scholarly journals Focusing of non-linear eccentric waves in astrophysical discs

2019 ◽  
Vol 488 (1) ◽  
pp. 1127-1140 ◽  
Author(s):  
Elliot M Lynch ◽  
Gordon I Ogilvie
Keyword(s):  
Linear Approximation ◽  
Short Wavelength ◽  
Lagrangian Method ◽  
Pressure Gradients ◽  
Linearized Equations ◽  
Wavelength Limit ◽  
Non Linear ◽  
Separation Of Scales ◽  
The Waves

ABSTRACT We develop a fully non-linear approximation to the short-wavelength limit of eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham. In this limit there is a separation of scales between the rapidly varying eccentric wave and the background disc. Despite having small eccentricities, such rapidly varying waves can be highly non-linear, potentially approaching orbital intersection, and this can result in strong pressure gradients in the disc. We derive conditions for the steepening of non-linearity and eccentricity as the waves propagate in a radially structured disc in this short-wavelength limit and show that the behaviour of the solution can be bounded by the behaviour of the WKB solution to the linearized equations.

Magnetised Wave Collapse in Solar System Plasmas

1993 ◽  
Vol 10 (4) ◽  
pp. 283-286 ◽  
Author(s):  
Andrew Melatos ◽  
Peter Robinson
Keyword(s):  
Solar System ◽  
Wave Packets ◽  
Particle Interactions ◽  
Coherent Wave ◽  
Wave Collapse ◽  
Non Linear ◽  
Acceleration Zone ◽  
The Waves ◽  
Linear Plasma

AbstractClumpy, intense wave packets observed in situ in the Jovian and terrestrial electron foreshocks, and in the Earth’s auroral acceleration zone, point to the existence of non-linear plasma turbulence in these regions. In non-linear turbulence, wave packets collapse to short scales and high fields, stopping only when coherent wave-particle interactions efficiently dissipate the energy in the waves. The purpose of this paper is to examine the shortest scales and highest fields achieved during collapse in a strongly magnetised plasma, and identify parts of the solar system where the magnetised aspects of wave collapse are important.

Linear and non-linear potential-flow calculations of free-surface waves with lift and induced drag

2000 ◽  
Vol 214 (6) ◽  
pp. 801-812
Author(s):  
C-E Janson
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Lift Force ◽  
Radiation Condition ◽  
Linear Potential ◽  
Surface Boundary ◽  
Model Approximation ◽  
Non Linear ◽  
Lifting Surfaces ◽  
The Waves

A potential-flow panel method is used to compute the waves and the lift force from surface-piercing and submerged bodies. In particular the interaction between the waves and the lift produced close to the free surface is studied. Both linear and non-linear free-surface boundary conditions are considered. The potential-flow method is of Rankine-source type using raised source panels on the free surface and a four-point upwind operator to compute the velocity derivatives and to enforce the radiation condition. The lift force is introduced as a dipole distribution on the lifting surfaces and on the trailing wake, together with a flow tangency condition at the trailing edge of the lifting surface. Different approximations for the spanwise circulation distribution at the free surface were tested for a surface-piercing wing and it was concluded that a double-model approximation should be used for low speeds while a single-model, which allows for a vortex at the free surface, was preferred at higher speeds. The lift force and waves from three surface-piercing wings, a hydrofoil and a sailing yacht were computed and compared with measurements and good agreement was obtained.

On the Effect of Hull Girder Flexibility on the Vertical Wave Bending Moment for Ultra Large Container Vessels

2012 ◽  
Author(s):  
Ingrid Marie Vincent Andersen ◽  
Jørgen Juncher Jensen
Keyword(s):  
Bending Moment ◽  
Main Concern ◽  
Hull Girder ◽  
Numerical Predictions ◽  
Strip Theory ◽  
Reliability Method ◽  
Non Linear ◽  
Large Container ◽  
The Waves ◽  
Good Agreement

Currently, a number of very large container ships are being built and more are on order, and some concerns have been expressed about the importance of the reduced hull girder stiffness to the wave-induced loads. The main concern is related to the fatigue life, but also a possible increase in the global hull girder loads as consequence of the increased hull flexibility must be considered. This is especially so as the rules of the classification societies do not explicitly account for the effect of hull flexibility on the global loads. In the present paper an analysis has been carried out for the 9,400 TEU container ship used as case-ship in the EU project TULCS (Tools for Ultra Large Container Ships). A non-linear time-domain strip theory is used for the hydrodynamic analysis of the vertical bending moment amidships in sagging and hogging conditions for a flexible and a rigid modelling of the ship. The theory takes into account non-linear radiation forces (memory effects) through the use of a set of higher order differential equations. The non-linear hydrostatic restoring forces and non-linear Froude-Krylov forces are determined accurately at the instantaneous position of the ship in the waves. Slamming forces are determined by a standard momentum formulation. The hull flexibility is modelled as a non-prismatic Timoshenko beam. Generally, good agreement with experimental results and more accurate numerical predictions has previously been obtained in a number of studies. The statistical analysis is done using the First Order Reliability Method (FORM) supplemented with Monte Carlo simulations. Furthermore, strip-theory calculations are compared to model tests in regular waves of different wave lengths using a segmented, flexible model of the case-ship and good agreement is obtained for the longest of the waves. For the shorter waves the agreement is less good. The discrepancy in the amplitudes of the bending moment can most probably be explained by an underestimation on the effect of momentum slamming in the strip-theory applied.

Plasma cavity formation caused by ion acoustic waves and nonlinear modulation of trapped waves

1999 ◽  
Vol 61 (3) ◽  
pp. 489-505
Author(s):  
T. HONZAWA ◽  
S. WATANABE ◽  
Y. SAITOU
Keyword(s):  
Acoustic Waves ◽  
Early Stage ◽  
Cavity Formation ◽  
Pressure Gradients ◽  
Trapped Waves ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Nonlinear Modulation ◽  
Ion Waves ◽  
The Waves

Externally amplitude-modulated ion acoustic waves with high frequencies of 200–320 kHz are experimentally shown to form plasma cavities and to be trapped in them at an early stage. Thereafter, the trapped waves are observed to suffer nonlinear modulation and create new lower-frequency waves with average frequencies as low as 20–40 kHz within the cavities. As a result, the externally excited high-frequency ion acoustic waves are found to be nonlinearly converted into lower-frequency ion waves in the cavities. Finally, the pressure gradients of the waves effective in cavity formation and nonlinear modulation of the trapped waves are discussed.

Coupled fields in inhomogeneous warm plasmas with static pressure gradients. I

1972 ◽  
Vol 72 (2) ◽  
pp. 285-297
Author(s):  
R. Burman
Keyword(s):  
Pressure Gradient ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Static Pressure ◽  
Pressure Gradients ◽  
Coupling Region ◽  
Electron Plasmas ◽  
Coupled Wave Equations ◽  
Electron Acoustic ◽  
The Waves

Abstract.This paper deals with small amplitude waves in inhomogeneous warm electron plasmas. The waves are coupled electromagnetic and electron-acoustic waves, and are described by Maxwell's equations together with single-fluid hydrodynamical equations. Here, previous work is generalized by including the effect of a static pressure gradient. Coupled wave equations are obtained and specialized to the case of a planar stratified plasma. Then, as a preliminary to a treatment of wave coupling, the behaviour of the solutions of the uncoupled wave equations in a coupling region is investigated. The static pressure gradient complicates the behaviour of the uncoupled field components; singularities occur at two points which coalesce as the static pressure gradient is allowed to tend to zero.

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