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TRINES, R. M. G. M., R. BINGHAM, L. O. SILVA, J. T. MENDONÇA, P. K. SHUKLA, C. D. MURPHY, M. W. DUNLOP i in. "Applications of the wave kinetic approach: from laser wakefields to drift wave turbulence". Journal of Plasma Physics 76, nr 6 (17.08.2010): 903–14. http://dx.doi.org/10.1017/s0022377810000449.
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AbstractNonlinear wave-driven processes in plasmas are normally described by either a monochromatic pump wave that couples to other monochromatic waves, or as a random phase wave coupling to other random phase waves. An alternative approach involves a random or broadband pump coupling to monochromatic and/or coherent structures in the plasma. This approach can be implemented through the wave-kinetic model. In this model, the incoming pump wave is described by either a bunch (for coherent waves) or a sea (for random phase waves) of quasi-particles. This approach has been applied to both photon acceleration in laser wakefields and drift wave turbulence in magnetized plasma edge configurations. Numerical simulations have been compared to experiments, varying from photon acceleration to drift mode-zonal flow turbulence, and good qualitative correspondences have been found in all cases.
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Riedel, Hans Peter, i Anthony Paul Byrne. "RANDOM BREAKING WAVES HORIZONTAL SEABED". Coastal Engineering Proceedings 1, nr 20 (29.01.1986): 68. http://dx.doi.org/10.9753/icce.v20.68.
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According to wave theories the depth limited wave height over a horizontal seabed has a wave height to water depth ratio (H/d) of about 0.8. Flume experiments with monochromatic waves over a horizontal seabed have failed to produce H/d ratios greater than 0.55. However designers still tend to use H/d 0.8 for their design waves. Experiments have been carried out using random wave trains in the flume over a horizontal seabed. These experiments have shown that the limiting H/d ratio of 0.55 applies equally well to random waves.
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Vladimirov, SV, i SI Popel. "Modulational Interactions of Two Monochromatic Waves and Packets of Random Waves". Australian Journal of Physics 47, nr 4 (1994): 375. http://dx.doi.org/10.1071/ph940375.
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The modulational instability of Langmuir waves in unmagnetised plasmas is reviewed for the cases when a pump consist of two monochromatic or a large number of random modes. It is demonstrated that the correct theory for the modulational instability operates with 'renormalised' equations for the linear dielectric function as well as for the effective third-order plasma response. This renormalisation is due to so-called interference terms. The appearance of interference terms is a specific feature of the multi-mode modulational instability in comparison with the well-known instability of a single mode. All calculations use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. The modulational instability of two pump Langmuir modes is considered for the case of comparatively small instability rates, when 'renormalised' expressions for linear and nonlinear plasma polarisation responses provide the maximum effect on the instability development. For instabilities of the broad spectra of random waves, the integral equations are presented for perturbations of wave field correlation functions. In the description of the modulational instability of random wave packets these equations play the same role as the set of coupled equations for the fields of modulational perturbations in the case of two monochromatic pumps. Rates and thresholds of the instabilities are found in various limits.
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Truitt, Clifford L., i John B. Herbich. "TRANSMISSION OF RANDOM WAVES THROUGH PILE BREAKWATERS". Coastal Engineering Proceedings 1, nr 20 (29.01.1986): 169. http://dx.doi.org/10.9753/icce.v20.169.
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Several previous investigators have conducted experiments leading to expressions for predicting the transformation of waves passing through closely-spaced pile breakwaters. The present study extends those earlier experiments using monochromatic waves to the case of a spectrum of random waves. Records of incident waves and of waves after transmission through a model pile breakwater were compared to determine a coefficient of transmission. Results are presented for several cases of pile spacing and pile diameter. Good agreement is found between observed transmission coefficients and those predicted using the expression proposed by Hayashi et al. (1966).
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Eadie, Robert W., i John B. Herbich. "SCOUR ABOUT A SINGLE, CYLINDRICAL PILE DUE TO COMBINED RANDOM WAVES AND A CURRENT". Coastal Engineering Proceedings 1, nr 20 (29.01.1986): 136. http://dx.doi.org/10.9753/icce.v20.136.
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There have been many studies of scour around piles caused by waves, and some studies of scour by waves and currents combined. However, almost all of the studies were conducted with monochromatic waves. The purpose of this investigation was to study what scouring effects various currents and random waves have on a single, cylindrical pile. These results were then compared with the results from previous studies of scour resulting from currents and monochromatic waves at Texas A&M University (Armbrust, 1982 and Wang, 1983). Experiments were conducted in a two-dimensional wave tank. The pile used in this study had a diameter of 1.5 inches. Two water depths, four currents, one sediment size and four random wave spectra were utilized. Using data obtained from the experiments, an attempt was made to describe scour in terms of relevant dimensionless parameters.
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Romaniega, Álvaro, i Andrea Sartori. "Nodal set of monochromatic waves satisfying the Random Wave Model". Journal of Differential Equations 333 (październik 2022): 1–54. http://dx.doi.org/10.1016/j.jde.2022.05.023.
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Jung, Jae-Sang, i Changhoon Lee. "Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction". Journal of Korean Society of Coastal and Ocean Engineers 33, nr 6 (31.12.2021): 275–86. http://dx.doi.org/10.9765/kscoe.2021.33.6.275.
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In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.
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Canzani, Yaiza, i Boris Hanin. "Local Universality for Zeros and Critical Points of Monochromatic Random Waves". Communications in Mathematical Physics 378, nr 3 (12.08.2020): 1677–712. http://dx.doi.org/10.1007/s00220-020-03826-w.
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Canzani, Yaiza, i Peter Sarnak. "Topology and Nesting of the Zero Set Components of Monochromatic Random Waves". Communications on Pure and Applied Mathematics 72, nr 2 (15.10.2018): 343–74. http://dx.doi.org/10.1002/cpa.21795.
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Ingremeau, Maxime, i Alejandro Rivera. "A lower bound for the Bogomolny–Schmit constant for random monochromatic plane waves". Mathematical Research Letters 26, nr 4 (2019): 1179–86. http://dx.doi.org/10.4310/mrl.2019.v26.n4.a9.
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Hatzakis, Iason, i Paul D. Sclavounos. "Active Motion Control of High-Speed Hydrofoil Vessels by State-Space Methods". Journal of Ship Research 50, nr 01 (1.03.2006): 49–62. http://dx.doi.org/10.5957/jsr.2006.50.1.49.
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Hydrofoil ships cruising at high speeds often operate in rough weather conditions and hence experience uncomfortable or even unsafe motions without the use of some form of motion control. The research described here concerns an active motion control mechanism for high-speed hydrofoil vessels, aiming at the significant reduction of the vessel motions in regular and random waves. The seakeeping equations of motion are cast into a linear state-space form leading to a linear-quadratic optimal controller shown to attenuate the vessel motion responses significantly. The deterministic control laws designed in the present study are found to perform satisfactorily both in monochromatic and random waves for high-speed vessels supported by hydrofoils and buoyancy.
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Nachbin, A., i G. C. Papanicolaou. "Water waves in shallow channels of rapidly varying depth". Journal of Fluid Mechanics 241 (sierpień 1992): 311–32. http://dx.doi.org/10.1017/s0022112092002052.
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We analyse the linear water-wave equations for shallow channels with arbitrary rapidly varying bottoms. We develop a theory for reflected waves based on an asymptotic analysis for stochastic differential equations when both the horizontal and vertical scales of the bottom variations are comparable to the depth but small compared to a typical wavelength so the shallow water equations cannot be used. We use the full, linear potential theory and study the reflection–transmission problem for time-harmonic (monochromatic) and pulse-shaped disturbances. For the monochromatic waves we give a formula for the expected value of the transmission coefficient which depends on depth and on the spectral density of the O(1) random depth perturbations. For the pulse problem we give an explicit formula for the correlation function of the reflection process. We compare our theory with numerical results produced using the boundary-element method. We consider several realizations of the bottom profile, let a Gaussian-shaped disturbance propagate over each topography sampled and record the reflected signal for each realization. Our numerical experiments produced reflected waves whose statistics are in good agreement with the theory.
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Henry, Pierre-Yves, Alf Tørum, Øivind Artsen, Dag Myrhaug i Muk Chen Ong. "PROBABILITY OF EXCEEDING THE CRITICAL SHEAR STRESS FOR SAND MOTION IN SPECIFIC WAVE AND CURRENT CONDITIONS". Coastal Engineering Proceedings 1, nr 33 (15.10.2012): 4. http://dx.doi.org/10.9753/icce.v33.sediment.4.
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This study is focusing on the threshold of sand motion under random waves combined with a following current. The analysis is based on some flume experiments realized over a natural sand bed for different flow conditions (waves and currents). The main result comes as a map of the probability to exceed the threshold of sand motion, as a function of a wave and a current mobility parameter. These observations are compared to methods predicting the bed shear stress using an equivalent monochromatic wave, and links between the probability of exceeding the critical shear stress for initiation of sand motion and the calculated maximum bed shear stress are found.
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Gogin, Aleksandr G., i Izmail G. Kantarzhi. "Numerical simulation of sea-wave diffraction with random phases on breakwaters". Vestnik MGSU, nr 4 (kwiecień 2023): 615–26. http://dx.doi.org/10.22227/1997-0935.2023.4.615-626.
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Introduction. Numerical simulation of sea gravity waves interaction with seaport barriers using modern numerical wave models is considered. The predictive power of some commonly used models is examined in relation to the diffraction of sea waves with a random phase in comparison with known analytical methods and experimental data.
Materials and methods. Numerical simulation is carried out using modern numerical wave models implemented in the DHI MIKE 21 software package. A spectral wave model with a function for correcting wave diffraction in shallow water and a phase-resolving wave model based on the Boussinesq equations are used.
Results. Distribution of diffraction coefficients behind the breakwaters of the conventional port water area has been obtained for all models. As a result of the comparison, it was found that models of irregular waves (waves with random phases) have better wave energy distribution behind the breakwaters as compared to regular (monochromatic) wave models. It is noted that the type of frequency distribution of random waves has almost no effect on the diffraction coefficients of the water area, while the angular distribution, on the contrary, has a significant effect.
Conclusions. The wave model based on the Boussinesq equations in the irregular wave approximation is determined as the numerical wave model with the best predictive ability. The spectral wave model with diffraction correction function, which is less demanding on computer power, also made it possible to obtain results close to the reference ones. It is confirmed that regular wave propagation modelling of sea waves can give incorrect results in those seaport water areas where wave diffraction effects are strong.
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Selvam, R. Panneer, i S. K. Bhattacharyya. "System Identification of a Coupled Two DOF Moored Floating Body in Random Ocean Waves". Journal of Offshore Mechanics and Arctic Engineering 128, nr 3 (23.12.2005): 191–202. http://dx.doi.org/10.1115/1.2199557.
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Dynamics of a large moored floating body in ocean waves involves frequency dependent added mass and radiation damping as well as the linear and nonlinear mooring line characteristics. Usually, the added mass and radiation damping matrices can be estimated either by potential theory-based calculations or by experiments. The nonlinear mooring line properties are usually quantified by experimental methods. In this paper, we attempt to use a nonlinear system identification approach, specifically the reverse multiple input-single output (R-MISO) method, to coupled surge-pitch response (two-degrees-of-freedom) of a large floating system in random ocean waves with linear and cubic nonlinear mooring line stiffnesses. The system mass matrix has both frequency independent and frequency dependent components whereas its damping matrix has only frequency dependent components. The excitation force and moment due to linear monochromatic waves which act on the system are assumed to be known that can either be calculated or obtained from experiments. For numerical illustration, a floating half-spheroid is adopted. The motion as well as the loading are simulated assuming Pierson-Moskowitz (PM) spectrum and these results have been analyzed by the R-MISO method yielding frequency dependent coupled added mass and radiation damping coefficients, as well as linear and nonlinear stiffness coefficients of mooring lines satisfactorily.
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Lei, Y., S. X. Zhao, X. Y. Zheng i W. Li. "Effects of Fish Nets on the Nonlinear Dynamic Performance of a Floating Offshore Wind Turbine Integrated with a Steel Fish Farming Cage". International Journal of Structural Stability and Dynamics 20, nr 03 (marzec 2020): 2050042. http://dx.doi.org/10.1142/s021945542050042x.
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This paper aims to study the effects of fish nets on the nonlinear dynamic performance of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC). Fully coupled aero-hydro-servo-elastic numerical models of FOWT-SFFC, with and without nets, are constructed to probe the nonlinear time-domain stochastic response. The first-order potential flow model with quadratic drag forces is employed to calculate the hydrodynamic loading on the foundation. The effects of nets on the damping ratios of 6 degree-of-freedom motions and on their displacement response amplitude operators (RAOs) are respectively investigated in numerical decay tests and monochromatic regular waves. The results show that the nets help to increase the damping level for the whole system and reduce motion RAOs when wave periods are around the natural periods of motions, while nets play insignificant role in motions when wave periods are far away from motion natural periods. The dynamic performances of FOWT-SFFC with and without nets under random ocean waves, the combined random wind and random waves as well as current are comprehensively compared and discussed. The simulation results indicate that in wind-sea dominated conditions, the nets tend to slightly increase the dynamic responses of FOWT-SFFC, especially the components corresponding to natural periods. Nonetheless, under sea states that comprise both wind-sea waves and swell, nets help to reduce the dynamic responses of FOWT-SFFC by introducing additional damping.
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Emmerhoff, O. J., i P. D. Sclavounos. "The slow-drift motion of arrays of vertical cylinders". Journal of Fluid Mechanics 242 (wrzesień 1992): 31–50. http://dx.doi.org/10.1017/s002211209200226x.
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The large-amplitude rectilinear ‘slow-drift’ oscillation of a floating body constrained by a weak restoring force in random waves is considered. The free-surface flow is approximated by a perturbation series expansion for a small slow-drift velocity and wave steepness. A model slow-drift equation of motion is derived, the time-dependent slow-drift excitation force and wave damping coefficient are defined and the complete series of free-surface problems governing their magnitude are formulated. The free-surface problem governing the wave-drift damping coefficient in monochromatic waves is studied and an explicit solution is obtained for a vertical circular cylinder of infinite draught. This solution is extended for arrays of vertical circular cylinders by employing an exact interaction theory. The wave-drift damping coefficient is evaluated for configurations of interest in practice and an expression is derived for the steady drifting velocity of an unconstrained body in regular waves.
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Herbich, John B., i Barry Douglas. "WAVE TRANSMISSION THROUGH A DOUBLE-ROW PILE BREAKWATER". Coastal Engineering Proceedings 1, nr 21 (29.01.1988): 165. http://dx.doi.org/10.9753/icce.v21.165.
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Several previous investigators have conducted experiments leading to expressions for predicting the transformation of waves passing through closely-spaced pile or large cylinder breakwaters. The present study extends the earlier experiments which used a single row of piles instead of a double row of piles forming a breakwater. The experiments using the double-pile breakwater were performed in the same facility as the experiments conducted on a single-pile breakwater and employed the same method of analysis for a more meaningful comparison. The experiments consisted of allowing waves to pass through a pile array and measuring the incident and transmitted wave heights. The variables were: depth, period, diameter, monochromatic and random waves. The experimental matrix was three water depths, four wave periods, two pile diameters, two gap dimensions between piles and four random wave spectra: Darbyshire, I.T.T.C., Pierson- Moskowitz and JONSWAP, two pile diameters and two gap dimensions between piles. The two-row breakwater had less wave transmission than the single-row breakwater, as expected. For a gap to a pile diameter ratio, or b/D = 0.2 (where b = gap spacing, D — pile diameter), the wave transmission was reduced by 15 percent, as compared with a single-row breakwater; for a gap ratio of b/D - 0.1, the wave transmission was reduced by 5 to 10 percent.
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Stive, M. J. F. "A MODEL FOR CROSS-SHORE SEDIMENT TRANSPORT". Coastal Engineering Proceedings 1, nr 20 (29.01.1986): 114. http://dx.doi.org/10.9753/icce.v20.114.
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A model for cross-shore sediment transport due to random waves is described which adopts a vertically integrated transport description for sheetflow situations. The formulation of the transport as a function of the instantaneous velocity field is based on the approach of Bailard (1981). This approach assumes in essence that the instantaneous transport is proportional to some power of the instantaneous near-bottom velocity. Implementation of this transport description in a time-dependent model requires a formulation of the time-mean and some low order moments of the near-bottom velocity field. An initial formulation based on a monochromatic, second order Stokes wave representation is presented. The model is checked on the basis of both field and laboratory data. Some consequences for further study are indicated.
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Nguyen, Duoc, Niels Jacobsen i Dano Roelvink. "Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method". Journal of Marine Science and Engineering 9, nr 1 (13.01.2021): 76. http://dx.doi.org/10.3390/jmse9010076.
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This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.
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Afanasyev, A. N., T. Van Doorsselaere i V. M. Nakariakov. "Excitation of decay-less transverse oscillations of coronal loops by random motions". Astronomy & Astrophysics 633 (styczeń 2020): L8. http://dx.doi.org/10.1051/0004-6361/201937187.
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Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation. Aims. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. Methods. With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise. Results. We found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and the generation of multiple harmonics detected recently. Conclusions. We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.
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Sharifineyestani, Elham, i Navid Tahvildari. "Nonlinear Wave Evolution in Interaction with Currents and Viscoleastic Muds". Journal of Marine Science and Engineering 9, nr 5 (14.05.2021): 529. http://dx.doi.org/10.3390/jmse9050529.
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A numerical model is extended to investigate the nonlinear dynamics of surface wave propagation over mud in the presence of currents. A phase-resolving frequency-domain model for wave-current interaction is improved to account for wave modulations due to viscoelastic mud of arbitrary thickness. The model compares well with published laboratory data and performs slightly better than the model with viscous mud-induced wave damping mechanism. Monochromatic and random wave simulations are conducted to examine the combined effect of currents, mud-induced wave dissipation and modulation, and nonlinear wave-wave interactions on surface wave spectra. Results indicate that current effects on wave damping over viscoelastic mud is not as straightforward as that over viscous mud. For example, while opposing currents consistently increase damping of random waves over viscous mud, they can decrease damping over viscoelastic mud due to high variations in frequency-dependent damping stemming from mud’s elasticity. It is shown that a model that assumes the mud layer to be thin for simplification can overestimate wave damping over thick mud layers.
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Lee, Jong-In, Young-Taek Kim i Sungwon Shin. "Experimental Studies on Wave Interactions of Partially Perforated Wall under Obliquely Incident Waves". Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/954174.
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This study presents wave height distribution in terms of stem wave evolution phenomena on partially perforated wall structures through three-dimensional laboratory experiments. The plain and partially perforated walls were tested to understand their effects on the stem wave evolution under the monochromatic and random wave cases with the various wave conditions, incident angle (from 10 to 40 degrees), and configurations of front and side walls. The partially perforated wall reduced the relative wave heights more effectively compared to the plain wall structure. Partially perforated walls with side walls showed a better performance in terms of wave height reduction compared to the structure without the side wall. Moreover, the relative wave heights along the wall were relatively small when the relative chamber width is large, within the range of the chamber width in this study. The wave spectra showed a frequency dependency of the wave energy dissipation. In most cases, the existence of side wall is a more important factor than the porosity of the front wall in terms of the wave height reduction even if the partially perforated wall was still effective compared to the plain wall.
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Kaiktsis, Lambros, George Em Karniadakis i Steven A. Orszag. "Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step". Journal of Fluid Mechanics 321 (25.08.1996): 157–87. http://dx.doi.org/10.1017/s0022112096007689.
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A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds numberRe= 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up toRe= 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ]Re[les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.
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Perrard, Stéphane, Adrián Lozano-Durán, Marc Rabaud, Michael Benzaquen i Frédéric Moisy. "Turbulent windprint on a liquid surface". Journal of Fluid Mechanics 873 (28.06.2019): 1020–54. http://dx.doi.org/10.1017/jfm.2019.318.
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We investigate the effect of a light turbulent wind on a liquid surface, below the onset of wave generation. In that regime, the liquid surface is populated by small disorganised deformations elongated in the streamwise direction. Formally identified recently by Paquier et al. (Phys. Fluids, vol. 27, 2015, art. 122103), the deformations that occur below the wave onset were named wrinkles. We provide here a theoretical framework for this regime, using the viscous response of a free liquid surface submitted to arbitrary normal and tangential interfacial stresses at its upper boundary. We relate the spatio-temporal spectrum of the surface deformations to that of the applied interfacial pressure and shear stress fluctuations. For that, we evaluate the spatio-temporal statistics of the turbulent forcing using direct numerical simulation of a turbulent channel flow, assuming no coupling between the air and the liquid flows. Combining theory and numerical simulation, we obtain synthetic wrinkles fields that reproduce the experimental observations. We show that the wrinkles are a multi-scale superposition of random wakes generated by the turbulent fluctuations. They result mainly from the nearly isotropic pressure fluctuations generated in the boundary layer, rather than from the elongated shear stress fluctuations. The wrinkle regime described in this paper naturally arises as the viscous-saturated asymptotic of the inviscid growth theory of Phillips (J. Fluid Mech., vol. 2 (05), 1957, pp. 417–445). We finally discuss the possible relation between wrinkles and the onset of regular quasi-monochromatic waves at larger wind velocity. Experiments indicate that the onset of regular waves increases with liquid viscosity. Our theory suggests that regular waves are triggered when the wrinkle amplitude reaches a fraction of the viscous sublayer thickness. This implies that the turbulent fluctuations near the onset may play a key role in the triggering of exponential wave growth.
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ARDHUIN, FABRICE, i RUDY MAGNE. "Scattering of surface gravity waves by bottom topography with a current". Journal of Fluid Mechanics 576 (28.03.2007): 235–64. http://dx.doi.org/10.1017/s0022112006004484.
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A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.
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Pinkel, Robert. "Advection, Phase Distortion, and the Frequency Spectrum of Finescale Fields in the Sea". Journal of Physical Oceanography 38, nr 2 (1.02.2008): 291–313. http://dx.doi.org/10.1175/2007jpo3559.1.
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Abstract Continuous depth–time measurements of upper-ocean velocity are used to estimate the wavenumber–frequency spectrum of shear. A fundamental characteristic of these spectra is that the frequency bandwidth increases linearly with increasing wavenumber magnitude. This can be interpreted as the signature of Doppler shifting of the observations by time-changing “background” currents as well as by instrument motion. Here, the hypothesis is posed that the apparently continuous wavenumber–frequency spectrum of oceanic shear results from the advective “smearing” of discrete spectral lines. In the Arctic Ocean, lines at the inertial (ω = −f ) and vortical (ω = 0) frequencies (where f is the Coriolis frequency) account for most of the variance in the shear spectrum. In the tropical ocean, two classes of inertial waves are considered, accounting for 70% of the observed shear variance. A simple model is introduced to quantify the effects of lateral advection, random vertical advection (“fine-structure contamination”), and deterministic (tidal) vertical advection on these “otherwise monochromatic” records. Model frequency spectra are developed in terms of the probability density and/or spectrum of the advecting fields for general but idealized situations. The model successfully mimics the increasing frequency bandwidth of the shear spectrum with increasing vertical wavenumber. Excellent fits to the observed frequency spectrum of shear are obtained for the Arctic (weak advection and short-spatial-scale inertial waves) and low-latitude (strong advection and long and short inertial waves) observations. While successfully replicating the wavenumber–frequency spectrum of shear, the model does not even consider motion at scales greater than ∼250 m, the “energy containing” scales of the internal wave field. To a first approximation, the waves with the majority of the kinetic and potential energy constitute a population apart from those with the momentum, shear, and strain.
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Serhiienko, S. P., V. G. Krizhanovski, D. V. Chernov i L. V. Zagoruiko. "The use of non-steady state noise interferences to counteract passive eavesdropping devices". Radiotekhnika, nr 207 (24.12.2021): 132–38. http://dx.doi.org/10.30837/rt.2021.4.207.14.
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The use of noise interference has become a common practice for information security. Recently appeared publications showing a potential possibility to use the noise radio frequency interference for information skimming by passive radio eavesdropping device. In particular, the vulnerability of the premises protected from eavesdropping devices is increased, if the radio frequency noising is switched on when confidential negotiations are being conducted. The use of radio noise waves energy for eavesdropping makes such devices invisible to nonlinear locators for listening devices if they activated only by noise signals. The paper shows that the use of non-steady state noise allows counteracting the unauthorized pickup of information. The analysis of non-steady state radio frequency noise effectiveness was carried out using the correlation receiver model. The correlation receiver has the highest sensitivity, and it works more efficiently with noise-like signals. It is shown that for counteracting the information pickup, it is necessary to use a noise, amplitude modulated by a random signal, whose spectrum coincides with a spectrum of a potential informational signal. Imposition a more powerful modulation noise to a weak informational signal makes impossible the information transfer. It is shown on the example of changing the power of a monochromatic signal while “beetle” transmits using steady-state and non-steady state noises, that due to the signal energy parametric redistribution over the non-steady-state noise modulation spectrum, the power of monochromatic signal is reduced by more than 10 dB compared to the transmission of the same signal using a steady-state noise. It can be concluded that the use of non-steady state noise signals for radio frequency suppression makes impossible their use for passive eavesdropping devices operation.
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Raghukumar, Kaustubha, Grace Chang, Frank Spada, Craig Jones, Tim Janssen i Andrew Gans. "Performance Characteristics of “Spotter,” a Newly Developed Real-Time Wave Measurement Buoy". Journal of Atmospheric and Oceanic Technology 36, nr 6 (czerwiec 2019): 1127–41. http://dx.doi.org/10.1175/jtech-d-18-0151.1.
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AbstractThe Spotter is a low-cost, real-time, solar-powered wave measurement buoy that was recently developed by Spoondrift Technologies, Inc. (Spoondrift). To evaluate the data quality of the Spotter device, we performed a series of validation experiments that included comparisons between Spotter-derived motions and prescribed wave motions (monochromatic and random waves) on a custom-built, motion-controlled validation stand and simultaneous in-water measurements using a conventional wave measurement buoy, the Datawell DWR-G4 (Datawell). Spotter evaluations included time-domain validation (i.e., wave by wave) and comparisons of wave spectra, directional moments, and bulk statistical parameters such as significant wave height, peak period, mean wave direction, and directional spread. Spotter wave measurements show excellent fidelity and lend a high degree of confidence in data quality. Overall, Spotter-derived bulk statistical parameters were within 10% of respective Datawell-derived quantities. The Spotter’s low cost and compact form factor enabled unique field deployments of multiple wave measurement buoys for direct measurements of wave characteristics such as ocean wave decorrelation length scales, wave speed, and directional spread. Wave decorrelation lengths were found to be inversely proportional to the width of the spectrum, and wave speeds compared well against linear wave theory.
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Herrera-Vázquez, Carlos F., Nicolas Rascle, Francisco J. Ocampo-Torres, Pedro Osuna i Héctor García-Nava. "On the Measurement of Ocean Near-Surface Current from a Moving Buoy". Journal of Marine Science and Engineering 11, nr 8 (1.08.2023): 1534. http://dx.doi.org/10.3390/jmse11081534.
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This paper studies the error that occurs when measuring surface currents with a current meter mounted on a buoy or a mooring line whose horizontal and vertical motions respond to the presence of waves. The error is defined with respect to an Eulerian reference measurement where the sensor does not move. First, we present the subject with a theoretical analysis in the case of a monochromatic wave. That idealized model allows us to study particular sensor or mooring line motions. Second, a realistic numerical model is implemented to reconstruct the current field with a high resolution near the surface. Wave orbital velocities are generated with a random phase model. An Ekman-type current, uniform in the horizontal but with a vertical shear, is also incorporated. The results indicate that the error in the current measurement is highly dependent on the sensor motion induced by waves. The error magnitude is proportional to the wave momentum or Stokes drift and depends on the wave development state and the wind-generated current’s magnitude. The error obtained in the current measurement is analyzed by considering that the buoy only responds to low-frequency waves up to a maximum frequency. That maximum frequency is referenced concerning the peak frequency of the third moment of the spectrum (i.e., the Stokes drift spectrum). It allows us to classify the current time average into three ranges with respect to the maximum frequency: (1) Eulerian average, (2) wave-following average, and (3) intermediate case of undulating average where results cannot be generalized. The measurement error is most important in the region above the wave troughs. However, the error is also considerable in the region confined below the wave troughs and down to the Stokes drift e-folding depth. The error is particularly relevant in conditions of developed and energetic waves (Hs>3 m), where the surface Stokes drift can reach values above 0.1 m/s. It should be noted that measurement error can exceed the value of the Stokes drift at the sensor depth for certain mooring line motions. Those results should help better interpret in situ near-surface current measurements obtained from various devices.
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Bracewell, RN. "Sunspot Number Series Envelope and Phase". Australian Journal of Physics 38, nr 6 (1985): 1009. http://dx.doi.org/10.1071/ph851009.
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The sunspot number series R( t) from 1700 to date is found to be representable by R( t) = I Jf' {Re( E( t) exp[i {wo t + ( t) I]) + U( t) 1 I, where Wo is the angular frequency corresponding to a period of 22 years, E(t) is the instantaneous envelope amplitude, (t) is the instantaneous phase of a complex time-varying analytic function, U(t) is an undulation of low amplitude and period about 30 (22-year) cycles and jy is a nonlinear operator whose main effect is to introduce a small amount of third harmonic (period about 7 years). The justification for the 22-year period is the known fact that the observable sunspot magnetic fields reverse polarity every 11 years or so at the time of sunspot minimum; the undulation has been demonstrated, and its period determined, in fossil records discovered by Williams; and the third harmonic is an expected consequence of minor nonlinearity in the dependence of the arbitrarily defined R( t) on the physical cause of sunspots. The algebraic representation is established by the Hilbert transform method of forming a complex analytic function as proposed by Gabor. The method reveals three obscuring features that may be alleviated as follows: use the alternating series R� (t) in which alternate II-year cycles take opposite signs, remove the third harmonic, and subtract the undulation. These justifiable steps remove artificial components, such as sum and difference frequencies, that are gratuitously and nonlinearly introduced by conventional Fourier analysis as applied to the rectified, or absolute, value of the 22-year oscillation. Then a complex envelope E( t) exp {i ( t)j can be discerned whose intrinsic behaviour can be studied to reveal statistics that bear on the physical origin of the solar cycle. The results favour a deep monochromatic oscillator whose influence is propagated to the observable surface via a time-varying medium. The r.m.s. value of the component of E(t) is 0�4 of the mean and the characteristic time is a century. Frequency analysis of the envelope does not support a 78-year period in the modulation noticed by Wolf. Both the statistical frequency distribution of the amplitude E( t) and its spectrum are subject to refinement by analysis of fossil solar records. The results do not favour the theory that the 22-year period is set by the natural frequency of a resonator with characteristic damping subject to random turbulent excitation. Also disfavoured is the theory of energy release at intervals determined by a relaxation process. Correlation has been found between the phase departure ~(t) from linear and envelope amplitude and attributed to propagation of the magnetic .cycles through a time-varying, such as a convecting, medium. A correlation not depending on Hilbert transform analysis is predicted between the reciprocal cycle length and envelope amplitude and found to� exist. Variability of the sunspot cycle length can be viewed as a Doppler shift due to propagation in a time-varying medium and the Wolf modulation then represents the concomitant intensity change. Agreement has been found between E(t) and '(t) but not explained. If the explanation is dispersion in the propagation of the assumed magnetic flux waves then there is a mode of oscillation. that has the characteristics required for the undulation U( t). Extra buoyancy possessed by the magnetic field of strong cycles accounts for the fast rise time of strong cycles.
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Enciso, Alberto, Daniel Peralta-Salas i Álvaro Romaniega. "Asymptotics for the Nodal Components of Non-Identically Distributed Monochromatic Random Waves". International Mathematics Research Notices, 29.07.2020. http://dx.doi.org/10.1093/imrn/rnaa178.
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Abstract We study monochromatic random waves on ${\mathbb{R}}^n$ defined by Gaussian variables whose variances tend to zero sufficiently fast. This has the effect that the Fourier transform of the monochromatic wave is an absolutely continuous measure on the sphere with a suitably smooth density, which connects the problem with the scattering regime of monochromatic waves. In this setting, we compute the asymptotic distribution of the nodal components of random monochromatic waves, showing that the number of nodal components contained in a large ball $B_R$ grows asymptotically like $R/\pi $ with probability $p_n>0$ and is bounded uniformly in $R$ with probability $1-p_n$ (which is positive if and only if $n\geqslant 3$). In the latter case, we show the existence of a unique noncompact nodal component. We also provide an explicit sufficient stability criterion to ascertain when a more general Gaussian probability distribution has the same asymptotic nodal distribution law.
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Vittori, Giovanna, Paolo Blondeaux, Giovanni Coco i R. T. Guza. "Subharmonic edge wave excitation by narrow-band, random incident waves". Journal of Fluid Mechanics 868 (12.04.2019). http://dx.doi.org/10.1017/jfm.2019.214.
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A monochromatic, small amplitude, normally incident standing wave on a sloping beach is unstable to perturbation by subharmonic (half the frequency) edge waves. At equilibrium, edge wave shoreline amplitudes can exceed incident wave amplitudes. Here, the effect of incident wave randomness on subharmonic edge wave excitation is explored following a weakly nonlinear stability analysis under the assumption of narrow-band incident random waves. Edge waves respond to variations in both incident wave phase and amplitude, and the edge wave amplitudes and incident wave groups vary on similar time scales. When bottom friction is included, intermittent subharmonic edge wave excitation is predicted due to the combination of bottom friction and wave phase. Edge wave amplitude can be near zero for long times, but for short periods reaches relatively large values, similar to amplitudes with monochromatic incident waves and no friction.
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de Courcy-Ireland, Matthew. "Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds". International Mathematics Research Notices, 29.02.2020. http://dx.doi.org/10.1093/imrn/rnaa042.
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Abstract We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With high probability, equidistribution takes place close to the optimal wave scale and simultaneously over the whole manifold. The proof uses Weyl’s law to approximate the two-point correlation function of the ensemble, and a Chernoff bound to deduce concentration.
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Enciso, Alberto, Daniel Peralta-Salas i Álvaro Romaniega. "Beltrami fields exhibit knots and chaos almost surely". Forum of Mathematics, Sigma 11 (2023). http://dx.doi.org/10.1017/fms.2023.52.
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Abstract In this paper, we show that, with probability $1$ , a random Beltrami field exhibits chaotic regions that coexist with invariant tori of complicated topologies. The motivation to consider this question, which arises in the study of stationary Euler flows in dimension 3, is V.I. Arnold’s 1965 speculation that a typical Beltrami field exhibits the same complexity as the restriction to an energy hypersurface of a generic Hamiltonian system with two degrees of freedom. The proof hinges on the obtention of asymptotic bounds for the number of horseshoes, zeros and knotted invariant tori and periodic trajectories that a Gaussian random Beltrami field exhibits, which we obtain through a nontrivial extension of the Nazarov–Sodin theory for Gaussian random monochromatic waves and the application of different tools from the theory of dynamical systems, including Kolmogorov–Arnold–Moser (KAM) theory, Melnikov analysis and hyperbolicity. Our results hold both in the case of Beltrami fields on ${\mathbb {R}}^3$ and of high-frequency Beltrami fields on the 3-torus.
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Dong, Ran, Shaowen Ni i Soichiro Ikuno. "Nonlinear frequency analysis of COVID-19 spread in Tokyo using empirical mode decomposition". Scientific Reports 12, nr 1 (9.02.2022). http://dx.doi.org/10.1038/s41598-022-06095-w.
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AbstractEmpirical mode decomposition (EMD) was adopted to decompose daily COVID-19 infections in Tokyo from February 28, 2020, to July 12, 2021. Daily COVID-19 infections were nonlinearly decomposed into several monochromatic waves, intrinsic mode functions (IMFs), corresponding to their periodic meanings from high frequency to low frequency. High-frequency IMFs represent variabilities of random factors and variations in the number of daily PCR and antigen inspections, which can be nonlinearly denoised using EMD. Compared with a moving average and Fourier transform, EMD provides better performance in denoising and analyzing COVID-19 spread. After variabilities of daily inspections were weekly denoised by EMD, one low-frequency IMF reveals that the average period of external influences (public health and social measures) to stop COVID-19 spread was 19 days, corresponding to the measures response duration based on the incubation period. By monitoring this nonlinear wave, public health and social measures for stopping COVID-19 spread can be evaluated and visualized quantitatively in the instantaneous frequency domain. Moreover, another low-frequency IMF revealed that the period of the COVID-19 outbreak and retreat was 57 days on average. This nonlinear wave can be used as a reference for setting the timeframe for state of emergency declarations. Thus, decomposing daily infections in the instantaneous frequency domain using EMD represents a useful tool to improve public health and social measures for stopping COVID-19 spread.