Energy Content Characterization of Water Waves Using Linear and Nonlinear Spectral Analysis

2021 ◽  
pp. 1-30
Author(s):  
Ali Mohtat ◽  
Solomon Yim ◽  
Alfred R. Osborne
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Ad Hoc ◽  
Energy Content ◽  
Energy Calculation ◽  
Linear And Nonlinear ◽  
Definition Of ◽  
Exact Energy ◽  
Wave Modes

Abstract The survivability, safe operation, and design of marine vehicles and wave energy converters are highly dependent on accurate characterization and estimation of the energy content of the ocean wave field. In this study, analytical solutions of the nonlinear Schrödinger equation (NLS) using periodic inverse scattering transformation (IST) and its associated Riemann spectrum are employed to obtain the nonlinear wave modes (eigen functions of the nonlinear equation consisting of multiple phase-locked harmonic components). These nonlinear wave modes are used in two approaches to develop a more accurate definition of the energy content. First, in an ad hoc approach, the amplitudes of the nonlinear wave modes are used with a linear energy calculation resulting in a semi-linear energy estimate. Next, a novel, mathematically exact definition of the energy content taking into account the nonlinear effects up to fifth order is introduced in combination with the nonlinear wave modes, the exact energy content of the wave field is computed. Experimental results and numerical simulations were used to compute and analyze the linear, ad hoc, and exact energy contents of the wave field, using both linear and nonlinear spectra. The ratio of the ad hoc and exact energy estimates to the linear energy content were computed to examine the effect of nonlinearity on the energy content. In general, an increasing energy ratio was observed for increasing nonlinearity of the wave field, with larger contributions from higher-order harmonic terms. It was confirmed that the significant increase in nonlinear energy content with respect to its linear counterpart is due to the increase in the number of nonlinear phase-locked (bound wave) modes.

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

scholarly journals Establishing an ad hoc COVID-19 mortality surveillance during the first epidemic wave in Belgium, 1 March to 21 June 2020

2021 ◽  
Vol 26 (48) ◽  
Author(s):  
Françoise Renard ◽  
Aline Scohy ◽  
Johan Van der Heyden ◽  
Ilse Peeters ◽  
Sara Dequeker ◽  
...  
Keyword(s):  
Ad Hoc ◽  
Participation Rate ◽  
Term Care ◽  
Data Flows ◽  
Care Facilities ◽  
Definition Of ◽  
High Level ◽  
Mortality Surveillance ◽  
Related Mortality

Background COVID-19-related mortality in Belgium has drawn attention for two reasons: its high level, and a good completeness in reporting of deaths. An ad hoc surveillance was established to register COVID-19 death numbers in hospitals, long-term care facilities (LTCF) and the community. Belgium adopted broad inclusion criteria for the COVID-19 death notifications, also including possible cases, resulting in a robust correlation between COVID-19 and all-cause mortality. Aim To document and assess the COVID-19 mortality surveillance in Belgium. Methods We described the content and data flows of the registration and we assessed the situation as of 21 June 2020, 103 days after the first death attributable to COVID-19 in Belgium. We calculated the participation rate, the notification delay, the percentage of error detected, and the results of additional investigations. Results The participation rate was 100% for hospitals and 83% for nursing homes. Of all deaths, 85% were recorded within 2 calendar days: 11% within the same day, 41% after 1 day and 33% after 2 days, with a quicker notification in hospitals than in LTCF. Corrections of detected errors reduced the death toll by 5%. Conclusion Belgium implemented a rather complete surveillance of COVID-19 mortality, on account of a rapid investment of the hospitals and LTCF. LTCF could build on past experience of previous surveys and surveillance activities. The adoption of an extended definition of ‘COVID-19-related deaths’ in a context of limited testing capacity has provided timely information about the severity of the epidemic.

scholarly journals Ad Hoc or Institutional Arbitration - A Clear-Cut Distinction? A Closer Look at Borderline Cases

2017 ◽  
Author(s):  
Ulrich G. Schroeter
Keyword(s):  
Ad Hoc ◽  
Theory And Practice ◽  
Present Contribution ◽  
Borderline Cases ◽  
Institutional Rules ◽  
Clear Cut ◽  
Definition Of ◽  
Core Characteristics ◽  
Insight Into ◽  
Mix And Match

It is generally accepted in both theory and practice of arbitration that there are two basic forms of arbitration, ad hoc and institutional. This long established dichotomy has rarely been questioned, and it has mostly worked well in international arbitration practice.The present contribution investigates the traditional distinction between ad hoc and institutional arbitration in more detail by looking at "borderline cases", i.e. constellations that cannot easily be allocated to one of these two categories. Four groups of borderline cases are discussed: (1) UNCITRAL arbitrations, in particular those administered by arbitral institutions; (2) cases in which the parties have chosen institutional rules, but not the issuing institution (and vice versa), (3) the modification of institutional rules by the parties and the identification of a possible "mandatory" core of institutional rules, and (4) "mix and match" (or "hybrid") arbitrations combining one arbitral institution's rules with the case's administration by a different arbitral institution. By identifying the factors that were decisive for these borderline cases being regarded as institutional or ad hoc, the article is trying to gain insight into the core characteristics underlying each arbitration category. Drawing on these insights, it develops and explains a novel definition of "institutional arbitration".

Nonlinear Fourier Analysis for Shallow Water Waves

2021 ◽  
Author(s):  
Alfred R. Osborne
Keyword(s):  
Fourier Series ◽  
Fourier Analysis ◽  
Shallow Water ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Wave Equations ◽  
Superposition Principle ◽  
Broad Band ◽  
Kp Equation ◽  
Linear Superposition

Abstract I consider nonlinear wave motion in shallow water as governed by the KP equation plus perturbations. I have previously shown that broad band, multiply periodic solutions of the KP equation are governed by quasiperiodic Fourier series [Osborne, OMAE 2020]. In the present paper I give a new procedure for extending this analysis to the KP equation plus shallow water Hamiltonian perturbations. We therefore have the remarkable result that a complex class of nonlinear shallow water wave equations has solutions governed by quasiperiodic Fourier series that are a linear superposition of sine waves. Such a formulation is important because it was previously thought that solving nonlinear wave equations by a linear superposition principle was impossible. The construction of these linear superpositions in shallow water in an engineering context is the goal of this paper. Furthermore, I address the nonlinear Fourier analysis of experimental data described by shallow water physics. The wave fields dealt with here are fully two-dimensional and essentially consist of the linear superposition of generalized cnoidal waves, which nonlinearly interact with one another. This includes the class of soliton solutions and their associated Mach stems, both of which are important for engineering applications. The newly discovered phenomenon of “fossil breathers” is also characterized in the formulation. I also discuss the exact construction of Morison equation forces on cylindrical piles in terms of quasiperiodic Fourier series.

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

2021 ◽  
Author(s):  
Lingchao He ◽  
Jianwen Zhang ◽  
Zhonglong Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Water Waves ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Before And After

Abstract In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

Gender Violence Experiences of Urban Adult Indigenous Women

2016 ◽  
pp. 256-277
Author(s):  
M. Cruz Sánchez Gómez ◽  
Antonio V. Martín García ◽  
Ana María Pinto Llorente ◽  
Paula Andrea Fernández Dávila ◽  
Pamela Zapata Sepúlveda
Keyword(s):  
Domestic Violence ◽  
Ad Hoc ◽  
Health Indicators ◽  
Gender Violence ◽  
Group Discussions ◽  
Domestic Violence Against Women ◽  
Women’S Perceptions ◽  
Public Health Indicators ◽  
Definition Of ◽  
Ways Of Life

This chapter deals with the problem of gender violence, especially in Chilean Aymara women. The aim of the study is to make a diagnosis of the indices and forms of domestic violence against women on the basis of gender in a sample of Aymara women from the urban area in the Arica and Parinacota Region (Chile). The chapter assumes the definition of intrafamiliar violence, according to the formulation adopted by Chilean legislation, as a complex and multi-determined phenomenon, which happens in the context of a culture and certain social relationships that support and make it possible. In this sense, it is one of the most dramatic manifestations of discrimination experienced by women because of their sexual condition. It is conceptualized as any form of physical, psychological-emotional, sexual, and/or economic abuse, which happens within the couple relationship, regardless of the legality of the bond. The chapter deals with the description of conditions and ways of life of the Aymara ethnic group, from socio-demographic, economic, and public health indicators that may be related to these women's perceptions concerning their situation in view of the intrafamiliar violence phenomenon. The research is a quantitative and qualitative multimethod design. The qualitative side of this study consists of group discussions in which the object of the research is analyzed through an outline ad hoc. The quantitative side of the research consists of the application of two standardized scales of domestic violence (WASTT and ISA).

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