Fully nonlinear hydroelastic modeling and analytic solution of large-scale floating photovoltaics in waves

AbstractThe runup of long strongly nonlinear waves impinging on a vertical wall can exceed six times the far-field amplitude of the incoming waves. This outcome stems from a precursory evolution process in which the wave height undergoes strong amplification due to the combined action of nonlinear steepening and dispersion, resulting in the formation of nonlinearly dispersive wave trains, i.e. undular bores. This part of the problem is first analysed separately, with emphasis on the wave amplitude growth rate during the development of undular bores within an evolving large-scale background. The growth of the largest wave in the group is seen to reflect the asymptotic time scaling provided by nonlinear modulation theory rather closely, even in the case of fully nonlinear evolution and moderately slow modulations. In order to address the effect of such a dynamics on the subsequent wall runup, numerical simulations of evolving long-wave groups are then carried out in a computational wave tank delimited by vertical walls. Conditions for optimal runup efficiency are sought with respect to the main physical parameters characterizing the incident waves, namely the wavelength, the length of the propagation path and the initial amplitude. Extreme runup is found to be strongly correlated to the ratio between the available propagation time and the shallow-water nonlinear time scale. The problem is studied in the twofold mathematical framework of the fully nonlinear free-surface Euler equations and the strongly nonlinear Serre–Green–Naghdi model. The performance of the reduced model in providing accurate long-time predictions can therefore be assessed.

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Explicit nonlinear waves of fluid models on extended domains and unbounded growth with backscatter

10.5194/egusphere-egu2020-14052 ◽

2020 ◽

Author(s):

Artur Prugger ◽

Jens Rademacher

Keyword(s):

Nonlinear Waves ◽

Large Scale ◽

Water Model ◽

Explicit Solutions ◽

Stationary Waves ◽

Fluid Models ◽

Fully Nonlinear ◽

Geostrophic Balance ◽

Linear Waves ◽

Rotating Shallow Water

Large scale motions in geophysical fluid models are often characterised by linear waves, which are obtained by linearising the equations. But there are also many explicit solutions of the fully nonlinear equations when posed the full space. The exact solutions we are investigating often characterise Rossby waves, since they are in geostrophic balance. They also can be compositions of waves, some are interacting with each other and some do not, showing wave interactions as explicit solutions in the fully nonlinear problem.In this talk I will briefly introduce the idea behind these explicit nonlinear waves and show some of their properties, and their occurrence in different fluid models in extended domains.As an application, we especially focus on a rotating shallow water model with simplified backscatter. In this case one finds not only geostrophic explicit solutions, but also ageostrophic ones. Moreover, here energy accumulates in selected scales due to the backscatter terms and causes exponentially and unboundedly growing ageostrophic nonlinear waves. This also relates to instability of coexisting stationary waves and is an instance of the role of nonlinear waves in energy transfer, and illustrates their role in preventing energy equidistribution for general data.

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Numerical Investigation on Spectrum Evolution of Narrow-Banded Random Waves in Shallow Water Based on KdV and Fully Nonlinear Model

Volume 1: Offshore Technology; Offshore Geotechnics ◽

10.1115/omae2016-54169 ◽

2016 ◽

Cited By ~ 1

Author(s):

Jinghua Wang ◽

Q. W. Ma ◽

Shiqiang Yan

Keyword(s):

Shallow Water ◽

Large Scale ◽

Kdv Equation ◽

Nonlinear Effects ◽

Boundary Integral ◽

Engineering Practice ◽

Large Wave ◽

Density Spectrum ◽

Fully Nonlinear ◽

Long Duration

The wave energy density spectrum provides useful information for both coastal engineering practice and applied sciences. However, it is not always available at desired location which can be far away from the observation stations, and should be achieved using approximated approaches. Nevertheless, the spectrum at the desired location may differ significantly from the approximated one due to nonlinear effects. In this paper, long-duration and large-scale evolutions of the wave spectrum in shallow water is investigated numerically. Direct simulations of random seas are carried out by using the weakly nonlinear KdV equation and the fully nonlinear Enhanced Spectral Boundary Integral (ESBI) model respectively. Due to nonlinear effects, the spectral shape is modified and the energy is redistributed after a long-duration (∼1000 peak periods) and large-scale (∼128 peak wave lengths) evolution. The results obtained by using fully nonlinear ESBI model here demonstrate that the flatness occurs only when both the conditions, i.e., large Ursell number and large wave steepness, are satisfied; It will not happen if the Ursell number is large but the steepness is small. This is different from the existing understanding in literature, i.e. spectra tended to become flat (or nearly uniformly distributed) in low frequency part as long as Ursell number is sufficiently large.

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On the development of non-circular motions in the Galaxy

Symposium - International Astronomical Union ◽

10.1017/s0074180900101147 ◽

1967 ◽

Vol 31 ◽

pp. 319-321

Author(s):

H. L. Helfer

Keyword(s):

Large Scale ◽

Analytic Solution ◽

Orbital Motion ◽

Rapid Development ◽

Fluid Velocity ◽

Linear Equations ◽

Galactic Dynamics ◽

Approximate Analytic Solution ◽

The Galaxy ◽

Non Linear Equations

An approximate analytic solution of the non-linear equations governing the large-scale galactic dynamics of the interstellar medium is discussed. Non-circular orbital motion results in the rapid development of spiral-like loci upon which the fluid velocity and density tend to become multi-valued. For some simple cases, properties of these loci and of the fluid in their vicinity are given.

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Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution

Physical Review E ◽

10.1103/physreve.51.5609 ◽

1995 ◽

Vol 51 (6) ◽

pp. 5609-5627 ◽

Cited By ~ 113

Author(s):

M. Chertkov ◽

G. Falkovich ◽

I. Kolokolov ◽

V. Lebedev

Keyword(s):

Velocity Field ◽

Large Scale ◽

Analytic Solution ◽

Passive Scalar ◽

Two Dimensional

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Source of Gravity Waves within a Vortex-Dipole Jet Revealed by a Linear Model

Journal of the Atmospheric Sciences ◽

10.1175/2010jas3327.1 ◽

2010 ◽

Vol 67 (5) ◽

pp. 1438-1455 ◽

Cited By ~ 24

Author(s):

Shuguang Wang ◽

Fuqing Zhang

Keyword(s):

Linear Model ◽

Gravity Waves ◽

Large Scale ◽

Mesoscale Model ◽

Relative Vorticity ◽

Fully Nonlinear ◽

Vortex Dipole ◽

Potential Vorticity Inversion ◽

Large Scale Flow ◽

Thermodynamic Equations

Abstract This study develops a linear numerical model to address the source mechanism of the gravity waves generated within a vortex dipole simulated in a fully nonlinear nonhydrostatic mesoscale model. The background flow for this linear model is obtained from potential vorticity inversion constrained by the nonlinear balance equation. The forcing imposed in the linear model is derived from an imbalance in the large-scale flow—that is, the forcing or imbalance in the vorticity, divergence, and thermodynamic equations, respectively. The response from the sum of these imbalanced forcings obtained from the linear dynamics shows well-defined gravity wave signals, which compare reasonably well in terms of location, phase, and amplitude with the gravity waves simulated in a fully nonlinear nonhydrostatic mesoscale model. It is found that the vorticity forcing, largely due to the advection of balanced relative vorticity, is the leading contributor to the gravity waves in the exit region of the vortex-dipole jet.

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Bayesian cosmic density field inference from redshift space dark matter maps

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1864 ◽

2019 ◽

Vol 488 (2) ◽

pp. 2573-2604 ◽

Cited By ~ 4

Author(s):

E G Patrick Bos ◽

Francisco-Shu Kitaura ◽

Rien van de Weygaert

Keyword(s):

Dark Matter ◽

Large Scale ◽

Analytic Solution ◽

Power Spectra ◽

Matter Density ◽

Density Field ◽

Distortion Correction ◽

Time Step ◽

Intensity Mapping ◽

Dark Matter Density

Abstract We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after a cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zel’dovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true field defined by our mock observations. Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time-step in the Hamiltonian equations of motions. Our algorithm, dubbed barcode, promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few megaparsecs. This large-scale structure is implied by the observed spatial distribution of galaxy clusters – such as obtained from X-ray, Sunyaev–Zel’dovich, or weak lensing surveys – as well as that of the intergalactic medium sampled by the Ly α forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modelled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm.

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Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.560 ◽

2018 ◽

Vol 854 ◽

pp. 544-590 ◽

Cited By ~ 8

Author(s):

Joseph G. Fitzgerald ◽

Brian F. Farrell

Keyword(s):

Large Scale ◽

Second Order ◽

Two Dimensional ◽

Stratified Turbulence ◽

Stochastic Excitation ◽

Mean Flow ◽

Fully Nonlinear ◽

Statistical State ◽

Horizontal Flows ◽

Nonlinear Simulations

Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Restriction to 2D turbulence facilitates application of an analytically and computationally attractive implementation of SSD referred to as S3T, in which the SSD is expressed by coupling the equation for the horizontal mean structure with the equation for the ensemble mean perturbation covariance. This second-order SSD produces accurate statistics, through second order, when compared with fully nonlinear simulations. In particular, S3T captures the spontaneous emergence of the VSHF and associated density layers seen in simulations of turbulence maintained by homogeneous large-scale stochastic excitation. An advantage of the S3T system is that the VSHF formation mechanism, which is wave–mean flow interaction between the emergent VSHF and the stochastically excited large-scale gravity waves, is analytically understood in the S3T system. Comparison with fully nonlinear simulations verifies that S3T solutions accurately predict the scale selection, dependence on stochastic excitation strength, and nonlinear equilibrium structure of the VSHF. These results constitute a theory for VSHF formation applicable to interpreting simulations and observations of geophysical examples of turbulent jets such as the ocean’s equatorial deep jets.

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Measuring Child-Rearing Values. A Research Note

Social Change Review ◽

10.2478/scr-2013-0011 ◽

2012 ◽

Vol 10 (1) ◽

pp. 47-70 ◽

Cited By ~ 6

Author(s):

Bogdan Voicu

Keyword(s):

Large Scale ◽

Analytic Solution ◽

Original Data ◽

Child Rearing ◽

Convenience Sample ◽

Parental Values ◽

Individual Level ◽

Synthetic Indicators ◽

Report Data ◽

Q Sort

Abstract Large scale comparative studies, such as the value surveys (EVS and WVS) or the Eurobarometer, include measurements for parental/child-rearing values. This reflects a persistent interest for the topic, which produced salient studies starting with the first half of the twentieth century (Lynd and Lund 1929; Duvall 1946). Various scholars report data on parental values which use versions of the Q-sort methodology (Kohn 1977), ranking variables (Alwin 1990; Lenski 1961), scale indicators (Tulviste et al. 2007). Q-sort methodology remains the most widely employed. One of its versions is included in the value surveys as well. However, it fails to produce comparable indicators in different countries (Rabušic 2011; Xiao 2001) or at different moments in time (Wright and Wright 1976). This paper uses original data, provided by a Romanian convenience sample, to check if using various versions of the EVS/WVS items may lead to better ways to produce synthetic indicators for parental-values at individual level. SEM models are used to show that the best analytic solution would be to use individual items instead of producing summative indexes.

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Some comments about observations and image processing of comet 29P/Schwassmann-Wachmann 1

International Astronomical Union Colloquium ◽

10.1017/s0252921100031493 ◽

1999 ◽

Vol 173 ◽

pp. 243-248

Author(s):

D. Kubáček ◽

A. Galád ◽

A. Pravda

Keyword(s):

Image Processing ◽

Large Scale ◽

Harvard College ◽

Oak Ridge ◽

Large Scale Structures ◽

Short Period Comet ◽

Short Period ◽

Scale Structures ◽

Harvard College Observatory ◽

Period Comet

AbstractUnusual short-period comet 29P/Schwassmann-Wachmann 1 inspired many observers to explain its unpredictable outbursts. In this paper large scale structures and features from the inner part of the coma in time periods around outbursts are studied. CCD images were taken at Whipple Observatory, Mt. Hopkins, in 1989 and at Astronomical Observatory, Modra, from 1995 to 1998. Photographic plates of the comet were taken at Harvard College Observatory, Oak Ridge, from 1974 to 1982. The latter were digitized at first to apply the same techniques of image processing for optimizing the visibility of features in the coma during outbursts. Outbursts and coma structures show various shapes.

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