scholarly journals Self-similarity of wind-driven seas

2005 ◽  
Vol 12 (6) ◽  
pp. 891-945 ◽  
Author(s):  
S. I. Badulin ◽  
A. N. Pushkarev ◽  
D. Resio ◽  
V. E. Zakharov
Keyword(s):  
Water Waves ◽  
Numerical Solutions ◽  
Wind Wave ◽  
Numerical Study ◽  
Wave Age ◽  
Self Similarity ◽  
Limited Growth ◽  
Wide Range ◽  
Wind Input ◽  
Self Similar

Abstract. The results of theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp / U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp / U10.

On weakly turbulent scaling of wind sea in simulations of fetch-limited growth

2011 ◽  
Vol 669 ◽  
pp. 178-213 ◽  
Author(s):  
ELODIE GAGNAIRE-RENOU ◽  
MICHEL BENOIT ◽  
SERGEI I. BADULIN
Keyword(s):  
Numerical Simulations ◽  
Wave Energy ◽  
Water Waves ◽  
Wind Wave ◽  
Wind Waves ◽  
Initial Growth ◽  
Limited Growth ◽  
Wave Growth ◽  
Wide Range ◽  
Wind Sea

Extensive numerical simulations of fetch-limited growth of wind-driven waves are analysed within two approaches: a ‘traditional’ wind-speed scaling first proposed by Kitaigorodskii (Bull. Acad. Sci. USSR, Geophys. Ser., Engl. Transl., vol. N1, 1962, p. 105) in the early 1960s and an alternative weakly turbulent scaling developed recently by Badulin et al. (J. Fluid Mech.591, 2007, 339–378). The latter one uses spectral fluxes of wave energy, momentum and action as physical scales of the problem and allows for advanced qualitative and quantitative analysis of wind-wave growth and features of air–sea interaction. In contrast, the traditional approach is shown to be descriptive rather than proactive. Numerical simulations are conducted on the basis of the Hasselmann kinetic equation for deep-water waves in a wide range of wind speeds from 5 to 30 m s −1 and for the ideal case of fetch-limited growth: permanent wind blowing perpendicularly to a straight coastline. Two different wave input functions, Sin, and two methods for calculating the nonlinear transfer term Snl (Gaussian quadrature method, or GQM, a quasi-exact method based on the use of Gaussian quadratures, and the discrete interaction approximation, or DIA) are used in the simulations. Comparison of the corresponding results firstly shows the relevance of the analysis of wind-wave growth in terms of the proposed weakly turbulent scaling, and secondly, allows us to highlight some critical points in the modelling of wind-generated waves. Three stages of wind-wave development corresponding to qualitatively different balance of the source terms, Sin, Sdiss and Snl, are identified: initial growth, growing sea and fully developed sea. Validity of the asymptotic weakly turbulent approach for the stage of growing wind sea is determined by the dominance of nonlinear transfers, which results in a rigid link between spectral fluxes and wave energy. This stage of self-similar growth is investigated in detail and presented as a consequence of three sub-stages of qualitatively different coupling of air flow and growing wind waves. The key self-similarity parameter of the asymptotic theory is estimated to be αss = 0.68 ± 0.1.Further prospects of wind-wave modelling in the context of the presented weakly turbulent scaling are discussed.

scholarly journals Universal void density profiles from simulation and SDSS

2014 ◽  
Vol 11 (S308) ◽  
pp. 542-545 ◽  
Author(s):  
S. Nadathur ◽  
S. Hotchkiss ◽  
J. M. Diego ◽  
I. T. Iliev ◽  
S. Gottlöber ◽  
...  
Keyword(s):  
Fundamental Property ◽  
Watershed Algorithm ◽  
Void Size ◽  
Self Similarity ◽  
Density Profiles ◽  
Watershed Transform ◽  
Future Studies ◽  
Main Galaxy ◽  
Wide Range ◽  
Self Similar

AbstractWe discuss the universality and self-similarity of void density profiles, for voids in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. Voids are identified using a modified version of the ZOBOV watershed transform algorithm, with additional selection cuts. We find that voids in simulation areself-similar, meaning that their average rescaled profile does not depend on the void size, or – within the range of the simulated catalogue – on the redshift. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show auniversalbehaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.

scholarly journals A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees

2017 ◽  
Vol 284 (1846) ◽  
pp. 20162395 ◽  
Author(s):  
Kohei Koyama ◽  
Ken Yamamoto ◽  
Masayuki Ushio
Keyword(s):  
Lognormal Distribution ◽  
Species Abundance ◽  
Self Similarity ◽  
Lognormal Distributions ◽  
Multiplicative Effect ◽  
Wide Range ◽  
Error Distributions ◽  
Species Abundance Distributions ◽  
Self Similar ◽  
Ulmus Davidiana

Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees ( Ulmus davidiana ), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals Cauliflower fractal forms arise from perturbations of floral gene networks

Science ◽  
2021 ◽  
Vol 373 (6551) ◽  
pp. 192-197
Author(s):  
Eugenio Azpeitia ◽  
Gabrielle Tichtinsky ◽  
Marie Le Masson ◽  
Antonio Serrano-Mislata ◽  
Jérémy Lucas ◽  
...  
Keyword(s):  
Arabidopsis Thaliana ◽  
Gene Networks ◽  
Growth Dynamics ◽  
Self Similarity ◽  
Developmental Mechanisms ◽  
Wide Range ◽  
Self Similar ◽  
Experimental Analyses ◽  
Floral Gene ◽  
Similar Organization

Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the “memory” of their transient passage in a floral state. Additional mutations affecting meristem growth can induce the production of conical structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics.

scholarly journals Fractal-based techniques for physiological time series: An updated approach

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 741-750 ◽  
Author(s):  
José Luis Roca ◽  
German Rodríguez-Bermúdez ◽  
Manuel Fernández-Martínez
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Self Similarity ◽  
High Quality ◽  
Detailed Review ◽  
Physiological Time ◽  
Wide Range ◽  
Fractal Patterns ◽  
Self Similar ◽  
And Performance

AbstractAlong this paper, we shall update the state-of-the-art concerning the application of fractal-based techniques to test for fractal patterns in physiological time series. As such, the first half of the present work deals with some selected approaches to deal with the calculation of the self-similarity exponent of time series. They include broadly-used procedures as well as recent advances improving their accuracy and performance for a wide range of self-similar processes. The second part of this paper consists of a detailed review of high-quality studies carried out in the context of electroencephalogram signals. Both medical and non-medical applications have been deeply reviewed. This work is especially recommended to all those researchers especially interested in fractal pattern recognition for physiological time series.

scholarly journals A Population Study of Faint Compact Steep Spectrum Radio Sources: Self-Similar Growth

2003 ◽  
Vol 20 (1) ◽  
pp. 75-78 ◽  
Author(s):  
Wolfgang Tschager ◽  
Richard Schilizzi ◽  
Huub Röttgering ◽  
Ignas Snellen ◽  
George Miley ◽  
...  
Keyword(s):  
Population Study ◽  
Growth Process ◽  
Radio Galaxies ◽  
Radio Sources ◽  
Self Similarity ◽  
Spectrum Radio ◽  
Wide Range ◽  
Self Similar ◽  
Similar Growth ◽  
Intrinsic Characteristic

AbstractThe main topic of this contribution is the investigation of the morphological self-similarity of the growth process during the gigahertz peaked spectrum (GPS) and compact steep spectrum (CSS) phase of evolving radio galaxies. By investigating a new sample of faint CSS radio sources we establish that self-similar evolution must hold for peaked spectrum sources over a wide range of luminosities as well as physical sizes. Thus, we argue that self-similarity should be regarded as an essential, intrinsic characteristic of the growth process of young radio sources, and be treated as such, and not merely as a supplementary constraint for evolution models.

scholarly journals Ocean swell within the kinetic equation for water waves

2016 ◽  
Author(s):  
Sergei Badulin ◽  
Vladimir Zakharov
Keyword(s):  
Water Waves ◽  
Initial Conditions ◽  
Wind Waves ◽  
Radar Data ◽  
Wave Spectra ◽  
Self Similarity ◽  
Wave Interactions ◽  
Synthetic Aperture Radar Data ◽  
Wide Range ◽  
Basic Solutions

Abstract. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to 106 seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (Synthetic Aperture Radar) data. At the same time, the relatively fast weakening of wave-wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow at rather light winds.

scholarly journals Ocean swell within the kinetic equation for water waves

2017 ◽  
Vol 24 (2) ◽  
pp. 237-253 ◽  
Author(s):  
Sergei I. Badulin ◽  
Vladimir E. Zakharov
Keyword(s):  
Water Waves ◽  
Initial Conditions ◽  
Wind Waves ◽  
Radar Data ◽  
Wave Spectra ◽  
Self Similarity ◽  
Wave Interactions ◽  
Synthetic Aperture Radar Data ◽  
Wide Range ◽  
Basic Solutions

Abstract. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2  ×  106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height) due to wave–wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell). At longer times, wave–wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar) data. At the same time, the relatively fast weakening of wave–wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.

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