Strong Nonlinear Waves Research Articles

Convergence to strong nonlinear diffusion waves for solutions to p-system with damping

In this paper we consider the so-called p-system with linear damping, and we will prove an optimal decay estimates without any smallness conditions on the initial error. More precisely, if we restrict the initial data ( V 0 , U 0 ) in the space H 3 ( R + ) ∩ L 1 , γ ( R + ) × H 2 ( R + ) ∩ L 1 , γ ( R + ) , then we can derive faster decay estimates than those given in [P. Marcati, M. Mei, B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech. 7 (2) (2005) 224–240; H. Zhao, Convergence to strong nonlinear diffusion waves for solutions of p-system with damping, J. Differential Equations 174 (1) (2001) 200–236] and [M. Jian, C. Zhu, Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant, J. Differential Equations 246 (1) (2009) 50–77].

BEM-CADMAS-SURF 결합해석법에 기초한 수치조파수조의 응용

대수심의 유체운동을 포텐셜 운동으로 가정하여 자유수면의 거동을 신속히 해석하는 BEM 해석법과 구조물 근방에서 유체의 자유 수면 변화를 계산하기 위하여 NS방정식의 해석으로 CADMAS-SURF 기법을 결합하여 하이브리드 수치기법을 개발하였다. 하이브리드 해석법에서는 반사파를 고려해야 할 넓은 영역에서, 대수심의 영역은 BEM이, 천수역은 CADMAS-SURF가 계산하게 된다. 특히, 하이브리드 모델은 장시간에 걸친 불규칙파의 운동에 대해서는 단독의 CADMAS-SURF을 이용한 계산에 비해 거의 동일한 정확도로 월등히 신속하게 계산할 수 있다. 본 연구에서는 완경사 해저면을 가진 넓은 해역에서, 호안구조물에 내습하는 파랑의 처오름과 월파와 같은 강비선형 파랑장 계산에 결합해석모델을 적용하였다. 계산결과는 각각 토요시마(풍도(豊島))의 규칙과 처오름 실험과 고다(합전(合田))가 제안한 불규칙파의 월파량 산정도와 비교하였다. The hybrid numerical model is developed by combining BEM that can calculate the wave motion rapidly under the potential theory and CADMAS-SURF that solves Navier-Stokes equations for the free surface variation near the structure, In the hybrid model the calculation of wave motion in a wide field of wave reflection for deep water area is conducted by BEM but for shallow water area by CADMAS-SURF. Especially the hybrid model can calculate random wave motions for long term period more rapidly with almost similar accuracy than the calculation of wave motion which was carried out by CADMAS-SURF only. In this study the coupling model was applied to the calculation of the strong nonlinear wave motion such as wave runup and overtopping at the coastal structure on the mild-slope bottom and the results of numerical model were compared with the Toyosima's experiments of regular wave runup and Goda's design diagram of ramdom wave overtopping, respectively.

Shock compression of condensed matter using Eulerian multimaterial method: Applications to multidimensional shocks, deflagration, detonation, and laser ablation

The reactive flow analysis of high energy material is performed using hydro shock compression of condensed matter (SCCM) tool that is being developed for handling complex multimaterial dynamics involving energetic and inert matters. Typically, the reacting flows of high energy materials such as fires and explosions give rise to strong nonlinear shock waves and high strain rate deformation of metallic confinements at unusually high pressure and temperature. In order to address difficulties associated with analyzing such complex systems, we have developed a suite of modeling capabilities for elegantly handling large gradients and high strain rates in solids as well as reactive shock waves present in gaseous phase. Mathematical formulation of explosive dynamics involving condensed matter is explained with an emphasis on validating and application of hydro-SCCM to a series of problems of high-speed multimaterial dynamics in nature. A detailed numerical description of a level-set based reactive ghost fluid approach is reported in a separate paper.

Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant

In this paper, we consider the so-called p-system with linear damping on quadrant. We show that for a certain class of given large initial data ( v 0 ( x ) , u 0 ( x ) ) , the corresponding initial–boundary value problem admits a unique global smooth solution ( v ( x , t ) , u ( x , t ) ) and such a solution tends time-asymptotically, at the L p ( 2 ⩽ p ⩽ ∞ ) optimal decay rates, to the corresponding nonlinear diffusion wave ( v ¯ ( x , t ) , u ¯ ( x , t ) ) which satisfies (1.9) provided the corresponding prescribed initial error function ( V 0 ( x ) , U 0 ( x ) ) lies in ( H 3 ( R + ) ∩ L 1 ( R + ) ) × ( H 2 ( R + ) ∩ L 1 ( R + ) ) .

Shock compression of condensed matter using multimaterial reactive ghost fluid method

For the flow analysis of reactive compressible media involving energetic materials and deforming metallic boundaries, a HYDRO-SCCM (shock compression of condensed matter) tool is developed for handling multiphysics shock analysis of energetic and inert matters. The highly energetic flows give rise to the strong nonlinear shock waves and the high strain rate deformation of solid boundaries at high pressure and temperature. For handling the large gradients associated with these complex flows in the condensed phase as well as in the reactive gaseous phase, a new Eulerian multifluid method is formulated. The numerical methodology is described in this paper, while the extended applications and the capacity of the tool are discussed in a separate paper [J. J. Yoh and K. H. Kim, “Shock Compression of Condensed Matter using Eulerian Multimaterial Method: Applications to multi-dimensional shocks, deflagration, detonation, and laser ablation,” J. Appl. Phys. (accepted)].

THE FREAK WAVE MYSTERY ??A NEW HYPOTHESIS FOR ITS OCCURRENCE

Freak waves are known as a maritime myth, which have damaged large cargo and cruise ships. So far freak waves are explained by strong current focusing and nonlinear wave interaction. The latter may results in a single large wave. However this can still not explain the disappearance of the cargo ship Muenchen in December, 1978. This paper proposes a new hypothesis which stems from the wave/swell energy flux accumulation due to the moving wind system. Nature might play the game by controlling the moving speed to approach the wave/swell group velocity.

A two‐dimensional vertical non‐hydrostatic σ model with an implicit method for free‐surface flows

AbstractAn implicit finite difference model in the σ co‐ordinate system is developed for non‐hydrostatic, two‐dimensional vertical plane free‐surface flows. To accurately simulate interaction of free‐surface flows with uneven bottoms, the unsteady Navier–Stokes equations and the free‐surface boundary condition are solved simultaneously in a regular transformed σ domain using a fully implicit method in two steps. First, the vertical velocity and pressure are expressed as functions of horizontal velocity. Second, substituting these relationship into the horizontal momentum equation provides a block tri‐diagonal matrix system with the unknown of horizontal velocity, which can be solved by a direct matrix solver without iteration. A new treatment of non‐hydrostatic pressure condition at the top‐layer cell is developed and found to be important for resolving the phase of wave propagation. Additional terms introduced by the σ co‐ordinate transformation are discretized appropriately in order to obtain accurate and stable numerical results. The developed model has been validated by several tests involving free‐surface flows with strong vertical accelerations and non‐linear waves interacting with uneven bottoms. Comparisons among numerical results, analytical solutions and experimental data show the capability of the model to simulate free‐surface flow problems. Copyright © 2004 John Wiley & Sons, Ltd.

Directional noise and correlation of signal and noise variability in the ASIAEX South China Sea Experiment

As part of the 2001 ASIAEX South China Sea experiment, known acoustic signals and noise were recorded for 16 days with co-located horizontal and vertical receiving arrays in 120-m depth water at the edge of the continental shelf. The location was south of China and southwest of Taiwan. Vertical and horizontal directionality of both signals and noise can be estimated using the two arrays. Directionality can be linked to vertical mode bandwidth. Furthermore, because of mode stripping effects, it can indicate the amount of mode coupling in the vicinity of the receiver. Previously, arrival time and total energy of the signals have been shown to respond to the strong nonlinear internal waves and internal tides of the area. Here, we investigate the response of noise energy and directionality to the waves, and compare with the response of signal energy and directionality. The results can be compared to the Shelfbreak PRIMER experiment in the Mid-Atlantic Bight, where signal and noise parameters recorded with a VLA were correlated. Correlation of signal and noise violates assumptions used in many signal processing algorithms.

Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation

This paper is concerned with the large time behavior of global smooth solutions to the Cauchy problem of the $p-$system with relaxation. Former results in this direction indicate that such a problem possesses a global smooth solution provided that the first derivative of the solutions with respect to the space variable $x$ are sufficiently small. Under the same small assumption on the global smooth solution, we show that it converges to the corresponding nonlinear rarefaction wave and in our analysis, we do not ask the rarefaction wave to be weak and the initial error can also be chosen arbitrarily large.

Evidence of three-dimensional waveguide propagation in SWARM 95 data

During a period of the SWARM95 experiment, strong nonlinear internal waves passed across two tracks that had airgun pulses propagating along them. Environmental data for this period indicate that the angles between the tracks and the internal wave-fronts, which were roughly planar, were very different—one angle being close to zero, and the other approximately 42 deg. Two-dimensional PE simulations for these waveguides show dramatically different results for depth-averaged, pulse-integrated energy variations. Specifically, the observed levels can be reproduced for the waveguide with the large incidence angle, but not for the one with the small incidence angle. For the latter case, data show significant variations in pulse shapes and in the integrated energy (≊5 dB), while simulations show very small changes in both of these characteristics. Results from several recent computational and theoretical studies suggest that the cause may be three-dimensional effects from horizontal refraction and modal interference due to the nonlinear internal waves. The adiabatic mode parabolic equation [Collins, J. Acoust. Soc. Am. 94 (1993)] is used to quantify the three-dimensional influence of the internal waves on the integrated energy variations. The results demonstrate experimental evidence of three-dimensional effects from strong nonlinear internal waves. [Work supported by ONR.]

Observations and modeling of acoustic intensity fluctuations seen during the 1996 summer New England shelfbreak PRIMER experiment

In this paper we discuss the intensity fluctuation characteristics of 400-Hz acoustic transmissions made in the Mid-Atlantic Bight during the summer of 1996. The transmissions traversed variable topography, the dynamic shelfbreak front, and strong nonlinear internal waves, all of which affected the acoustic propagation. In studying the intensity fluctuations, we look both at data from the PRIMER vertical line array receiver and at output from a broadband parabolic equation model intended to simulate the experimental conditions with high fidelity. The statistics of the fluctuations, the physical causes of the fluctuations, and the correlation with the oceanographic forcing in different frequency bands (subtidal, tidal, and high frequency) all are examined. [Work supported by ONR.]

Effects of Wave Intermittency/Nonlinearity on Forces and Responses

The objective of this study is to investigate effects of both free surface fluctuation (i.e. wave intermittency) and the nonlinearity of wave kinematics on total wave forces and on the dynamic responses of offshore structures. The random wave considered herein is restricted to unidirectional, deep-water ocean waves. Monte Carlo simulations and time-domain techniques are employed so that all nonlinear phenomena can be accurately included. Numerical comparisons are carried out for total wave forces and structural responses according to either linear or second-order random wave theory and by either including or excluding surface fluctuation. The study finds that under a weakly nonlinear, deep-water wave condition, both surface fluctuation and kinematic nonlinearity can be omitted. However, for a relatively strong nonlinear wave condition, both free-surface intermittency effect and nonlinearity of wave kinematics are important.

Strong turbulence and nonlinear random waves in particle fluxes of hydrodynamic type

Strong turbulence and nonlinear random waves in particle fluxes of hydrodynamic type

Gravity wave saturation and eddy diffusion in the middle atmosphere

A discussion is given of gravity wave saturation and its relation to eddy diffusion in the middle atmosphere. Attention is focused on the saturation process and some of its observable manifestations. It does not serve as a review of all related work. Although a theoretical point of view is taken, the emphasis is on which wave parameters need be measured to predict quantitatively the influence of gravity waves on eddy transport. The following considerations are stressed: the variation of spectra with observation time T; that eddy diffusivities are determined by velocity spectra; the anisotropic nature of diffusivity; a unified approach to saturation; an attempt to make eddy diffusivity more precise; the relationship between eddy diffusivity and wave dissipation. The subjects of ‘wave drag’ (momentum flux deposition) and heat flux need only be treated briefly, because they are related to eddy diffusivity in simple ways. Consideration is also given to two different theoretical mechanisms of wave saturation—wave induced convective instability and strong nonlinear wave interactions. The saturation theory is then used to predict a globally averaged height profile of vertical diffusivity in the middle atmosphere. This calculation shows that gravity waves are a major contributor to eddy diffusion from heights of 40–110 km, and that they are significant down to 20 km. A more detailed calculation of wave induced eddy diffusion, including latitudinal and seasonal variations, can be made if wave velocity spectra become available. The paper closes with recommendations for future research.

Threshold conditions for electron trapping by nonlinear plasma waves

Numerical solutions of the nonlinear Vlasov equation show that the long time behavior of an electrostatic plasma wave depends critically on the value of the parameter γτ (γ is Landau's damping coefficient and τ is the electron bounce time), both for large and small initial wave amplitudes. When the initial wave amplitude is large, the initial nonlinear damping is stronger than Landau damping; for smaller initial amplitudes, the behavior is initially described by Landau's theory. For both types of problems if γτ > 0.5, the wave damps monotonically; if γτ < 0.5, the numerical results indicate that the plasma performs amplitude oscillations. When γτ ≈ 0.5, the plasma displays its critical behavior; here, after some initial damping the wave amplitude levels off at a constant value. The critical behavior observed for mild nonlinear problems is in good agreement with the experimental results of Franklin, Hamberger, and Smith. For a moderately strong nonlinear wave displaying the critical behavior, the wave performs periodic oscillations with a frequency smaller than Landau's linear frequency; this frequency shift is explained because the uniform electron distribution develops a plateau centered at Landau's phase velocity.

Nonlinear electric field oscillations in continuous media

Strong nonlinear potential and drift-velocity waves in a nonequilibrium medium, in which the current-carrier collision frequency depends on the electric field, are considered in the hydrodynamic approximation.