A combined computational algorithm for solving the problem of long surface waves runup on the shore

2016 ◽  
Vol 31 (4) ◽  
Author(s):  
Yurii I. Shokin ◽  
Alexander D. Rychkov ◽  
Gayaz S. Khakimzyanov ◽  
Leonid B. Chubarov
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Nonlinear Waves ◽  
Laboratory Experiments ◽  
Computational Algorithm ◽  
Analytic Solutions ◽  
Shallow Water Theory ◽  
Sph Method ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear

AbstractIn the present paper we study features and abilities of the combined TVD+SPH method relative to problems of numerical simulation of long waves runup on a shore within the shallow water theory. The results obtained by this method are compared to analytic solutions and to the data of laboratory experiments. Examples of successful application of the TVD+SPH method are presented for the case of study of runup processes for weakly nonlinear and strongly nonlinear waves, and also for

scholarly journals Nonlinear Waves in Force-Free Fibrils

1998 ◽  
Vol 167 ◽  
pp. 151-154
Author(s):  
Y.D. Zhugzhda ◽  
V.M. Nakariakov
Keyword(s):  
Magnetic Flux ◽  
Nonlinear Waves ◽  
Alfvén Waves ◽  
Nonlinear Dissipation ◽  
Weakly Nonlinear ◽  
Flux Tubes ◽  
Strongly Nonlinear ◽  
Local Increase ◽  
De Vries ◽  
Magnetic Flux Tubes

AbstractKorteweg-de Vries equations for slow body and torsional weakly nonlinear Alfvén waves in twisted magnetic flux tubes are derived. Slow body solitons appear as a narrowing of the tube in a low β plasma and widening of the tube, when β ≫ 1. Alfvén torsional solitons appear as a widening (β > 1) and narrowing (β < 1) of the tube, where there is a local increase of tube twisting. Two scenarios of nonlinear dissipation of strongly nonlinear waves in twisted flux tubes are proposed.

Instability of strongly nonlinear waves in vortex flows

1994 ◽  
Vol 269 ◽  
pp. 247-264 ◽  
Author(s):  
A. Kribus ◽  
S. Leibovich
Keyword(s):  
Linear Stability ◽  
Nonlinear Waves ◽  
Vortex Breakdown ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Vortex Flows ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Perturbation Problem ◽  
Bending Modes

Weakly nonlinear descriptions of axisymmetric cnoidal and solitary waves in vortices recently have been shown to have strongly nonlinear counterparts. The linear stability of these strongly nonlinear waves to three-dimensional perturbations is studied, motivated by the problem of vortex breakdown in open flows. The basic axisymmetric flow varies both radially and axially, and the linear stability problem is therefore nonseparable. To regularize the generalization of a critical layer, viscosity is introduced in the perturbation problem. In the absence of the waves, the vortex flows are linearly stable. As the amplitude of a wave constituting the basic flow increases owing to variation in the level of swirl, stability is first lost to non-axisymmetric ‘bending’ modes. This instability occurs when the wave amplitude exceeds a critical value, provided that the Reynolds number is larger enough. The critical wave amplitudes for instability typically are large, but not large enough to create regions of closed streamlines. Examination of the most-amplified eigenvectors shows that the perturbations tend to be concentrated downstream of the maximum streamline displacement in the wave, in a position consistent with the observed three-dimensional perturbations in the interior of a bubble type of vortex breakdown.

The growth of periodic waves in gas-fluidized beds

1996 ◽  
Vol 325 ◽  
pp. 261-282 ◽  
Author(s):  
S. E. Harris
Keyword(s):  
Nonlinear Waves ◽  
Fluidized Beds ◽  
Kdv Equation ◽  
Periodic Waves ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
The Kdv Equation ◽  
Weakly Nonlinear Waves ◽  
Gas Fluidized Beds ◽  
The One

In this paper, we analyse the development of initially small, periodic, voidage disturbances in gas-fluidized beds. The one-dimensional model was proposed by Needham & Merkin (1983), and Crighton (1991) showed that weakly nonlinear waves satisfied a perturbed Korteweg–de Vries or KdV equation. Here, we take periodic cnoidal wave solutions of the KdV equation and follow their evolution when the perturbation terms are amplifying. Initially, all such waves grow, but at a later stage a rescaling shows that shorter wavelengths are stabilized in a weakly nonlinear state. Longer wavelengths continue to develop and eventually strongly nonlinear solutions are required. Necessary conditions for periodic waves are found and matching back onto the growing cnoidal waves is possible. It is shown further that these fully nonlinear waves also reach an equilibrium state. A comparison with numerical results from Needham & Merkin (1986) and Anderson, Sundaresan & Jackson (1995) is then carried out.

Amplification and decay of long nonlinear waves

1973 ◽  
Vol 58 (3) ◽  
pp. 481-493 ◽  
Author(s):  
S. Leibovich ◽  
J. D. Randall
Keyword(s):  
Shallow Water ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Variable Coefficients ◽  
Finite Amplitude ◽  
Rotating Fluids ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves

The interaction of weakly nonlinear waves with slowly varying boundaries is considered. Special emphasis is given to rotating fluids, but the analysis applies with minor modifications to waves in stratified fluids and shallow-water aves. An asymptotic solution of a variant of the Korteweg–de Vries equation with variable coefficients is developed that produces a ‘Green's law’ for the amplification of waves of finite amplitude. For shallow-water waves in water of variable depth, the result predicts wave growth proportional to the $-\frac{1}{3}$ power of the depth.

Single shock and periodic sawtooth-shaped waves in media with non-analytic nonlinearities

2018 ◽  
Vol 13 (2) ◽  
pp. 18
Author(s):  
O.V. Rudenko ◽  
C.M. Hedberg
Keyword(s):  
Mathematical Models ◽  
Nonlinear Waves ◽  
Analytic Solutions ◽  
Strongly Nonlinear ◽  
The Past ◽  
Exact Analytic Solutions ◽  
Multiphase Systems ◽  
Qualitative Level ◽  
Propagation Of Waves ◽  
Physical Phenomena

The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Media with non-analytic nonlinearities exist among composites, meta-materials, inhomogeneous and multiphase systems. Some physical phenomena manifested in the propagation of waves in such media are described on the qualitative level of severity.

scholarly journals Head-on collision of internal waves with trapped cores

2017 ◽  
Author(s):  
Vladimir Maderich ◽  
Kyung Tae Jung ◽  
Kateryna Terletska ◽  
Kyeong Ok Kim
Keyword(s):  
Nonlinear Waves ◽  
Wave Amplitude ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Class Iii ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Conservation Of Momentum

Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves the trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly nonlinear waves without trapped cores, (ii) stable strongly nonlinear waves with trapped cores, and (iii) shear unstable strongly nonlinear waves. The wave phase shift grows as the amplitudes of the interacting waves increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum runup amplitude over the sum of the amplitudes of colliding waves almost linearly increases with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The waves of class (ii) with a normalized on thickness of pycnocline amplitude lose fluid trapped by the wave cores in the range approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of three-dimensional instability and turbulence. The dependence of loss of energy on the wave amplitude is not monotonous. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

scholarly journals COMBINED REFRACTION-DIFFRACTION OF NONLINEAR WAVES IN SHALLOW WATER

1984 ◽  
Vol 1 (19) ◽  
pp. 68
Author(s):  
James T. Kirby ◽  
Philip L.F. Liu ◽  
Sung B. Yoon ◽  
Robert A. Dalrymple
Keyword(s):  
Shallow Water ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Evolution Equations ◽  
Boussinesq Equations ◽  
Two Dimensions ◽  
Parabolic Approximation ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Dimensional Domain

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow water waves. Two methods of approach are taken. In the first method Boussinesq equations are used to derive evolution equations for spectral wave components in a slowly varying two-dimensional domain. The second method modifies the equation of Kadomtsev s Petviashvili to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data and previous numerical calculations.

The transition from density-driven to wave-dominated isolated flows

1998 ◽  
Vol 361 ◽  
pp. 253-274 ◽  
Author(s):  
RICHARD MANASSEH ◽  
CHANG-YUN CHING ◽  
HARINDRA J. S. FERNANDO
Keyword(s):  
Solitary Wave ◽  
Laboratory Experiments ◽  
Gravity Current ◽  
Temperature Inversion ◽  
Transitional Regime ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Ice Cap ◽  
Flow Parameters ◽  
Wave Effects

An isolated fluid mass travelling horizontally in a stratified layer is a phenomenon described alternatively as a detached gravity-current head or a strongly nonlinear solitary wave. A key feature of this flow is the transport of mass. Laboratory experiments examine the transition in time from a regime in which the flow is density driven, to one in which it is wave dominated. A simple means of creating this transitional regime, an isolated flow that exhibits both density and wave effects, is achieved by dropping a thermal into a linearly stratified layer. This transitional regime is called an ‘isolated propagating flow’. Parameters for which the transitional regime occurs are identified. Particle-tracking studies reveal the vertical flow structure. There is an upper zone that is wave dynamical, and a lower zone in which transport of mass occurs. The transported mass slowly leaks out, until the phenomenon resembles a weakly nonlinear solitary wave. The experiments mimic a thunderstorm microburst impacting a temperature inversion, which has aviation safety implications. In the ocean, cracks in the ice cap (polar leads) cause similar flows impacting the thermocline.

NUMERICAL SIMULATION OF TWO-PHASES FLOW ON PUMPS INLET SYSTEM FOR SHALLOW WATER

2019 ◽  
Author(s):  
Livio Sebastián Maglione ◽  
Guillermo Muschiatto ◽  
Raúl Alberto DEAN
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Inlet System ◽  
Two Phases ◽  
Two Phases Flow
Sign in / Sign up

Export Citation Format

Share Document