Search Results (6)

The article describes a hard- and software controlled complex for gas-strain monitoring, consisting of stationary laser strainmeters and a laser nanobarograph, a stationary gas analyzer, and a weather station installed at Shultz Cape in the Sea of Japan; and a mobile shipboard complex, consisting of a gas analyzer and a weather station installed in a scientific research vessel. In the course of trial methodological measurements on these systems, general patterns were identified in the dynamics of greenhouse gases and deformation of the Earth’s crust in the range of diurnal and semi-diurnal tides, and also in the range of ultra-low frequencies, caused by atmospheric wave processes and, possibly, individual tones of the Earth’s eigen oscillations. Full article

Sea waves constitute a natural phenomenon with a great impact on human activities, and their monitoring is essential for meteorology, coastal safety, navigation, and renewable energy from the sea. Therefore, the main measurement techniques for their monitoring are here reviewed, including buoys, satellite observation, coastal radars, shipboard observation, and microseism analysis. For each technique, the measurement principle is briefly recalled, the degree of development is outlined, and trends are prospected. The complementarity of such techniques is also highlighted, and the need for further integration in local and global networks is stressed. Full article

Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves. Full article

To expand the scope of ocean wave observations, a shipboard coherent S-band wave radar system was developed recently. The radar directly measures the wave orbital velocity from the Doppler shift of the received radar signal. The sources of this Doppler shift are analyzed. After removing the Doppler shifts caused by the ocean current and platform, the radial velocities of water particles of the surface gravity waves are retrieved. Subsequently, the wavenumber spectrum can be obtained based on linear wave theory. Later, the significant wave height and wave periods (including mean wave period and peak wave period) can be calculated from the wavenumber spectrum. This radar provides a calibration-free way to measure wave parameters and is a novel underway coherent microwave wave radar. From 9 September to 11 September 2018, an experiment involving radar-derived and buoy-measured wave measurements was conducted in the South China Sea. The Doppler spectra obtained when the ship was in the state of navigation or mooring indicated that the quality of the radar echo was fairly good. The significant wave heights and wave periods measured using the radar are compared with those obtained from the wave buoy. The correlation coefficients of wave heights and mean wave periods between these two instruments both exceed 0.9 while the root mean square differences are respectively less than 0.15 m and 0.25 s, regardless of the state of motion of the ship. These results indicate that this radar has the capability to accurately measure ocean wave heights and wave periods. Full article

I address the problem of breather turbulence in ocean waves from the point of view of the exact spectral solutions of the nonlinear Schrödinger (NLS) equation using two tools of mathematical physics: (1) the inverse scattering transform (IST) for periodic/quasiperiodic boundary conditions (also referred to as finite gap theory (FGT) in the Russian literature) and (2) quasiperiodic Fourier series, both of which enhance the physical and mathematical understanding of complicated nonlinear phenomena in water waves. The basic approach I refer to is nonlinear Fourier analysis (NLFA). The formulation describes wave motion with spectral components consisting of sine waves, Stokes waves and breather packets that nonlinearly interact pair-wise with one another. This contrasts to the simpler picture of standard Fourier analysis in which one linearly superposes sine waves. Breather trains are coherent wave packets that “breath” up and down during their lifetime “cycle” as they propagate, a phenomenon related to Fermi-Pasta-Ulam (FPU) recurrence. The central wave of a breather, when the packet is at its maximum height of the FPU cycle, is often treated as a kind of rogue wave. Breather turbulence occurs when the number of breathers in a measured time series is large, typically several hundred per hour. Because of the prevalence of rogue waves in breather turbulence, I call this exceptional type of sea state a breather sea or rogue sea. Here I provide theoretical tools for a physical and dynamical understanding of the recent results of Osborne et al. (Ocean Dynamics, 2019, 69, pp. 187–219) in which dense breather turbulence was found in experimental surface wave data in Currituck Sound, North Carolina. Quasiperiodic Fourier series are important in the study of ocean waves because they provide a simpler theoretical interpretation and faster numerical implementation of the NLFA, with respect to the IST, particularly with regard to determination of the breather spectrum and their associated phases that are here treated in the so-called nonlinear random phase approximation. The actual material developed here focuses on results necessary for the analysis and interpretation of shipboard/offshore platform radar scans and for airborne lidar and synthetic aperture radar (SAR) measurements. Full article

Wave-induced motion and load responses are important criteria for ship performance evaluation. Physical experiments have long been an indispensable tool in the predictions of ship’s navigation state, speed, motions, accelerations, sectional loads and wave impact pressure. Currently, majority of the experiments are conducted in laboratory tank environment, where the wave environments are different from the realistic sea waves. In this paper, a laboratory tank testing system for ship motions and loads measurement is reviewed and reported first. Then, a novel large-scale model measurement technique is developed based on the laboratory testing foundations to obtain accurate motion and load responses of ships in realistic sea conditions. For this purpose, a suite of advanced remote control and telemetry experimental system was developed in-house to allow for the implementation of large-scale model seakeeping measurement at sea. The experimental system includes a series of technique sensors, e.g., the Global Position System/Inertial Navigation System (GPS/INS) module, course top, optical fiber sensors, strain gauges, pressure sensors and accelerometers. The developed measurement system was tested by field experiments in coastal seas, which indicates that the proposed large-scale model testing scheme is capable and feasible. Meaningful data including ocean environment parameters, ship navigation state, motions and loads were obtained through the sea trial campaign. Full article