scholarly journals Singular solutions of the BBM equation: analytical and numerical study

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 388-410
Author(s):  
Sergey Gavrilyuk ◽  
Keh-Ming Shyue
Keyword(s):  
Phase Velocity ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wave Train ◽  
Wave Length ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Constant State ◽  
Bbm Equation ◽  
Good Agreement

Abstract We show that the Benjamin–Bona–Mahony (BBM) equation admits stable travelling wave solutions representing a sharp transition from a constant state to a periodic wave train. The constant state is determined by the parameters of the periodic wave train: the wave length, amplitude and phase velocity, and satisfies both the generalized Rankine–Hugoniot conditions for the exact BBM equation and for its wave averaged counterpart. Such stable shock-like travelling structures exist if the phase velocity of the periodic wave train is not less than the solution wave averaged. To validate the accuracy of the numerical method, we derive the (singular) solitary limit of the Whitham system for the BBM equation and compare the corresponding numerical and analytical solutions. We find good agreement between analytical results and numerical solutions.

Drifting Rogue Packets

2018 ◽  
Author(s):  
Amin Chabchoub ◽  
Norbert Hoffmann ◽  
Nail Akhmediev ◽  
Takuji Waseda
Keyword(s):  
Modulation Instability ◽  
Wave Train ◽  
Modulation Frequency ◽  
Phase Speed ◽  
Periodic Wave ◽  
Unstable Wave ◽  
Extreme Waves ◽  
Wave Groups ◽  
The Waves ◽  
Good Agreement

Modulation instability (MI) is one possible mechanism to explain the formation of extreme waves in uni-directional and narrow-banded seas. It can be triggered, when side-bands around the main frequency are excited and subsequently follow an exponential growth. In physical domain this dynamics translates to periodic pulsations of wave groups that can reach heights up to three times the initial amplitude of the wave train. It is well-known that these periodic wave groups propagate with approximately half the waves phase speed in deep-water. We report an experimental study on modulationally unstable wave groups that propagate with a velocity that is higher than the group velocity since the modulation frequency is complex. It is shown that when this additional velocity to the wave groups is small a good agreement with exact nonlinear Schrödinger (NLS) models, that describe the nonlinear stage of MI, is reached. Otherwise a significant deviation is observed that could be compensated when increasing accuracy of the water wave modeling beyond NLS.

Incompressible Navier-Stokes Computation of the NREL Airfoils Using a Symmetric Total Variational Diminishing Scheme

1994 ◽  
Vol 116 (4) ◽  
pp. 174-182 ◽  
Author(s):  
S. L. Yang ◽  
Y. L. Chang ◽  
O. Arici
Keyword(s):  
Turbulence Model ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wind Tunnel Test ◽  
Factorization Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Approximate Factorization ◽  
Two Dimensional Flow ◽  
Good Agreement

The purpose of this paper is to present a numerical study of flow fields for the NREL S805 and S809 airfoils using a spatially second-order symmetric total variational diminishing scheme. The steady two-dimensional flow is modeled as turbulent, viscous, and incompressible and is formulated in the pseudo-compressible form. The turbulent flow is closed by the Baldwin-Lomax algebraic turbulence model. Numerical solutions are obtained by the implicit approximate-factorization method. The accuracy of the numerical results is compared with the Delft two-dimensional wind tunnel test data. For comparison, the Eppler code results are also included. Numerical solutions of pressure and lift coefficients show good agreement with the experimental data, but not the drag coefficients. To properly simulate the post-stall flow field, a better turbulence model should be used.

Turbulent airflow over water waves-a numerical study

1984 ◽  
Vol 148 ◽  
pp. 225-246 ◽  
Author(s):  
M. A. Al-Zanaidi ◽  
W. H. Hui
Keyword(s):  
Water Waves ◽  
Field Experiments ◽  
Numerical Study ◽  
Wave Train ◽  
Viscous Sublayer ◽  
Smooth Flow ◽  
Fractional Rate ◽  
Wave Phase Velocity ◽  
Turbulent Airflow ◽  
Good Agreement

Turbulent airflow over a Stokes water-wave train of small amplitude is studied numerically based on the two-equation closure model of Saffman & Wilcox (1974) together with appropriate boundary conditions on the wave surface. The model calculates, instead of assuming, the viscous sublayer flow, and it is found that the energy transfer between wind and waves depends significantly on the flow being hydraulically rough, transitional or smooth. Systematic computations have yielded a simple approximate formula for the fractional rate of growth per radian \[ \zeta = \delta_{\rm i}\frac{\rho}{\rho_{\rm w}}\left(\frac{U_{\lambda}}{c}-1 \right)^2, \] with δi = 0.04 for transitional or smooth flow and δi = 0.06 for rough flow, where ρ is density of air, ρw that of water, Uλ wind speed at one wavelength height and c the wave phase velocity. This formula is in good agreement with most existing data from field experiments and from wave-tank experiments. In the case of waves travelling against wind, the corresponding values are δi = −0.024 for transitional and smooth flow, and δi = −0.04 for rough flow.

PROPAGATION OF ULTRASOUND IN SOLID CYLINDERS (TRANSVERSE WAVES)

1932 ◽  
Vol 7 (1) ◽  
pp. 86-94 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Phase Velocity ◽  
Wave Length ◽  
Flexural Waves ◽  
Natural Period ◽  
Transverse Waves ◽  
Mechanical Coupling ◽  
Resonance Effects ◽  
Different Types ◽  
Pass Through ◽  
Good Agreement

The expression giving the phase velocity c with which flexural waves pass through long solid rods is deduced for frequencies varying between zero and over 1,000,000 cycles per sec. and rods of any diameter. As the frequency increases, the velocity c increases gradually from very low values toward c2 = mE/2s(m+1), reached when the wave-length is much smaller than the diameter of the rod. Published experimental results for transverse waves are in good agreement with the theory given. In general at least four effects enter into the propagation of ultrasound through solid cylinders: first, longitudinal waves, for which the phase velocity decreases toward c as the frequency increases; second, transverse waves, for which the phase velocity increases toward c as the frequency increases; third, pure radial waves at certain frequencies; fourth, resonance effects between the different types of waves, which, on account of the mechanical coupling existing between them, change the natural period of vibration of the rod without affecting the velocity.

Stochastic generalised KPP equations

1996 ◽  
Vol 126 (5) ◽  
pp. 957-983 ◽  
Author(s):  
I. M. Davies ◽  
A. Truman ◽  
H. Z. Zhao
Keyword(s):  
White Noise ◽  
Numerical Solutions ◽  
Travelling Waves ◽  
Wave Structure ◽  
Travelling Wave ◽  
Wave Form ◽  
Kpp Equations ◽  
Image Position ◽  
Theoretical Results ◽  
Good Agreement

We classify multiplicative white noise perturbationsk(·)dw, of generalised KPP equations and their effects on deterministic approximate travelling wave solutions by the behaviour of, the solutions of the stochastic generalised KPP equations converge to deterministic approximate travelling waves and ifbeing an associated potential energy, Фsa solution of the corresponding classical mechanical equations of Newton,Dbeing a certain domain inR1×Rrthen the white noise perturbations essentially destroy the wave structure and force the solutions to die down.For the case(suppose the existence of the limit) we show that there is a residual wave form but propagating at a different speed from that of the unperturbed equations. Numerical solutions are included and give good agreement with theoretical results.

Thermal Performance Analysis of a Rectangular Longitudinal Finned Solar Air Heater With Semicircular Absorber Plate

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Satyender Singh ◽  
Prashant Dhiman
Keyword(s):  
Thermal Performance ◽  
Numerical Solutions ◽  
Solar Air Heater ◽  
Duct Flow ◽  
Balance Equations ◽  
Absorber Plate ◽  
Ansys Fluent ◽  
Air Heater ◽  
Glass Cover ◽  
Good Agreement

Thermal performance of a single-pass single-glass cover solar air heater consisting of semicircular absorber plate finned with rectangular longitudinal fins is investigated. The analysis is carried out for different hydraulic diameters, which were obtained by varying the diameter of the duct from 0.3–0.5 m. One to five numbers of fins are considered. Reynolds number ranges from 1600–4300. Analytical solutions for energy balance equations of different elements and duct flow of the solar air heater are presented; results are compared with finite-volume methodology based numerical solutions obtained from ansys fluent commercial software, and a fairly good agreement is achieved. Moreover, analysis is extended to check the effect of double-glass cover and the recycle of the exiting air. Results revealed that the use of double-glass cover and recycle operation improves the thermal performance of solar air heater.

scholarly journals Experimental and Numerical Buckling Analyses of Laminated Composite Plates under Temperature Effects

2010 ◽  
Vol 19 (4) ◽  
pp. 096369351001900 ◽  
Author(s):  
Emin Ergun
Keyword(s):  
Composite Plate ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Buckling Load ◽  
Fibre Reinforcement ◽  
Stacking Sequence ◽  
Laminated Composite Plates ◽  
Different Temperatures ◽  
Good Agreement

The aim of this study is to investigate, experimentally and numerically, the change of critical buckling load in composite plates with different ply numbers, orientation angles, stacking sequences and boundary conditions as a function of temperature. Buckling specimens have been removed from the composite plate with glass-fibre reinforcement at [0°]i and [45°]i (i= number of ply). First, the mechanical properties of the composite material were determined at different temperatures, and after that, buckling experiments were done for those temperatures. Then, numerical solutions were obtained by modelling the specimens used in the experiment in the Ansys10 finite elements package software. The experimental and numerical results are in very good agreement with each other. It was found that the values of the buckling load at [0°] on the composite plates are higher than those of other angles. Besides, symmetrical and anti-symmetrical conditions were examined to see the effect of the stacking sequence on buckling and only numerical solutions were obtained. It is seen that the buckling load reaches the highest value when it is symmetrical in the cross-ply stacking sequence and it is anti-symmetrical in the angle-ply stacking sequence.

A Compact Model for Spherical Rough Contacts

2004 ◽  
Author(s):  
M. Bahrami ◽  
M. M. Yovanovich ◽  
J. R. Culham
Keyword(s):  
Pressure Distribution ◽  
Entire Range ◽  
Present Model ◽  
Numerical Solutions ◽  
Contact Radius ◽  
Bulk Deformation ◽  
Dimensional Parameters ◽  
Maximum Contact ◽  
Good Agreement ◽  
Key Parameter

The contact of rough spheres is of high interest in many tribological, thermal, and electrical fundamental analyses. Implementing the existing models is complex and requires iterative numerical solutions. In this paper a new model is presented and a general pressure distribution is proposed that encompasses the entire range of spherical rough contacts including the Hertzian limit. It is shown that the non-dimensional maximum contact pressure is the key parameter that controls the solution. Compact expressions are proposed for calculating the pressure distribution, radius of the contact area, elastic bulk deformation, and the compliance as functions of the governing non-dimensional parameters. The present model shows the same trends as those of the Greenwood and Tripp model. Correlations proposed for the contact radius and the compliance are compared with experimental data collected by others and good agreement is observed.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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