As we can see from Figure 14 and Figure 15, there are no anomalous amplitude signals similar to the anomalous signal shown in Figure 13 in the records of the laser strainmeter and laser nanobarograph.

In the records of the supersensitive detector of hydrosphere pressure variations, classical examples of a solitary “two sisters” disturbance are observed; an example of one of them is shown in Figure 16. Spectral processing of record sections of the same size (2048 points at sampling frequency of 2 Hz) before the anomalous signal, during the anomalous signal, and after the anomalous signal showed that the records spectra before and after the anomalous signal are approximately the same in terms of total power, and the total power during the anomalous signal is 2.5–3 times greater. This happens due to appearance of infragravity signals with periods of about 4 min 56.6 s (amplitude is 1872.9 Pa) and 3 min 29.3 s (amplitude is 1291.7 Pa) in the spectrum. In the gravity range, peaks with periods 5.7 s (the amplitude is 1734.9 Pa) and 6.9 s (the amplitude is 595.2 Pa) are distinguished. The signal processing was carried out using the maximum likelihood spectral method with 20 harmonics. During processing the section of the instrument record before the anomalous signal, maxima are observed with periods of 7.4 s (amplitude is 729.5 Pa), 6.2 s (amplitude is 713.9 Pa), 8.0 s (amplitude is 536.8 Pa), and 5.9 s (amplitude is 532.0 Pa). During processing the section of the instrument record after the anomalous signal, maxima are observed with periods of 6.0 s (amplitude is 949.1 Pa), 7.4 s (amplitude is 227.9 Pa), 6.2 s (amplitude is 509.2 Pa), and 8.6 s (388.6 Pa). From the above paragraph, we can note that during the anomalous signal, the maximum amplitude is observed for the harmonic of the infragravity range, and before and after the anomalous signal, the harmonic of the gravity range has the maximum.

To clarify the nature of presence of anomalous signals, similar to those registered by the supersensitive detector of hydrosphere pressure variations in the Earth’s crust or in the atmosphere, we analyzed the laser strainmeter and laser nanobarograph records in the same time period. Figure 17 shows a section of the laser strainmeter record and Figure 18 shows a section of the laser nanobarograph record, both synchronous with Figure 16.

As we can see from Figure 17 and Figure 18, there are no anomalous amplitude signals similar to the anomalous signal shown in Figure 16 in the records of the laser strainmeter and laser nanobarograph. During spectral processing of the series shown in Figure 17 and Figure 18, maxima are distinguished at periods of about 5.5 and 3.5 min. In the above laser strainmeter record, there is also a peak of about 5 min. Thus, analyzing the records shown in Figure 16, Figure 17 and Figure 18, we can state that the oscillations singled out from the records of the laser strainmeter and laser nanobarograph at periods of about 5.5 min have the same origin, which, apparently, is associated with deformation processes, since they are not defined on the submersible instrument record. The oscillations singled out from the records of all three laser devices with periods of about 3.5 min have one source, apparently associated with atmospheric processes. Oscillations singled out from the record of the laser strainmeter and the supersensitive detector of hydrosphere pressure variations with period of about 5 min, apparently, are associated with infragravity sea waves of the shelf area of the Sea of Japan adjacent to Shultz Cape.

In the records of the supersensitive detector of hydrosphere pressure variations, classical examples of a solitary “three sisters” disturbance are observed; an example of one of them is shown in Figure 19. Spectral processing of record sections of the same size (2048 points at sampling frequency of 2 Hz) before the anomalous signal, during the anomalous signal, and after the anomalous signal showed that the records spectra before and after the anomalous signal are approximately the same in terms of total power, and the total power during the anomalous signal is 5–5.5 times greater. This happens due to appearance of infragravity signals with periods of about 5 min 25.7 s (amplitude is 11,443.4 Pa) and 3 min 21.9 s (amplitude is 7646.1 Pa) in the spectrum. In the gravity range, a peak with period 5.8 s (the amplitude is 1766.4 Pa) is distinguished. The signal processing was carried out using the maximum likelihood spectral method with 20 harmonics. When processing the section of the instrument record before the anomalous signal, maxima are observed with periods of 7.6 s (amplitude is 2106.1 Pa), 7.1 s (amplitude is 1807.2 Pa), 11.4 s (amplitude is 1762.2 Pa), and 13.7 s (the amplitude is 1636.9 Pa). In processing of the instrument record section after the anomalous signal, maxima are observed with periods of 11.5 s (amplitude is 2197.5 Pa), 12.4 s (amplitude is 1270.9 Pa), and 2 min 02.4 s (amplitude is 1784.7 Pa). From the above paragraph, we can note that during the anomalous signal, the maximum amplitude is observed for the harmonic of the infragravity range, and before and after the anomalous signal, the harmonic of the gravity range has the maximum.

To clarify the nature of presence of anomalous signals, similar to those registered by the supersensitive detector of hydrosphere pressure variations, in the Earth’s crust or in the atmosphere, we analyzed the laser strainmeter and laser nanobarograph records in the same time period. Figure 20 shows a section of the laser strainmeter record and Figure 21 shows a section of the laser nanobarograph record, both synchronous with Figure 19.

As we can see from Figure 20 and Figure 21, there are no anomalous amplitude signals similar to the anomalous signal shown in Figure 19 in the records of the laser strainmeter and laser nanobarograph.

4. Conclusions

Solitary nonlinear hydrophysical disturbances against the background of regular sea waves occur when quasi-harmonic soliton-like single, double, or triple signals with main infragravity periods of about 5.5, 5.0, 4.5, 3.5, and 2.5 min of large amplitude appear in this area. In relatively quiet time intervals and in various observation periods, oscillations with similar periods are distinguished, which we previously attributed to infragravity sea waves in this area of the Sea of Japan shelf. These quasi-harmonic solitary formations, “superimposed” on the surface wind waves, form solitary nonlinear hydrophysical disturbances of the “potential well”, “one sister”, “two sisters”, “three sisters” types.

The main distinguished nonlinear hydrophysical disturbances of large amplitude are caused by interaction of hydrophysical fields of different frequency ranges: gravity sea waves and hydrophysical disturbances of the infragravity range. We have established that during spectral processing of data on these nonlinear formations, the maximum energy is concentrated in the spectral components of the infragravity range, although in neighboring regions outside anomalous hydrophysical disturbances the maximum energy is concentrated on the spectral components of the gravity range.

Our measuring system was on the bottom of the sea at a depth of 25 m. We processed the in-situ data obtained from it. Therefore, all the results that we received during processing are “tied” to this depth. We did not consider the magnitudes of the registered waves of gravity and infragravity ranges, nor other registered disturbances, beyond the location of the measuring system, e.g., on the water surface. This is an almost unsolvable problem due to its complexity; despite attempts to solve it, we only can obtain approximate answers. For example, let us consider the waves of gravity range, i.e., wind or swell waves. When processing the anomalous fragment shown in Figure 3, we receive the following results: infragravity signals with periods of about 3 min 39.8 s (amplitude is 3373.3 Pa) and 1 min 18.4 s (amplitude is 3353.3 Pa) stand out; in the gravity range, a peak with period of 6.4 s (amplitude is 1445.9 Pa). If the period of 6.4 s is the period of a progressive wind wave (swell), then the height of the wave on the water surface can be determined approximately by the formula $a=\frac{Pch\left(2\pi h/\lambda \right)}{g\rho }$ [18] (where: $P$—pressure at the bottom, $h$—depth, $\lambda$—wavelength, $g$—acceleration of free fall in the place of the experiment, and $\rho$ is the density of sea water). Taking into account that the instrument is at an intermediate depth (the conditions of a shallow or deep sea are not met), the speed should be determined by the formula $c^2=\left(g\lambda /2\pi \right)th\left(2\pi h/\lambda \right)$; and with a known period and a calculated speed, we can determine the wavelength. This is not solved analytically. We can only get approximate solutions. However, we do not set such a task in the present work. There is one more thing. We consider a wave with a period of 6.4 s to be progressive, which is almost absolutely true. However, what if it is a standing wave, formed as a result of interaction of progressive waves with period of 12.8 s? Then the height of the wave on the water surface should be calculated by the formula $a=P/g\rho$. Everything said about the gravity sea waves also applies to the infragravity waves, and we know a lot less about those. Therefore, we limited ourselves to the results of processing the in-situ data with a “tie” to the location of the recording instrument, i.e., to the depth of 25 m.

Now let us dwell on the in-situ records of the instrument, shown in Figure 3, Figure 10, Figure 13, Figure 16 and Figure 19. In the synchronous records of atmosphere pressure variations (laser nanobarograph) and the Earth’s crust deformations (laser strainmeter) in the place of recording, there are no similar images. One can, of course, come up with a fantasy about special channels of these atmospheric or deformational disturbances’ propagation past the laser nanobarograph and the laser strainmeter. This only testifies to the fact that these anomalous signals were formed in the sea. Let us now discuss the magnitudes of these disturbances on the water surface. Figure 3 and Figure 13 show clear records of gravity sea waves (swell waves) before and after the anomalous disturbance. The instrument captured changes in hydrospheric pressure at the depth of 25 m, caused by various atmospheric and hydrospheric processes. These disturbances were not registered in the atmosphere. From the above, we can conclude that these anomalous signals generated in the water will also be observed on the water surface, together with gravity sea waves. Taking into account the duration of anomalous signals in Figure 3 and Figure 13, the magnitude on the water surface can be estimated by the formula $a=P/g\rho$. For other cases, with shorter duration of anomalous disturbances, these estimates may not be valid, and we will have to account for the law of the exponential drop in the amplitude of infragravity waves with depth. However, these tasks are the subject of further research. In addition, the space–time intervals and the duration of these disturbances are interesting, in which the nonlinearity compensates for the dispersion. It is also possible that these nonlinear disturbances are local in nature and do not propagate over long distances, “collapsing” due to a significant excess of nonlinearity over dispersion, and vice versa, “scattering” due to a significant excess of dispersion over nonlinearity.

In further studies, the main focus should be on determining the boundary conditions for formation of the nonlinear hydrophysical disturbances described above. In experimental (in situ) studies, the main attention should be paid to the peak of the amplitude–frequency values of gravity and infragravity sea waves, at which non-linear hydrophysical disturbances occur. Additionally, it is important to explore the “boundaries” between the nonlinear and linear behavior of waves in the gravity and infragravity ranges during their interaction. Considering that in the data of the laser strainmeter we did not find areas similar in behavior to the records of the supersensitive detector of hydrosphere pressure variations, containing nonlinear hydrophysical disturbances, it is necessary to establish the features of their propagation in the aquatic environment and the conditions for transformation at the interface between the media.