Waves caused by a moving disturbance in a shallow channel of finite width

Ertekin, R. Cengiz; Webster, William C.; Wehausen, John V.

doi:10.1017/s0022112086000630

Cited by 200 publications

(110 citation statements)

References 15 publications

Supporting

Mentioning

101

Contrasting

Order By: Relevance

“…Systematic experiments reported by Huang et al (1982), Ertekin et al (1984) and Lee et al (1989) established the presence of upstream propagating solitary waves. As well as the numerical simulations of the fKdV equation, simulations of a generalized Boussinesq equations by and Lee et al (1989), and of a Green-Naghdi model by Ertekin et al (1986) also confirmed the generation of upstream propagating solitary waves by transcritical flow over an obstacle.…”

Section: Introductionmentioning

confidence: 56%

Generation of solitary waves by transcritical flow over a step

2007

View full text Add to dashboard Cite

It is well-known that transcritical flow over a localised obstacle generates upstream and downstream nonlinear wavetrains. The flow has been successfully modeled in the framework of the forced Korteweg-de Vries equation, where numerical and asymptotic analytical solutions have shown that the upstream and downstream nonlinear wavetrains have the structure of unsteady undular bores, connected by a locally steady solution over the obstacle, which is elevated on the upstream side and depressed on the downstream side. In this paper we consider the analogous transcritical flow over a step, primarily in the context of water waves. We use numerical and asymptotic analytical solutions of the forced Korteweg-de Vries equation, together with numerical solutions of the full Euler equations, to demonstrate that a positive step generates only an upstream-propagating undular bore, and a negative step generates only a downstream-propagating undular bore.

show abstract

Section: Introductionmentioning

confidence: 56%

Generation of solitary waves by transcritical flow over a step

2007

View full text Add to dashboard Cite

show abstract

“…Hence, numerical filtering of the result is necessary. Shown by Ertekin et al [17] for similar problems as that studied here, a combination of the five-(second-order) and seven-point (third-order) linear filtering schemes, developed by Shapiro [63], would ensure stability, while not altering the shape of the incident wave or the results. This includes the use of a third-order filtering in the direction normal to the prevailing wave crests, the ξ direction, and a second-order filtering parallel to the wave crests, the η direction.…”

Section: Numerical Solutionmentioning

confidence: 88%

“…The Level I GN equations are given here in the same form first presented by Ertekin [11] and Ertekin et al [17]. In this form of the equations, the fluid is inviscid, and the flow is incompressible, but irrotationality is not required.…”

Section: The Green-naghdi Equationsmentioning

confidence: 99%

Diffraction of cnoidal waves by vertical cylinders in shallow water

Hayatdavoodi

Neill

Ertekin

2018

Theor. Comput. Fluid Dyn.

View full text Add to dashboard Cite

Diffraction of nonlinear waves by single or multiple in-line vertical cylinders in shallow water is studied by use of different nonlinear, shallow-water wave theories. The fixed, in-line, vertical circular cylinders extend from the free surface to the seafloor and are located in a row parallel to the incident wave direction. The wave-structure interaction problem is studied by use of the nonlinear generalized Boussinesq equations, the Green-Naghdi shallow-water wave equations, and the linearized version of the shallow-water wave equations. The wave-induced force and moment of the Green-Naghdi and the Boussinesq equations are presented when the incoming waves are cnoidal, and the forces are compared with the experimental data when available. Results of the linearized equations are compared with the nonlinear results. It is observed that nonlinearity is very important in the calculation of the wave loads on circular cylinders in shallow water. The variation of wave loads with wave height, wavelength and the spacing between cylinders is studied. Effect of the neighboring cylinders, and the shielding effect of upwave cylinders on the wave-induced loads on downwave cylinders are discussed.

show abstract

“…In the last two decades, various studies were carried out by Wu and Wu,11,12 Akylas, 13 Ertekin, Webster and Wehausen, 14 Mei, 15 Lee, Yates and Wu, 16 Ertekin, Qian and Wehausen, 17 Teng and Wu 18,19 and others to investigate the nonlinear phenomenon of periodic production of upstreamradiating solitary waves ͑also called run-away solitons͒ by disturbances steadily moving at critical speeds in rectangular channels. Results showed that, for a rectangular channel, whether the disturbances ͑such as submerged moving objects͒ are two-or three-dimensional, the run-away solitons generated by them are invariably two-dimensional with a uniform crest across the channel.…”

Section: ͑1͒mentioning

confidence: 99%

Effects of channel cross-sectional geometry on long wave generation and propagation

Teng

1997

Physics of Fluids

View full text Add to dashboard Cite

Joint theoretical and experimental studies are carried out to investigate the effects of channel cross-sectional geometry on long wave generation and propagation in uniform shallow water channels. The existing channel Boussinesq and channel KdV equations are extended in the present study to include the effects of channel sidewall slope at the waterline in the first-order section-mean equations. Our theoretical results show that both the channel cross-sectional geometry below the unperturbed water surface ͑characterized by a shape factor ) and the channel sidewall slope at the waterline ͑represented by a slope factor ␥) affect the wavelength ( ) and time period (T s ) of waves generated under resonant external forcing. A quantitative relationship between , T s , , and ␥ is given by our theory which predicts that, under the condition of equal mean water depth and equal mean wave amplitude, and T s increase with increasing and ␥. To verify the theoretical results, experiments are conducted in two channels of different geometries, namely a rectangular channel with ϵ1, ␥ϭ0 and a trapezoidal channel with ϭ1.27, ␥ϭ0.16, to measure the wavelength of free traveling solitary waves and the time period of wave generation by a towed vertical hydrofoil moving with critical speed. The experimental results are found to be in broad agreement with the theoretical predictions.

show abstract

Waves caused by a moving disturbance in a shallow channel of finite width

Cited by 200 publications

References 15 publications

Generation of solitary waves by transcritical flow over a step

Generation of solitary waves by transcritical flow over a step

Diffraction of cnoidal waves by vertical cylinders in shallow water

Effects of channel cross-sectional geometry on long wave generation and propagation

Contact Info

Product

Resources

About