Subharmonic resonance of proposed storm gates for Venice Lagoon

1994 ◽  
Vol 444 (1920) ◽  
pp. 257-265 ◽  
Keyword(s):  
Experimental Evidence ◽  
Incident Wave ◽  
Laboratory Tests ◽  
Venice Lagoon ◽  
Subharmonic Resonance ◽  
Horizontal Axis ◽  
Trapped Modes ◽  
Resonance Mechanism ◽  
Trapped Mode ◽  
Incident Waves

A recent design of storm barriers at the inlets of Venice Lagoon consists of a number of articulated inclined gates hinged on a horizontal axis on the seabed. In laboratory tests with normally incident waves the gates have been found to oscillate at half of the incident wave frequency and out of phase with their immediate neighbours. In this paper we identify the resonance mechanism by first showing the existence of trapped modes as a consequence of the articulated construction. Experimental evidence is shown for the trapped mode and its subharmonic resonance by normally incident waves.

Subharmonic resonance of Venice gates in waves. Part 1. Evolution equation and uniform incident waves

1997 ◽  
Vol 349 ◽  
pp. 295-325 ◽  
Author(s):  
PAOLO SAMMARCO ◽  
HOANG H. TRAN ◽  
CHIANG C. MEI
Keyword(s):  
Evolution Equation ◽  
Nonlinear Theory ◽  
Laboratory Experiments ◽  
Vertical Plane ◽  
Venice Lagoon ◽  
Subharmonic Resonance ◽  
Sea Waves ◽  
Stormy Weather ◽  
Incident Waves ◽  
Theoretical Results

For flood protection against storm tides, barriers of box-like gates hinged along a bottom axis have been designed to span the three inlets of the Venice Lagoon. While on calm days the gates are ballasted to rest horizontally on the seabed, in stormy weather they are raised by buoyancy to act as a dam which is expected to swing to and fro in unison in response to the normally incident sea waves. Previous laboratory experiments with sinusoidal waves have revealed however that neighbouring gates oscillate out of phase, at one half the wave frequency, in a variety of ways, and hence would reduce the effectiveness of the barrier. Extending the linear theory of trapped waves by Mei et al. (1994), we present here a nonlinear theory for subharmonic resonance of mobile gates allowed to oscillate about a vertical plane of symmetry. In this part (1) the evolution equation of the Landau–Stuart type is first derived for the gate amplitude. The effects of gate geometries on the coefficients in the equation are examined. After accounting for dissipation effects semi-empirically the theoretical results on the equilibrium amplitude excited by uniform incident waves are compared with laboratory experiments.

Interaction of water waves with three-dimensional periodic topography

2001 ◽  
Vol 434 ◽  
pp. 301-335 ◽  
Author(s):  
R. PORTER ◽  
D. PORTER
Keyword(s):  
Incident Wave ◽  
Water Waves ◽  
Homogeneous Problem ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Trapped Waves ◽  
Trapped Mode ◽  
Bed Elevation ◽  
Input Mode ◽  
Incident Waves

The scattering and trapping of water waves by three-dimensional submerged topography, infinite and periodic in one horizontal coordinate and of finite extent in the other, is considered under the assumptions of linearized theory. The mild-slope approximation is used to reduce the governing boundary value problem to one involving a form of the Helmholtz equation in which the coefficient depends on the topography and is therefore spatially varying.Two problems are considered: the scattering by the topography of parallel-crested obliquely incident waves and the propagation of trapping modes along the periodic topography. Both problems are formulated in terms of ‘domain’ integral equations which are solved numerically.Trapped waves are found to exist over any periodic topography which is ‘sufficiently’ elevated above the unperturbed bed level. In particular, every periodic topography wholly elevated above that level supports trapped waves. Fundamental differences are shown to exist between these trapped waves and the analogous Rayleigh–Bloch waves which exist on periodic gratings in acoustic theory.Results computed for the scattering problem show that, remarkably, there exist zeros of transmission at discrete wavenumbers for any periodic bed elevation and for all incident wave angles. One implication of this property is that total reflection of an incident wave of a particular frequency will occur in a channel with a single symmetric elevation on the bed. The zeros of transmission in the scattering problem are shown to be related to the presence of a ‘nearly trapped’ mode in the corresponding homogeneous problem.The scattering of waves by multiple rows of periodic topography is also considered and it is shown how Bragg resonance – well-established in scattering of waves by two-dimensional ripple beds – occurs in modes other than the input mode.

Trapped modes and scattering for oblique waves in a two-layer fluid

2014 ◽  
Vol 753 ◽  
pp. 427-447 ◽  
Author(s):  
M. I. Romero Rodríguez ◽  
P. Zhevandrov
Keyword(s):  
Scattering Problem ◽  
Total Reflection ◽  
Unperturbed System ◽  
Trapped Modes ◽  
Theoretical Understanding ◽  
Transmission Coefficients ◽  
Trapped Mode ◽  
Geometric Conditions ◽  
Small Height ◽  
Incident Waves

AbstractThe system describing time-harmonic motions of a two-layer fluid in the linearised shallow-water approximation is considered. It is assumed that the depth is constant, with a cylindrical protrusion (an underwater ridge) of small height. For obliquely incident waves, the system reduces to a pair of coupled ordinary differential equations. The values of frequency for which wave propagation in the unperturbed system is possible are bounded from below by a cutoff, to the left of which no propagating modes exist. Under the perturbation, a trapped mode appears to the left of the cutoff and, if a certain geometric requirement is imposed upon the shape of the perturbation (for example, if the ridge is a rectangular barrier of certain width), a trapped mode appears whose frequency is embedded in the continuous spectrum. When these geometric conditions are not satisfied, the embedded trapped mode transforms into a complex pole of the reflection and transmission coefficients of the corresponding scattering problem, and the phenomenon of almost total reflection is observed when the frequency coincides with the real part of the pole. Exact formulae for the trapped modes are obtained explicitly in the form of infinite series in powers of the small parameter characterising the perturbation. The results provide a theoretical understanding of analogous phenomena observed numerically in the literature for the full problem for the potentials in a two-layer fluid in the presence of submerged cylinders, and furnish explicit formulae for the frequencies at which total reflection occurs and the trapped modes exist.

scholarly journals Trapped modes in a waveguide with a long obstacle

2000 ◽  
Vol 403 ◽  
pp. 251-261 ◽  
Author(s):  
N. S. A. KHALLAF ◽  
L. PARNOVSKI ◽  
D. VASSILIEV
Keyword(s):  
Two Dimensional ◽  
Trapped Modes ◽  
Acoustic Waveguide ◽  
Trapped Mode ◽  
Rectangular Obstacle

Consider an infinite two-dimensional acoustic waveguide containing a long rectangular obstacle placed symmetrically with respect to the centreline. We search for trapped modes, i.e. modes of oscillation at particular frequencies which decay down the waveguide. We provide analytic estimates for trapped mode frequencies and prove that the number of trapped modes is asymptotically proportional to the length of the obstacle.

scholarly journals GROIN LENGTH AND THE GENERATION OF EDGE WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 85 ◽  
Author(s):  
Michael K. Gaughan ◽  
Paul D. Komar
Keyword(s):  
Incident Wave ◽  
Wave Length ◽  
Critical Length ◽  
Beach Erosion ◽  
Rip Currents ◽  
Edge Waves ◽  
Normal Waves ◽  
Wave Basin ◽  
Incident Waves ◽  
Selection Of

A series of wave basin experiments were undertaken to better understand the selection of groin spacings and lengths. Rather than obtaining edge waves with the same period as the normal incident waves, subharmonic edge waves were produced with a period twice that of the incoming waves and a wave length equal to the groin spacing. Rip currents were therefore not formed by the interactions of the synchronous edge waves and normal waves as proposed by Bowen and Inman (1969). Rips were present in the wave basin but their origin is uncertain and they were never strong enough to cause beach erosion. The generation of strong subharmonic edge waves conforms with the work of Guza and Davis (1974) and Guza and Inman (1975). The subharmonic edge waves interacted with the incoming waves to give an alternating sequence of surging and collapsing breakers along the beach. Their effects on the swash were sufficient to erode the beach in some places and cause deposition in other places. Thus major rearrangements of the sand were produced between the groins, but significant erosion did not occur as had been anticipated when the study began. By progressively decreasing the length of the submerged portions of the groins, it was found that the strength (amplitude) of the edge waves decreases. A critical submerged groin length was determined whereby the normally incident wave field could not generate resonant subharmonic edge waves of mode zero with a wavelength equal to the groin spacing. The ratio of this critical length to the spacing of the groins was found in the experiments to be approximately 0.15 to 0.20, and did not vary with the steepness of the normal incident waves.

Rayleigh–Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides

1999 ◽  
Vol 386 ◽  
pp. 233-258 ◽  
Author(s):  
R. PORTER ◽  
D. V. EVANS
Keyword(s):  
Finite Number ◽  
Surface Waves ◽  
Cross Section ◽  
Electromagnetic Waves ◽  
Mode Shapes ◽  
Special Choice ◽  
Trapped Mode ◽  
Uniform Cross Section ◽  
New Type ◽  
Incident Waves

Rayleigh–Bloch surface waves are acoustic or electromagnetic waves which propagate parallel to a two-dimensional diffraction grating and which are exponentially damped with distance from the grating. In the water-wave context they describe a localized wave having dominant wavenumber β travelling along an infinite periodic array of identical bottom-mounted cylinders having uniform cross-section throughout the water depth. A numerical method is described which enables the frequencies of the Rayleigh–Bloch waves to be determined as a function of β for an arbitrary cylinder cross-section. For particular symmetric cylinders, it is shown how a special choice of β produces results for the trapped mode frequencies and mode shapes in the vicinity of any (finite) number of cylinders spanning a rectangular waveguide or channel. It is also shown how one particular choice of β gives rise to a new type of trapped mode near an unsymmetric cylinder contained within a parallel-sided waveguide with locally-distorted walls. The implications for large forces due to incident waves on a large but finite number of such cylinders in the ocean is discussed.

scholarly journals BEACH PROFILES AT TORREY PINES, CALIFORNIA

1976 ◽  
Vol 1 (15) ◽  
pp. 75 ◽  
Author(s):  
David G. Aubrey ◽  
Douglas L. Inman ◽  
Charles E. Nordstrom
Keyword(s):  
Sediment Transport ◽  
Incident Wave ◽  
Wave Energy ◽  
Energy Conditions ◽  
Beach Profile ◽  
High Wave ◽  
Wave Characteristics ◽  
Spectral Estimates ◽  
High Wave Energy ◽  
Incident Waves

Beach profiles have been measured at Torrey Pines Beach, California for four years and correlated with tides and accurate spectral estimates of the incident wave field. Characteristic equilibrium beach profiles persist for time spans of up to at least two weeks in response to periods of uniform incident waves. These changes in the beach profiles are primarily due to on-offshore sediment transport which can be related to variations in wave characteristics and tidal phase. The most rapid readjustment of the beach profile occurs during high wave energy conditions coincident with spring tides. Alternatively, the highest berm building is associated with moderate to low waves that coincide with spring tides.

scholarly journals WAVE INTERCEPTION BY SEA-BALLOON BREAKWATER

1986 ◽  
Vol 1 (20) ◽  
pp. 173 ◽  
Author(s):  
Takahiko Uwatoko ◽  
Takeshi Ijima ◽  
Yukimitsu Ushifusa ◽  
Haruyuki Kojima
Keyword(s):  
Incident Wave ◽  
Fluid Motion ◽  
Fluid Pressure ◽  
Vertical Axis ◽  
Boundary Integral ◽  
Long Waves ◽  
Boundary Integral Method ◽  
Wave Crest ◽  
Airflow Resistance ◽  
Incident Waves

When a submerged, flexible bag is filled with air about 60~T0 % of its full volume ( it is called " sea-balloon " ), it has a stable shape with vertical axis of symmetry, on which several vertical wrinkles appear with folds of membrane. If two or more such sea-balloons are arranged to the direction of wave travel and connected pneumatically, balloons are deformed periodically and the air flows reciprocally in connecting pipe, following to the fluid pressure fluctuation due to incident waves. Such a system of sea-balloon intercepts incident waves effectively ( it is called " sea-balloon breakwater "). The wave interception by the breakwater is analyzed numerically by three-dimensional boundary integral method, assuming that the fluid motions both in- and out-side of the balloon are potential and that the tension in balloon membrane is proportional to the apparent elongation of membrane with virtual elastic constant. After analysis and experiments, it is made clear that in relatively long waves the incident wave is canceled by the radiation wave which is generated by volumetric change of sea-balloons, being affected by airflow resistance in connecting pipe. In short waves, sea-balloons seem to behave like as rigid piles and the incident wave is absorbed by airflow resistance in pipe and by the turbulence of fluid motion around balloons. Moreover, the effect of gaps between sea-balloons along wave crest on wave interception for relatively long waves is expressed by a simple empirical formula, by which the transmission coefficients at various types of sea-balloon breakwater is easily estimated by twodimensional computation. For the improvement of wave interception effect and from the point of practical use, the effects of other sea-balloon breakwater system are investigated by two-dimensional computation and experiments.

scholarly journals Trapped modes around a row of circular cylinders in a channel

1999 ◽  
Vol 386 ◽  
pp. 259-279 ◽  
Author(s):  
T. UTSUNOMIYA ◽  
R. EATOCK TAYLOR
Keyword(s):  
Expansion Method ◽  
Wave Theory ◽  
Multipole Expansion ◽  
Circular Cylinders ◽  
Large Radius ◽  
Trapped Modes ◽  
Resonant Phenomenon ◽  
Trapped Mode ◽  
Linear Water Wave Theory ◽  
Multipole Expansion Method

Trapped modes around a row of bottom-mounted vertical circular cylinders in a channel are examined. The cylinders are identical, and their axes equally spaced in a plane perpendicular to the channel walls. The analysis has been made by employing the multipole expansion method under the assumption of linear water wave theory. At least the same number of trapped modes is shown to exist as the number of cylinders for both Neumann and Dirichlet trapped modes, with the exception that for cylinders having large radius the mode corresponding to the Dirichlet trapped mode for one cylinder will disappear. Close similarities between the Dirichlet trapped modes around a row of cylinders in a channel and the near-resonant phenomenon in the wave diffraction around a long array of cylinders in the open sea are discussed. An analogy with a mass–spring oscillating system is also presented.

Sign in / Sign up

Export Citation Format

Share Document