scholarly journals The choice of optimal Discrete Interaction Approximation to the kinetic integral for ocean waves

2003 ◽  
Vol 10 (4/5) ◽  
pp. 425-434 ◽  
Author(s):  
V. G. Polnikov

Abstract. A lot of discrete configurations for the four-wave nonlinear interaction processes have been calculated and tested by the method proposed earlier in the frame of the concept of Fast Discrete Interaction Approximation to the Hasselmann's kinetic integral (Polnikov and Farina, 2002). It was found that there are several simple configurations, which are more efficient than the one proposed originally in Hasselmann et al. (1985). Finally, the optimal multiple Discrete Interaction Approximation (DIA) to the kinetic integral for deep-water waves was found. Wave spectrum features have been intercompared for a number of different configurations of DIA, applied to a long-time solution of kinetic equation. On the basis of this intercomparison the better efficiency of the configurations proposed was confirmed. Certain recommendations were given for implementation of new approximations to the wave forecast practice.

2010 ◽  
Vol 40 (4) ◽  
pp. 667-683 ◽  
Author(s):  
Alexander V. Babanin ◽  
Kakha N. Tsagareli ◽  
I. R. Young ◽  
David J. Walker

Abstract Numerical simulations of the wind-wave spectrum evolution are conducted by means of new observation-based wind-input and wave dissipation functions obtained in the Lake George field experiment. This experiment allowed simultaneous measurements of the source functions in a broad range of conditions, including extreme wind-wave circumstances. Results of the experiment revealed new physical mechanisms in the processes of spectral input/dissipation of wave energy, which are presently not accounted for in wave forecast models. These features had been parameterized as source terms in a form suitable for spectral wave models; in the present study, they were tested, calibrated, and validated on the basis of such a model. Physical constraints were imposed on the source functions in terms of the known experimental dependences for the total wind-wave momentum flux and for the ratio between the total input and total dissipation. Enforcing the constraints in the course of wave-spectrum evolution allowed calibration of the free experimental parameters of the new input (Part I of the study) and dissipation functions; the latter is the topic of the present paper. The approach allows separate calibration of the source functions before they are employed in the evolution tests. The evolution simulations were conducted by means of the one-dimensional research WAVETIME model with an exact solution for the nonlinear term. The resulting time-limited evolution of integral, spectral, and directional wave properties, based on implementation of the new physically justified source/sink terms and constraints, is then analyzed. Good agreement of the simulated evolution with known experimental dependences is demonstrated.


Author(s):  
Alfred R. Osborne

Deterministic Modeling of ocean surface rogue waves is often done with highly complex spectral codes for the nonlinear Schrödinger equation and its higher order versions, the Zakharov equation or the full Euler equations in two-space and one-time dimensions. Wind/Wave Modeling is normally conducted with a kinetic equation derived from a deterministic equation: the nonlinear four wave interactions are normally computed with the Discrete Interaction Approximation (DIA) algorithm, the Webb-Resio-Tracy (WRT) algorithm or the full Boltzmann integral. I give an overview of these methods and show how a fully self-consistent approach can simultaneously yield all of these methods while computing a multidimensional Fourier series that contains rogue wave packets as “coherent structures” or “nonlinear Fourier components” in the theory. The methods also lead to hyperfast codes in which deterministic evolution is millions of times faster than traditional spectral codes on a large multicore computer. This method could lead the way to an ideal future in which there are single codes that can simultaneously compute the deterministic and probabilistic evolution of surface waves.


2020 ◽  
Vol 8 (4) ◽  
pp. 251 ◽  
Author(s):  
Sonia Ponce de León ◽  
Alfred R. Osborne

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements of ocean waves over the past decades and found that the measured power spectrum has (a) a very high central peak (characterized by the parameter γ, developed in the 1970s in the JONSWAP program) and (b) enhanced high-frequency channels which lead to the phenomenon of “bimodality”, also a well-known phenomenon. We discuss how a numerical hindcast of the Draupner storm (1995) with the standard code WAVEWATCH-III with full Boltzmann interactions also reflects these previously experimentally determined spectral shapes. Our results suggest that the use of the full Boltzmann interactions (as opposed to the discrete interaction approximation often employed for forecasting/hindcasting) is important for obtaining this characteristic physical spectral shape of the power spectrum.


2009 ◽  
Vol 618 ◽  
pp. 263-277 ◽  
Author(s):  
M. ONORATO ◽  
A. R. OSBORNE ◽  
P. A. E. M. JANSSEN ◽  
D. RESIO

We investigate theoretically the irreversibile energy transfer in flat bottom shallow water waves. Starting from the oldest weakly nonlinear dispersive wave model in shallow water, i.e. the original quadratic Boussinesq equations, and by developing a statistical theory (kinetic equation) of the aforementioned equations, we show that the four-wave resonant interactions are naturally part of the shallow water wave dynamics. These interactions are responsible for a constant flux of energy in the wave spectrum, i.e. an energy cascade towards high wavenumbers, leading to a power law in the wave spectrum of the form of k−3/4. The nonlinear time scale of the interaction is found to be of the order of (h/a)4 wave periods, with a the wave amplitude and h the water depth. We also compare the kinetic equation arising from the Boussinesq equations with the arbitrary-depth Hasselmann equation and show that, in the limit of shallow water, the two equations coincide. It is found that in the narrow band case, both in one-dimensional propagation and in the weakly two-dimensional case, there is no irreversible energy transfer because the coupling coefficient in the kinetic equation turns out to be identically zero on the resonant manifold.


2019 ◽  
Vol 47 (1) ◽  
pp. 103-106
Author(s):  
A.N. Pushkarev ◽  
V.E. Zakharov

The absence of mathematically justified criteria in the models of prediction of wind waves of the ocean, used by the world’s largest centers NOAA (USA) and ECMWF (UK), based on numerical modeling of the Hasselmann kinetic equation, led to erroneous hierarchy and erroneous nonlinear interaction approximation, wind forcing and waves dissipation terms due to wave-breaking. Existing models of wind waves operate in the paradigm of the adjustable «black box», each time requiring reconfiguration. On the basis of numerical simulation, we were able to construct a model, taking into account the wind forcing of the power type in combination with the «implicit» dissipation.


2004 ◽  
Vol 34 (136) ◽  
pp. 455-468
Author(s):  
Hartwig Berger

The article discusses the future of mobility in the light of energy resources. Fossil fuel will not be available for a long time - not to mention its growing environmental and political conflicts. In analysing the potential of biofuel it is argued that the high demands of modern mobility can hardly be fulfilled in the future. Furthermore, the change into using biofuel will probably lead to increasing conflicts between the fuel market and the food market, as well as to conflicts with regional agricultural networks in the third world. Petrol imperialism might be replaced by bio imperialism. Therefore, mobility on a solar base pursues a double strategy of raising efficiency on the one hand and strongly reducing mobility itself on the other.


2020 ◽  
Author(s):  
Claudia Mazzuca ◽  
Matteo Santarelli

The concept of gender has been the battleground of scientific and political speculations for a long time. On the one hand, some accounts contended that gender is a biological feature, while on the other hand some scholars maintained that gender is a socio-cultural construct (e.g., Butler, 1990; Risman, 2004). Some of the questions that animated the debate on gender over history are: how many genders are there? Is gender rooted in our biological asset? Are gender and sex the same thing? All of these questions entwine one more crucial, and often overlooked interrogative. How is it possible for a concept to be the purview of so many disagreements and conceptual redefinitions? The question that this paper addresses is therefore not which specific account of gender is preferable. Rather, the main question we will address is how and why is even possible to disagree on how gender should be considered. To provide partial answers to these questions, we suggest that gender/sex (van Anders, 2015; Fausto-Sterling, 2019) is an illustrative example of politicized concepts. We show that no concepts are political in themselves; instead, some concepts are subjected to a process involving a progressive detachment from their supposed concrete referent (i.e., abstractness), a tension to generalizability (i.e., abstraction), a partial indeterminacy (i.e., vagueness), and the possibility of being contested (i.e., contestability). All of these features differentially contribute to what we call the politicization of a concept. In short, we will claim that in order to politicize a concept, a possible strategy is to evidence its more abstract facets, without denying its more embodied and perceptual components (Borghi et al., 2019). So, we will first outline how gender has been treated in psychological and philosophical discussions, to evidence its essentially contestable character thereby showing how it became a politicized concept. Then we will review some of the most influential accounts of political concepts, arguing that currently they need to be integrated with more sophisticated distinctions (e.g., Koselleck, 2004). The notions gained from the analyses of some of the most important accounts of political concepts in social sciences and philosophy will allow us to implement a more dynamic approach to political concepts. Specifically, when translated into the cognitive science framework, these reflections will help us clarifying some crucial aspects of the nature of politicized concepts. Bridging together social and cognitive sciences, we will show how politicized concepts are abstract concepts, or better abstract conceptualizations.


Water Waves ◽  
2021 ◽  
Author(s):  
M. D. Groves

AbstractIn the applied mathematics literature solitary gravity–capillary water waves are modelled by approximating the standard governing equations for water waves by a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). These formal arguments have been justified by sophisticated techniques such as spatial dynamics and centre-manifold reduction methods on the one hand and variational methods on the other. This article presents a complete, self-contained account of an alternative, simpler approach in which one works directly with the Zakharov–Craig–Sulem formulation of the water-wave problem and uses only rudimentary fixed-point arguments and Fourier analysis.


Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1117
Author(s):  
Bin Li ◽  
Zhikang Jiang ◽  
Jie Chen

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.


2020 ◽  
Vol 13 (1) ◽  
pp. 31
Author(s):  
Enrico Creaco ◽  
Giacomo Galuppini ◽  
Alberto Campisano ◽  
Marco Franchini

This paper presents a two-step methodology for the stochastic generation of snapshot peak demand scenarios in water distribution networks (WDNs), each of which is based on a single combination of demand values at WDN nodes. The methodology describes the hourly demand at both nodal and WDN scales through a beta probabilistic model, which is flexible enough to suit both small and large demand aggregations in terms of mean, standard deviation, and skewness. The first step of the methodology enables generating separately the peak demand samples at WDN nodes. Then, in the second step, the nodal demand samples are consistently reordered to build snapshot demand scenarios for the WDN, while respecting the rank cross-correlations at lag 0. The applications concerned the one-year long dataset of about 1000 user demand values from the district of Soccavo, Naples (Italy). Best-fit scaling equations were constructed to express the main statistics of peak demand as a function of the average demand value on a long-time horizon, i.e., one year. The results of applications to four case studies proved the methodology effective and robust for various numbers and sizes of users.


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