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Method of Studying Modulation Effects of Wind and Swell Waves on Tidal and Seiche Oscillations

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Journal of Marine Science and Engineering Article Method of Studying Modulation Effects of Wind and Swell Waves on Tidal and Seiche Oscillations Grigory Ivanovich Dolgikh 1,2,* and Sergey Sergeevich Budrin 1,2,* 1 V.I. Il’ichev Pacific Oceanological Institute, Far Eastern Branch Russian Academy of Sciences, 690041 Vladivostok, Russia 2 Institute for Scientific Research of Aerospace Monitoring “AEROCOSMOS”, 105064 Moscow, Russia * Correspondence: [email protected] (G.I.D.); [email protected] (S.S.B.) Abstract: This paper describes a method for identifying modulation effects caused by the interaction of waves with different frequencies based on regression analysis. We present examples of its applica- tion on experimental data obtained using high-precision laser interference instruments. Using this method, we illustrate and describe the nonlinearity of the change in the period of wind waves that are associated with wave processes of lower frequencies—12- and 24-h tides and seiches. Based on data analysis, we present several basic types of modulation that are characteristic of the interaction of wind and swell waves on seiche oscillations, with the help of which we can explain some peculiarities of change in the process spectrum of these waves. Keywords: wind waves; swell; tides; seiches; remote probing; space monitoring; nonlinearity; modulation 1. Introduction Citation: Dolgikh, G.I.; Budrin, S.S. The phenomenon of modulation of short-period waves on long waves is currently Method of Studying Modulation widely used in the field of non-contact methods for sea surface monitoring. These processes Effects of Wind and Swell Waves on are mainly investigated during space monitoring by means of analyzing optical [1,2] and Tidal and Seiche Oscillations. J. Mar. radar images [3,4] received from the satellites to restore the structure of the rough sea Sci. Eng. 2021, 9, 926. https:// surface. A two-scale model of the sea surface was used in analysis of radar images. The doi.org/10.3390/jmse9090926 effect of short waves was taken into account in the framework of the Bragg scattering mechanism, and the effect of the large-scale component is taken into account by changing Academic Editor: Lev Shemer the slope of the surface. As a result, the small-scale wave component turned out to be responsible for the backscattering of radar signals, and the large-scale component was Received: 19 June 2021 responsible for spatial modulation of the scattered signals [5,6]. Accepted: 22 August 2021 Of particular interest during remote probing of seas and oceans in these types of Published: 26 August 2021 research is the study of internal waves (IW) [7], current fields [8,9], and anthropogenic impacts on the aquatic environment [10]. Internal waves propagating in the ocean appear Publisher’s Note: MDPI stays neutral on the sea surface due to horizontal components of orbital velocities near the surface, which with regard to jurisdictional claims in published maps and institutional affil- lead to variations in the characteristics of short wind waves. Thus, on the sea surface, IWs iations. appear in the form of stripes and spots with increased (tidal rip) and decreased (slick) intensity of short gravity waves [11–13]. Modulation effects can occur in a wide range of wind waves. The modulation of wind waves can be described and explained within the kinematic mechanism framework [14], but there are also other theories [15,16]. For example, the authors of [17] propose a model where an increment modulation effect caused Copyright: © 2021 by the authors. by the variation of the wind speed field over the water surface on which there is a field Licensee MDPI, Basel, Switzerland. of currents generated by internal waves (IW) acts as the mechanism of this model. The This article is an open access article distributed under the terms and modulation effect of wind increments is being actively discussed nowadays [18]. conditions of the Creative Commons There are many works and studies devoted to modulation of infragravity (IG) waves. Attribution (CC BY) license (https:// For example, [19] presents the results of studying short IG length changes, while longer creativecommons.org/licenses/by/ waves move on the surface. In [20], the changes in wavelengths and amplitudes of a 4.0/). short-period wave process are carefully calculated with regard to the nonlinear interactions J. Mar. Sci. Eng. 2021, 9, 926. https://doi.org/10.3390/jmse9090926 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 926 2 of 13 between two wave processes. The change in the energy of short waves, in this case, corresponds to the effect of longer waves against the radiation stress of short waves, which was previously neglected. The radiation wave stress should be understood as an overflow of the impulse caused by wind waves, or, more exactly, by their nonlinearity. In [21], on the basis of field data and numerical models of sea surface gravity waves, it is shown that in the coastal zone during nonlinear wave-wave interaction, energy is transferred from low-frequency long waves back to higher-frequency motions. This explains the tidal modulation of the energy of IG waves, observed in the records of near-bottom pressure on the southern shelf of Sakhalin Island. Similar results were obtained in [22], where the strong tidal modulation of infragravity (200 to 20 s period) waves observed on the southern California shelf is shown to be the result of nonlinear transfers of energy from these low-frequency long waves to higher-frequency motions. What is interesting is question of the evolution of the wind wave spectrum, which has many mechanisms. For example, [23,24] describes the mechanism of change in the wave spectrum, while waves are going out to a shallow; in this case, due to nonlinear interactions with the bottom, the frequency of the wave process decreases. In [25], numerical and experimental studies of the process of nonlinear energy transfer between two main spectral maxima conditioned by the mechanism of dispersive focusing indicate that nonlinear energy transfer plays a greater role than linear superposition. There is also a large number of works devoted to the evolution of the wave spectrum associated with the modulation effect caused by the interaction of wind waves and swell waves [26,27]. In this paper, we will try to show how the effects of the modulation of wind waves at long waves, such as tides and seiches, can affect changes in the wave spectrum. We should also note the participation of modulation effects in the emergence of rogue waves. For example, in [28], it is stated that rogue waves (extreme waves) naturally originate as a result of evolution of spectrally narrow packets of gravity waves. We can say that rogue waves are a nonlinear stage of modulation instability. In [29], the Euler equation was solved for liquid with a free surface in deep water. Periodic and boundary conditions were created in the form of a Stokes wave, which was slightly modulated by a low frequency (10−5). At the same time, such a wave is unstable and modulation should increase with time, thereby generating an extremely high wave. This paper presents a method for studying the effects of modulation of wind and swell waves on tidal and seiche oscillations. This method was developed and tested on hydrophysical data obtained from high-precision, modern instruments based on laser interference methods [30]. The paper also presents the results of using this method for processing and analyzing experimental data, the results of which several main types of modulation of wind waves on seiche oscillations were identified and described. The possibility of introducing this method for processing hydrophysical data received in real time mode is being considered. All of the experimental data presented in this work were obtained using laser meters of hydrosphere pressure variations [31]. These devices were installed on the bottom for a period from several days to several months, transmitting data in real time to laboratory rooms located at Shultz Cape, the Sea of Japan, in the Primorsky Territory of the Russian Federation. There are also mobile versions of these devices, with which we conduct measurements of tidal and seiche oscillations in various harbors of the Posiet Bay and the Peter the Great Gulf of the Sea of Japan. Although most of the data presented were obtained in Vityaz Bay, the Sea of Japan, we also analyzed and compared the results obtained in other bays. Thus, the presented results will be valid for other closed water areas of the World Ocean. 2. Wave Modulation Research Method As we know, the main change in the period of swell waves during propagation from the point of generation occurs due to dispersion during propagation; this change in the period is linear and has a decreasing character. However, if we consider large time-scale J. Mar. Sci. Eng. 2021, 9, 926 3 of 13 phenomena, such as typhoons, which originate hundreds of kilometers from the place of registration, the process of swell wave propagation can take several days. Additionally, in addition to dispersion, waves can be influenced by both large-scale phenomena, such as tides, and local phenomena, such as seiche oscillations that occur in closed sea areas and, as a result of these phenomena, the process of changing the period becomes nonlinear. At the same time, in order to study the emerging nonlinear processes, it is first necessary to separate the process of changing the period associated with dispersion from other processes that affect the variations in the period of wind waves and swell waves. Earlier, from the fragments of the record, which contained swell waves created by passing typhoons, we derived the general function of period change [32,33].
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