scholarly journals WKB APPROXIMATION TO THE MODIFIED MILD-SLOPE EQUATION

2012 ◽  
Vol 1 (33) ◽  
pp. 3
Author(s):  
Seung-Nam Seo
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Scattering ◽  
Wkb Approximation ◽  
Linear Wave ◽  
Water Wave Scattering ◽  
Mild Slope Equation ◽  
Water Conditions ◽  
Rapidly Varying Topography ◽  
Present Equation

WKB approximation for water wave scattering by rapidly varying topography is obtained from a modified mild-slope equation of the general form by Porter (2003). The present WKB solution is reduced to the previous study where shallow water conditions are present. WKB models from the transformed mild-slope equation, without the described bottom curvature modification, show better performance than those by the original developed mild-slope equation. The underlying significance of the present equation is discussed in the context of linear wave scattering. The selected figures representing our results further characterize main feature of this study.

A new model for the three-dimensional propagation of water waves in the presence of vertically sheared, horizontally varying currents

2020 ◽  
Author(s):  
Julien Touboul ◽  
Kostas Belibassakis
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Wave Scattering ◽  
Three Dimensional ◽  
Water Wave Scattering ◽  
Coupled Equations ◽  
Coupled Mode ◽  
Constant Shear ◽  
Mild Slope Equation ◽  
Sea Bed

<p>In coastal areas, steep bathymetries and strong currents are often observed. Among several causes, the presence of cliffs, rocky beds, or human structures may cause strong variations of the sea bed, while oceanic circulation, tides, wind action or wave breaking can be responsible for the generation of strong currents. For both coastal safety and engineering purposes, there are many interests in providing efficient models predicting the nonlinear, phase resolved behavior of water waves in such areas. The difficulty is known to be important, and many models achieving that goal are described in the related literature.</p><p>Recently, it was established that beneath the influence of vertically uniform currents, the vorticity involved in depth varying mean flows could have significant impact on the propagation of water waves (Rey et al. 2014). This gave rise to new derivations of equations aimed to describe this interaction. First, an extended mild slope equation was obtained (Touboul et al. 2016). Then, the now classical coupled mode theory was introduced in the system to obtain a set of coupled equations, which could be compared to the system derived by Belibassakis et al (2011) but considering currents which may present constant shear with depth (Belibassakis et al. 2017, Belibassakis et al., 2019). In these works, the currents were assumed to vary linearly with depth, presenting a constant shear. However, this approach was recently extended to more general configurations (Belibassakis & Touboul, 2019; Touboul & Belibassakis, 2019).</p><p>In this work, we extend this model to three dimensional configurations. It is emphasized that the model is able to describe rotational waves, as expected, for example, when water waves propagate with a non-zero angle with respect to the current direction (see e.g. Ellingsen, 2016).</p><p>[1] Rey, V., Charland, J., Touboul, J., Wave – current interaction in the presence of a 3d bathymetry: deep water wave focusing in opposite current conditions. Phys. Fluids 26, 096601, 2014.</p><p>[2] Touboul J., Charland J., Rey V., Belibassakis K., Extended Mild-Slope equation for surface waves interacting with a vertically sheared current, Coastal Engineering, 116, 77–88, 2016.</p><p>[3] Belibassakis, K.A., Gerostathis, Th., Athanassoulis, G.A. A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography, Applied Ocean Res. 33, 384– 397, 2011.</p><p>[4] Belibassakis K.A., Simon B., Touboul J., Rey V., A coupled-mode model for water wave scattering by vertically sheared currents in variable bathymetry regions, Wave Motion, vol.74, 73-92, 2017.</p><p>[5] Belibassakis K., Touboul J., Laffitte E., Rey  V., A mild-slope system for Bragg scattering of water waves by sinusoidal bathymetry in the presence of vertically sheared currents,  J. Mar. Sci. Eng., Vol.7(1), 9, 2019.</p><p>[6] Belibassakis K.A., Touboul J. A nonlinear coupled-mode model for waves propagating in</p><p>vertically sheared currents in variable bathymetry-collinear waves and currents, Fluids, 4(2),</p><p>61, 2019.</p><p>[7] J. Touboul & K. Belibassakis, A novel method for water waves propagating in the presence of vortical mean flows over variable bathymetry, J. Ocean Eng. and Mar. Energy, https://doi.org/10.1007/s40722-019-00151-w, 2019.</p><p>[8] Ellingsen, S.A., Oblique waves on a vertically sheared current are rotational, Eur. J. Mech. B-Fluid 56, 156–160, 2016.</p>

Analysis of water wave scattering by a submerged perforated reef ball using multipole method

Meccanica ◽  
2019 ◽  
Vol 54 (11-12) ◽  
pp. 1747-1765
Author(s):  
Ai-jun Li ◽  
Xiao-lei Sun ◽  
Yong Liu ◽  
Hua-jun Li
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Water Wave Scattering ◽  
Multipole Method

scholarly journals Water wave scattering by two submerged nearly vertical barriers

2006 ◽  
Vol 48 (1) ◽  
pp. 107-117 ◽  
Author(s):  
B. N. Mandal ◽  
Soumen De
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Shape Function ◽  
Integral Theorem ◽  
Water Wave Scattering ◽  
First Order ◽  
Transmission Coefficients ◽  
Definite Integrals ◽  
Vertical Barriers ◽  
Two Barriers

AbstractThe problem of surface water wave scattering by two thin nearly vertical barriers submerged in deep water from the same depth below the mean free surface and extending infinitely downwards is investigated here assuming linear theory, where configurations of the two barriers are described by the same shape function. By employing a simplified perturbational analysis together with appropriate applications of Green's integral theorem, first-order corrections to the reflection and transmission coefficients are obtained. As in the case of a single nearly vertical barrier, the first-order correction to the transmission coefficient is found to vanish identically, while the correction for the reflection coefficient is obtained in terms of a number of definite integrals involving the shape function describing the two barriers. The result for a single barrier is recovered when two barriers are merged into a single barrier.

Step approximation of water wave scattering caused by tension-leg structures over uneven bottoms

2018 ◽  
Vol 166 ◽  
pp. 208-225 ◽  
Author(s):  
Chia-Cheng Tsai ◽  
Wei Tai ◽  
Tai-Wen Hsu ◽  
Shih-Chun Hsiao
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Water Wave Scattering ◽  
Step Approximation

WATER WAVE SCATTERING BY A VERTICAL POROUS BARRIER WITH TWO GAPS

2019 ◽  
Vol 61 (1) ◽  
pp. 47-63 ◽  
Author(s):  
M. SIVANESAN ◽  
S. R. MANAM
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Original Problem ◽  
Analytical Procedure ◽  
Explicit Solutions ◽  
Scattering Problems ◽  
Geometrical Structures ◽  
Water Wave Scattering ◽  
Weakly Singular ◽  
Porous Barrier

Explicit solutions are rarely available for water wave scattering problems. An analytical procedure is presented here to solve the boundary value problem associated with wave scattering by a complete vertical porous barrier with two gaps in it. The original problem is decomposed into four problems involving vertical solid barriers. The decomposed problems are solved analytically by using a weakly singular integral equation. Explicit expressions are obtained for the scattering amplitudes and numerical results are presented. The results obtained can be used as a benchmark for other wave scattering problems involving complex geometrical structures.

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