commite2a1c2f1180ac53c44caf6a4911ded3e0c9a8d7dparent519c07be78bdc5531156ddab7269fc3f7810d577Author:Ivan Gankevich <igankevich@ya.ru>Date:Fri, 26 May 2017 17:07:53 +0300 Add bibliography.Diffstat:

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refs.bib | | | 50 | ++++++++++++++++++++++++++++++++++++++++++++++++++ |

2 files changed, 79 insertions(+), 27 deletions(-)diff --git a/arma.org b/arma.org@@ -28,20 +28,20 @@ description of wind waves, which are the major disturbance that displaces the vessel from equilibrium. Currently, the most popular models for describing wind waves, are models based on the linear expansion of a stochastic moving surface as a system of independent random variables. These include models by St. Denis & -Pearson (1953), Rosenblatt (1957), Sveshnikov (1959), and Longuet-Higgins -(1962). The most popular model is that of Longuet---Higgins, which is based on a -stochastic approximation of the moving wave front as a superposition of -elementary harmonic waves with random phases \(\epsilon_n\) and random -amplitudes \(c_n\): +Pearson cite:st1953motions, Rosenblatt cite:rosenblatt1956random, Sveshnikov +cite:sveshnikov1959determination, and Longuet---Higgins +cite:longuet1957statistical. The most popular model is that of +Longuet---Higgins, which is based on a stochastic approximation of the moving +wave front as a superposition of elementary harmonic waves with random phases +\(\epsilon_n\) and random amplitudes \(c_n\): \begin{equation} \label{eq-lhmodel} \zeta(x,y,t) = \sum\limits_n c_n \cos(u_n x + v_n y - \omega_n t + \epsilon_n), \end{equation} -where the wave number \((u_n,v_n)\) is continuously -distributed on the \((u,v)\) plane, i.e. the unit area -\(du \times dv\) contains an infinite number of wave numbers. -The frequency \(\omega_n\) associated with wave -numbers \((u_n,v_n)\) is given by a dispersion relation +where the wave number \((u_n,v_n)\) is continuously distributed on the \((u,v)\) +plane, i.e. the unit area \(du \times dv\) contains an infinite number of wave +numbers. The frequency \(\omega_n\) associated with wave numbers \((u_n,v_n)\) +is given by a dispersion relation \begin{equation*} \omega_n = \omega(u_n,v_n). \end{equation*} @@ -66,8 +66,7 @@ continuity: \label{eq-continuity} \frac{\partial{\rho}}{\partial{t}} = \vec{\nabla} \cdot \left(\rho\vec{V}\right) = 0, \end{equation} -where \(\rho\) is the density of the liquid, and \(V\) the -fluid velocity. +where \(\rho\) is the density of the liquid, and \(V\) the fluid velocity. In relation to ocean waves, we can make the assumptions of incompressibility and isotropy within the marine environment. In this case eq.\nbsp{}eqref:eq-continuity @@ -83,8 +82,8 @@ The physics of wind waves is defined primarily by the action of gravitational forces, which simplifies nature of the phenomenon under investigation. This approach allows us to consider the irrotational motion of the fluid and introduce the velocity potential \(\phi\). Then eq.\nbsp{}eqref:eq-continuity & -eqref:eq-continuity-2 reduce to Laplace's equation, which is the most general field -equation for the problem of wave motions of a liquid: +eqref:eq-continuity-2 reduce to Laplace's equation, which is the most general +field equation for the problem of wave motions of a liquid: \begin{equation*} \Delta\phi = \frac{\partial^2{\phi_x}}{\partial{x^2}} + @@ -99,7 +98,7 @@ of the boundary conditions is (a) applied on the surface of the undisturbed fluid \((z=0)\) and (b) all nonlinear terms in the boundary conditions are ignored. The Laplace equation is linear and its solution can be found using Fourier transforms. Thus, for plane waves a well-known solution is given in the -form of a definite integral (Kochin, et al., 1964): +form of a definite integral cite:kochin1964theoretical: \begin{equation*} \phi(x,z,t) = \int\limits_{0}^{\infty} @@ -129,22 +128,22 @@ serious shortcomings inherent in models of this class: challenge. - Models of this class are periodic and need a very large set of frequencies to re-creating long-term simulation. -- In the numerical implementation of the Longuet-Higgins model, it appears that - the rate of convergence of eqref:eq-lhmodel is very slow. This is seen as a - distortion of the energy spectrum of the simulated process (i.e. not provided - by the convergence of \((u, v)\)), and the laws for the distribution of - elementary waves, especially in terms of extreme events (not ensured by the +- In the numerical implementation of the Longuet---Higgins model, it appears + that the rate of convergence of eqref:eq-lhmodel is very slow. This is seen as + a distortion of the energy spectrum of the simulated process (i.e. not + provided by the convergence of \((u, v)\)), and the laws for the distribution + of elementary waves, especially in terms of extreme events (not ensured by the convergence of \(\epsilon\)). This problem becomes especially significant when - simulating complex waves that have a broad spectrum with many-peaks. + simulating complex waves that have a broad spectrum with many peaks. The latter point becomes particularly critical in numerical simulation. In a time domain computation of the responses of a vessel in a random seaway, the -repeated evaluation of the apparently simple equation, eqref:eq-lhmodel at hundreds -of points on the hull for thousands of time steps can becomes a major factor -determining the execution speed of the code (Beck & Reed, 2001). This becomes an -even more significant issue in a nonlinear computation where the wave model is -even more complex. Thus identifying a significantly less time intensive method -for modelling the ambient ocean-wave environment has the potential for +repeated evaluation of the apparently simple equation, eqref:eq-lhmodel at +hundreds of points on the hull for thousands of time steps can becomes a major +factor determining the execution speed of the code cite:beck2001modern. This +becomes an even more significant issue in a nonlinear computation where the wave +model is even more complex. Thus identifying a significantly less time intensive +method for modelling the ambient ocean-wave environment has the potential for significantly speeding the total simulation process. * Related work @@ -167,3 +166,6 @@ significantly speeding the total simulation process. ** Evaluation ** Discussion * Conclusion + +bibliographystyle:plain +bibliography:refs.bibdiff --git a/refs.bib b/refs.bib@@ -0,0 +1,50 @@ +@techreport{st1953motions, + title={On the motions of ships in confused seas}, + author={St Denis, Manley and Pierson Jr, Willard J}, + year={1953}, + institution={NEW YORK UNIV BRONX SCHOOL OF ENGINEERING AND SCIENCE} +} + +@techreport{rosenblatt1956random, + title={A random model of the sea surface generated by a hurricane}, + author={Rosenblatt, Murray}, + year={1956}, + institution={DTIC Document} +} + +@article{sveshnikov1959determination, + title={Determination of the probability characteristics of three-dimensional sea waves}, + author={Sveshnikov, AA}, + journal={Math. Akad. Mechanics and Engineering}, + volume={3}, + pages={32--41}, + year={1959} +} + +@article{longuet1957statistical, + title={The statistical analysis of a random, moving surface}, + author={Longuet-Higgins, Michael S}, + journal={Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}, + volume={249}, + number={966}, + pages={321--387}, + year={1957}, + publisher={The Royal Society} +} + +@book{kochin1964theoretical, + title={Theoretical hydromechanics}, + author={Kochin, Nikola{\u\i}} and Iliia, A Kibel and Roze, Nikola{\u\i}}}, + year={1964}, + publisher={Interscience} +} + +@article{beck2001modern, + title={Modern computational methods for ships in a seaway}, + author={BECK, Robert F and REED, Arthur M and SCLAVOUNOS, Paul D and HUTCHISON, Bruce L}, + journal={Transactions-Society of Naval Architects and Marine Engineers}, + volume={109}, + pages={1--51}, + year={2001}, + publisher={Society of Naval Architects and Marine Engineers} +}