Wave evolution over a gradual slope with turbulent friction

1983 ◽  
Vol 133 ◽  
pp. 207-216 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Friction Coefficient ◽  
Gravity Wave ◽  
Solitary Waves ◽  
Periodic Sequence ◽  
Relative Amplitude ◽  
Sinusoidal Wave ◽  
Turbulent Friction ◽  
Weakly Nonlinear ◽  
Wave Evolution

The evolution of a weakly nonlinear, weakly dispersive gravity wave in water of depth d over a bottom of gradual slope δ and Chezy friction coefficient Cf is studied. It is found that an initially sinusoidal wave evolves into a periodic sequence of solitary waves with relative amplitude a/d = α1 = 15δ/4Cf if α1 < αb, where αb is the relative amplitude above which breaking occurs. This prediction is supported by observations (Wells 1978) of the evolution of swell over mudflats.

Transcritical two-layer flow over topography

1987 ◽  
Vol 178 ◽  
pp. 31-52 ◽  
Author(s):  
W. K. Melville ◽  
Karl R. Helfrich
Keyword(s):  
Steady Flow ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Single Layer ◽  
Cubic Nonlinearity ◽  
Arbitrary Length ◽  
Weakly Nonlinear ◽  
Flow Over Topography ◽  
Layer Flow

The evolution of weakly-nonlinear two-layer flow over topography is considered. The governing equations are formulated to consider the effects of quadratic and cubic nonlinearity in the transcritical regime of the internal mode. In the absence of cubic nonlinearity an inhomogeneous Korteweg-de Vries equation describes the interfacial displacement. Numerical solutions of this equation exhibit undular bores or sequences of Boussinesq solitary waves upstream in a transcritical regime. For sufficiently large supercritical Froude numbers, a locally steady flow is attained over the topography. In that regime in which both quadratic and cubic nonlinearity are comparable, the evolution of the interface is described by an inhomogeneous extended Kortewegde Vries (EKdV) equation. This equation displays undular bores upstream in a subcritical regime, but monotonic bores in a transcritical regime. The monotonic bores are solitary wave solutions of the corresponding homogeneous EKdV equation. Again, locally steady flow is attained for sufficiently large supercritical Froude numbers. The predictions of the numerical solutions are compared with laboratory experiments which show good agreement with the solutions of the forced EKdV equation for some range of parameters. It is shown that a recent result of Miles (1986), which predicts an unsteady transcritical regime for single-layer flows, may readily be extended to two-layer flows (described by the forced KdV equation) and is in agreement with the results presented here.Numerical experiments exploiting the symmetry of the homogeneous EKdV equation show that solitary waves of fixed amplitude but arbitrary length may be generated in systems described by the inhomogeneous EKdV equation.

scholarly journals Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas

2004 ◽  
Vol 11 (2) ◽  
pp. 219-228 ◽  
Author(s):  
S. S. Ghosh ◽  
G. S. Lakhina
Keyword(s):  
Solitary Waves ◽  
Nonlinear Theory ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Magnetized Plasma ◽  
Amplitude Variation ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

The Interaction of Katabatic Flow and Mountain Waves. Part II: Case Study Analysis and Conceptual Model

2007 ◽  
Vol 64 (6) ◽  
pp. 1857-1879 ◽  
Author(s):  
Gregory S. Poulos ◽  
James E. Bossert ◽  
Thomas B. McKee ◽  
Roger A. Pielke
Keyword(s):  
Conceptual Model ◽  
Gravity Wave ◽  
Wave Breaking ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Wave System ◽  
Katabatic Flow ◽  
Mountain Wave ◽  
Mountain Waves ◽  
Wave Evolution

Via numerical analysis of detailed simulations of an early September 1993 case night, the authors develop a conceptual model of the interaction of katabatic flow in the nocturnal boundary layer with mountain waves (MKI). A companion paper (Part I) describes the synoptic and mesoscale observations of the case night from the Atmospheric Studies in Complex Terrain (ASCOT) experiment and idealized numerical simulations that manifest components of the conceptual model of MKI presented herein. The reader is also referred to Part I for detailed scientific background and motivation. The interaction of these phenomena is complicated and nonlinear since the amplitude, wavelength, and vertical structure of the mountain-wave system developed by flow over the barrier owes some portion of its morphology to the evolving atmospheric stability in which the drainage flows develop. Simultaneously, katabatic flows are impacted by the topographically induced gravity wave evolution, which may include significantly changing wavelength, amplitude, flow magnitude, and wave breaking behavior. In addition to effects caused by turbulence (including scouring), perturbations to the leeside gravity wave structure at altitudes physically distant from the surface-based katabatic flow layer can be reflected in the katabatic flow by transmission through the atmospheric column. The simulations show that the evolution of atmospheric structure aloft can create local variability in the surface pressure gradient force governing katabatic flow. Variability is found to occur on two scales, on the meso-β due to evolution of the mountain-wave system on the order of one hour, and on the microscale due to rapid wave evolution (short wavelength) and wave breaking–induced fluctuations. It is proposed that the MKI mechanism explains a portion of the variability in observational records of katabatic flow.

Weakly nonlinear kink-type solitary waves in a fully relativistic plasma

2010 ◽  
Vol 17 (8) ◽  
pp. 082309 ◽  
Author(s):  
Mouloud Tribeche ◽  
Soufiane Boukhalfa ◽  
Taha Houssine Zerguini
Keyword(s):  
Solitary Waves ◽  
Relativistic Plasma ◽  
Weakly Nonlinear

On the free-surface flow of very steep forced solitary waves

2013 ◽  
Vol 739 ◽  
pp. 1-21 ◽  
Author(s):  
Stephen L. Wade ◽  
Benjamin J. Binder ◽  
Trent W. Mattner ◽  
James P. Denier
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Flow Problem ◽  
Nonlinear Approximation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Weakly Nonlinear ◽  
Nonlinear Solutions

AbstractThe free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 1. Stability of solitary waves

2007 ◽  
Vol 73 (2) ◽  
pp. 215-229 ◽  
Author(s):  
M.A. ALLEN ◽  
S. PHIBANCHON ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves ◽  
Stability Of Solitary Waves

Abstract.Weakly nonlinear waves in strongly magnetized plasma with slightly non-isothermal electrons are governed by a modified Zakharov–Kuznetsov (ZK) equation, containing both quadratic and half-order nonlinear terms, which we refer to as the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation. We present a method to obtain an approximation for the growth rate, γ, of sinusoidal perpendicular perturbations of wavenumber, k, to SKdVZK solitary waves over the entire range of instability. Unlike for (modified) ZK equations with one nonlinear term, in this method there is no analytical expression for kc, the cut-off wavenumber (at which the growth rate is zero) or its corresponding eigenfunction. We therefore obtain approximate expressions for these using an expansion parameter, a, related to the ratio of the nonlinear terms. The expressions are then used to find γ for k near kc as a function of a. The approximant derived from combining these analytical results with the ones for small k agrees very well with the values of γ obtained numerically. It is found that both kc and the maximum growth rate decrease as the electron distribution becomes progressively less peaked than the Maxwellian. We also present new algebraic and rarefactive solitary wave solutions to the equation.

The Flat Solitary Waves Due to a Submerged Moving Body in a Two-Layer Fluid With a Free Surface

2005 ◽  
Author(s):  
Gang Wei ◽  
Xiao-Bing Su ◽  
Yun-Xiang You
Keyword(s):  
Free Surface ◽  
Theoretical Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Experimental Results ◽  
Stable System ◽  
Weakly Nonlinear ◽  
Submerged Body ◽  
Moving Body

The flat solitary wave with the behavior of conjugate flow, generated by a submerged body moving in a two-layer fluid, is investigated. A criteria about the existence of weakly nonlinear weakly dispersive flat solitary wave is given. The condition of the stable system of conjugate flow is obtained. The solution of the flat solitary wave satisfying the criteria is numerically verified to be unique. Theoretical analysis is qualitatively consistent with the experimental results obtained by the authors.

Effect of finite ion-temperature on ion-acoustic solitary waves in an inhomogeneous plasma

1981 ◽  
Vol 59 (6) ◽  
pp. 719-721 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Acoustic Waves ◽  
Inhomogeneous Plasma ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Velocity Of Propagation

The propagation of weakly nonlinear ion–acoustic waves in an inhomogeneous plasma is studied taking into account the effect of finite ion temperature. It is found that, whereas both the amplitude and the velocity of propagation decrease as the ion–acoustic solitary wave propagates into regions of higher density, the effect of a finite ion temperature is to reduce the amplitude but enhance the velocity of propagation of the solitary wave.

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