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Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime // Zhou Zhang.
Author:	Zhang, Zhou,
Description:	1 electronic resource (117 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
Contained By:	Dissertations Abstracts International86-07B.
Subject:	Engineering. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31871418
ISBN:	9798346891222

Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime /
Zhang, Zhou,

Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime /Zhou Zhang. - 1 electronic resource (117 pages)

Source: Dissertations Abstracts International, Volume: 86-07, Section: B.

Wave turbulence theory (WTT) provides a statistical description of systems with many dispersive waves subject to nonlinear interactions. In this framework, a kinetic equation (KE) is derived to model the spectral evolution of wave fields. The analytical stationary solution of the KE yields a wave spectrum with a power-law form in the inertial range, which is known as the Kolmogorov-Zakharov (KZ) spectra. A constant energy flux from large (forcing) to small (dissipation) scales is also predicted in this solution, as analogous to the energy cascade in hydrodynamic turbulence. WTT has been applied to various physical systems including surface gravity waves, capillary waves, internal gravity waves, plasma waves, and gravitational waves. In the context of surface gravity waves, the KE was first developed by Hasselmann and then widely used in physical oceanography as the theoretical foundation for wave-forecasting models (e.g., WAVEWATCH, WAM, SWAN). Despite the extensive application of the Hasselmann equation, both numerical and laboratory experiments often exhibit deviations from WTT due to the violation of its assumptions. Indeed, the KE is derived in the infinite domain and weak nonlinearity limits which can not be rigorously achieved in any real system. In practical conditions (say a wave tank), the KE is only applicable when the nonlinearity level is high enough to overcome the wavenumber discreteness caused by the finite domain size, yet not so high as to induce coherent structures like rogue waves or wave breaking. Additionally, the validity of the KE for surface gravity waves is based on the dominance of four-wave resonant interactions as the resonant triad is absent. However, it is found in recent works that bound waves generated from non-resonant interactions can play a role in the formation of the wave spectra.In this dissertation, we aim to obtain a comprehensive understanding of surface gravity wave turbulence through a set of numerical and theoretical investigations. We start from a review of the theoretical derivation of the KE and the KZ spectra from the primitive Euler equations, with the emphasis on clarifying the assumptions used in the WTT framework. Then a numerical study is conducted simulating Euler equations for surface gravity waves under different forcing/free-decay conditions. We demonstrate that the kinetic regime, where the predictions from KE become valid, is approached at sufficiently high nonlinearity level with sufficient quasi-resonances. With the decrease of nonlinearity, steeper spectra and reduced energy flux are observed suggesting deviations from WTT. Through the spatial-temporal analysis and a tricoherence study, we elucidate the mechanisms of bound waves and finite-size effect leading to the behaviors at low nonlinearity level.Based on our understanding obtained from the previous study, we investigate the properties of wave fields beyond the kinetic regime with further considerations on the finite-size effect and bound waves. Due to the finite-size effect, the discrete wave turbulence regime is realized when the nonlinearity level is sufficiently low such that only exact resonances contribute to the nonlinear dynamics. We examine the possibility of direct and inverse cascades through exact resonances in a finite wavenumber domain using a kinematic model. Our results reveal the characteristics including the frozen turbulence and unlimited cascades for wave systems in the discrete regime. In addition, we perform another numerical study with the focus on the role of non-resonant triad interactions which are the origins of bound waves. With a decomposition technique, we numerically track the contributions from the triad and quartet interactions to the spectral evolution. We find that triad interactions can be connected to form resonant quartet interactions as well as distribute energy in bound and free waves.Finally, we explore the behavior of the spectral tail in surface gravity wave turbulence considering both the finite-size effect and the non-resonant interactions. By analogy with the Kolmogorov scale in hydrodynamic turbulence, we define the cutoff wavenumber kc separating the inertial and dissipation ranges in the wave spectra. It is found that in the limit of zero viscosity, kc approaches a constant value due to insufficient energy flux at reduced nonlinearity level caused by the finite-size effect. We also confirm that the scaling of kc with the intensity of dissipation is determined by the balance between the viscosity and nonlinear interactions. The roles of both quartet and triad interactions in this balance are discussed.

English

ISBN: 9798346891222Subjects--Topical Terms:

586835
Engineering.
Subjects--Index Terms:

Wave turbulence

Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime /
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245 1 0 $a Numerical Investigations of Surface Gravity Wave Turbulence Within and Beyond Kinetic Regime / $c Zhou Zhang.
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500 $a Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
500 $a Advisors: Pan, Yulin Committee members: Fidkowski, Krzysztof; Johnsen, Eric; Maki, Kevin J.
502 $b Ph.D. $c University of Michigan $d 2024.
520 $a Wave turbulence theory (WTT) provides a statistical description of systems with many dispersive waves subject to nonlinear interactions. In this framework, a kinetic equation (KE) is derived to model the spectral evolution of wave fields. The analytical stationary solution of the KE yields a wave spectrum with a power-law form in the inertial range, which is known as the Kolmogorov-Zakharov (KZ) spectra. A constant energy flux from large (forcing) to small (dissipation) scales is also predicted in this solution, as analogous to the energy cascade in hydrodynamic turbulence. WTT has been applied to various physical systems including surface gravity waves, capillary waves, internal gravity waves, plasma waves, and gravitational waves. In the context of surface gravity waves, the KE was first developed by Hasselmann and then widely used in physical oceanography as the theoretical foundation for wave-forecasting models (e.g., WAVEWATCH, WAM, SWAN). Despite the extensive application of the Hasselmann equation, both numerical and laboratory experiments often exhibit deviations from WTT due to the violation of its assumptions. Indeed, the KE is derived in the infinite domain and weak nonlinearity limits which can not be rigorously achieved in any real system. In practical conditions (say a wave tank), the KE is only applicable when the nonlinearity level is high enough to overcome the wavenumber discreteness caused by the finite domain size, yet not so high as to induce coherent structures like rogue waves or wave breaking. Additionally, the validity of the KE for surface gravity waves is based on the dominance of four-wave resonant interactions as the resonant triad is absent. However, it is found in recent works that bound waves generated from non-resonant interactions can play a role in the formation of the wave spectra.In this dissertation, we aim to obtain a comprehensive understanding of surface gravity wave turbulence through a set of numerical and theoretical investigations. We start from a review of the theoretical derivation of the KE and the KZ spectra from the primitive Euler equations, with the emphasis on clarifying the assumptions used in the WTT framework. Then a numerical study is conducted simulating Euler equations for surface gravity waves under different forcing/free-decay conditions. We demonstrate that the kinetic regime, where the predictions from KE become valid, is approached at sufficiently high nonlinearity level with sufficient quasi-resonances. With the decrease of nonlinearity, steeper spectra and reduced energy flux are observed suggesting deviations from WTT. Through the spatial-temporal analysis and a tricoherence study, we elucidate the mechanisms of bound waves and finite-size effect leading to the behaviors at low nonlinearity level.Based on our understanding obtained from the previous study, we investigate the properties of wave fields beyond the kinetic regime with further considerations on the finite-size effect and bound waves. Due to the finite-size effect, the discrete wave turbulence regime is realized when the nonlinearity level is sufficiently low such that only exact resonances contribute to the nonlinear dynamics. We examine the possibility of direct and inverse cascades through exact resonances in a finite wavenumber domain using a kinematic model. Our results reveal the characteristics including the frozen turbulence and unlimited cascades for wave systems in the discrete regime. In addition, we perform another numerical study with the focus on the role of non-resonant triad interactions which are the origins of bound waves. With a decomposition technique, we numerically track the contributions from the triad and quartet interactions to the spectral evolution. We find that triad interactions can be connected to form resonant quartet interactions as well as distribute energy in bound and free waves.Finally, we explore the behavior of the spectral tail in surface gravity wave turbulence considering both the finite-size effect and the non-resonant interactions. By analogy with the Kolmogorov scale in hydrodynamic turbulence, we define the cutoff wavenumber kc separating the inertial and dissipation ranges in the wave spectra. It is found that in the limit of zero viscosity, kc approaches a constant value due to insufficient energy flux at reduced nonlinearity level caused by the finite-size effect. We also confirm that the scaling of kc with the intensity of dissipation is determined by the balance between the viscosity and nonlinear interactions. The roles of both quartet and triad interactions in this balance are discussed.
546 $a English
590 $a School code: 0127
650 4 $a Engineering. $3 586835
650 4 $a Physics. $3 516296
650 4 $a Ocean engineering. $3 660731
653 $a Wave turbulence
653 $a Surface gravity waves
653 $a Hasselmann equation
690 $a 0547
690 $a 0605
690 $a 0537
710 2 $a University of Michigan. $b Naval Architecture & Marine Engineering. $e degree granting institution. $3 3816900
720 1 $a Pan, Yulin $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-07B.
790 $a 0127
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31871418