Short small-amplitude wave interaction in a weakly dispersive plasma. II

In this paper we consider the dynamic behavior of granular solids in the context of a one-dimensional, linearized theory. Uniqueness of solutions for unbounded domains is established and two wave propagation problems are solved. In particular, the dispersion relations for small-amplitude sinusoidal progressive waves are obtained and the evolution of small-amplitude shock waves is exhibited.

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A new Hamiltonian formulation for fluids and plasmas. Part 2. MHD models

Journal of Plasma Physics ◽

10.1017/s0022377800018821 ◽

1996 ◽

Vol 55 (2) ◽

pp. 261-278 ◽

Cited By ~ 8

Author(s):

Jonas Larsson

Keyword(s):

Perfect Fluid ◽

Small Amplitude ◽

Hamiltonian Formulation ◽

Wave Interaction ◽

Mathematical Structure ◽

Rigorous Proof ◽

Ideal Mhd ◽

Fluid Equations ◽

Stationary Background

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD models, including for example ideal MHD and the Chew–Goldberger–Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows.

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Dynamics of steep two-dimensional gravity–capillary solitary waves

Journal of Fluid Mechanics ◽

10.1017/s0022112010004714 ◽

2010 ◽

Vol 664 ◽

pp. 466-477 ◽

Cited By ~ 47

Author(s):

PAUL A. MILEWSKI ◽

J.-M. VANDEN-BROECK ◽

ZHAN WANG

Keyword(s):

Solitary Waves ◽

Small Amplitude ◽

Two Dimensional ◽

Amplitude Wave ◽

Linear Dispersion ◽

Infinite Depth ◽

Linear Dispersion Relation ◽

Dimensional Gravity ◽

Nonlinear Free Surface ◽

The Waves

In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.

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NUMERICAL MODEL OF BREAKING WAVE AROUND A RIVER MOUTH

Coastal Engineering Proceedings ◽

10.9753/icce.v20.97 ◽

1986 ◽

Vol 1 (20) ◽

pp. 97

Author(s):

Jong-Sup Lee ◽

Toru Sawaragi ◽

Ichiro Deguchi

Keyword(s):

Numerical Model ◽

Wave Breaking ◽

Small Amplitude ◽

River Mouth ◽

Wave Theory ◽

Experimental Result ◽

Breaking Wave ◽

Linear Wave ◽

Amplitude Wave ◽

Current Interaction

Equations for wave kinematics and wave dynamics based on small amplitude wave theory have been used in the prediction of wave deformations and wave-indused currents. However, the applicability of the linear wave theory is questionable in a river mouth where forced wave breaking and strong wave-current interaction take place. A numerical model based on the non-linear dispersive wave theory has been developed, the results by this model was compared with the values of the experiments and the linear theory. Wave transformations including shoaling, wave-current interaction and wave breaking by the model showed a good agreement with the experimental result. In the prediction of wave-induced currents, the excess momentum flux (Pxx) computed by the model has more reasonable value than the radiation stress ( Sxx) calculated by the small amplitude wave theory.

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WAVE PRESSURES ON LARGE CIRCULAR CYLINDRICAL STRUCTURE

Coastal Engineering Proceedings ◽

10.9753/icce.v15.133 ◽

1976 ◽

Vol 1 (15) ◽

pp. 133

Author(s):

Hiroshi Nakamura

Keyword(s):

Power Plant ◽

Small Amplitude ◽

Nuclear Power ◽

Cooling Water ◽

Wave Theory ◽

Field Observations ◽

Amplitude Wave ◽

Cylindrical Structures ◽

Cylindrical Structure ◽

Intake Structure

The field observations on wave pressures on large circular cylindrical structures are performed at the cooling water intake structure for Hamaoka nuclear power plant, which is located at the coast of Pacific Ocean. In this report, the results of the field observation on wave pressures are compared with the results of the calculation by small amplitude wave theory considering wave diffraction around the cylinder.

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