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Modelling the interaction of water waves with varying current is an important issue, especially in nearshore and coastal areas and for a variety of engineering applications.
These applications include wave structure interactions, with the problematics related to oil and naval industries, but also renewable energies.
The problematic is also important when considering coastal management, and harbour maintenance and exploitation.
Also, this interaction often leads to the formation of extreme wave events with detrimental effects.
Significant scientific effort was undertaken during the last fifty years to model linear, weakly or strongly nonlinear water waves with constant, or slowly varying currents.
When variations are stronger, the difficulty remains important.
In this session, contributions are invited relating experimental, numerical and theoretical works designed to improve the understanding of water waves and current interactions, including wave and current stability, wave dynamics, and energy propagation.
Contributions describing the specific problematics, from the point of the applications, are also deeply welcome.

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Co-organized by NH5/OS2
Convener: Julien Touboul | Co-conveners: Konstandinos Belibassakis, Anne-Claire Bennis, Efim Pelinovsky
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| Thu, 07 May, 10:45–12:30 (CEST)

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Chat time: Thursday, 7 May 2020, 10:45–12:30

D2881 |
EGU2020-929
Sahaj k v and Nasar Thuvanismail

Liquid motion in partially filled tanks may cause large structural loads if the period of tank motion is close to the natural period of fluid inside the tank. This phenomenon is called sloshing. Sloshing means any motion of a free liquid surface inside a container. The effect of severe sloshing motion on global seagoing vessels is an important factor in safety design of such containers. In order to examine the sloshing effects, a shake table experiments were conducted for different water fill depth of aspect ratio 0.163, 0.325 and 0.488. The parametric studies were carried out to show the liquid sloshing effects in terms of slosh frequencies, maximum free surface elevation and hydrodynamic forces acting on the tank wall. Sloshing oscillation for the excitation frequency f1, f2, f3, f4 and f5 are observed and analysed. The excitation frequencies is varied between 0.4566 Hz to 1.9757 Hz and constant amplitudes of 7.5mm was adopted. The movement of fluid in a rectangular tank has been studied using experimental approach and different baffle configurations were adopted for analysing the sloshing oscillation, natural frequencies and variation in wave deflection. The adopted porosities in the present study is 15% – 25 %. Porous screen is placed inside the tank at L/2 location and study is extended for single porous screen for better wave energy absorption. Capacitance wave probes have been placed at tank ends to record the free surface water elevation. Load cells are used to measure the sloshing force inside the tank. Linear variable displacement transducers is used to measure the displacement of shake table. In the present study single porous screen under the action of wave were analysed to understand the wave control performance due to porosity parameters. A boundary element model is developed to calculate problems of wave interaction with a porous screen structure. The numerical results from the present boundary element methods (BEM) are compared with series of experiments conducted in a rectangular tank with various baffle porosities and submerged depths.

 

D2882 |
EGU2020-2322
Ton van den Bremer, James Steer, Dimitris Stagonas, Eugeny Buldakov, and Alistair Borthwick

We examine experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional  1D+1 constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from 0 to -0,87 s-1 For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95% confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between 0 and -0.48 s-1. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.

D2883 |
EGU2020-3878
Artem Rodin, Natalia Rodina, Andrey Kurkin, Julien Touboul, and Efim Pelinovsky

 The collision of solitary waves has been studied analytically and numerically in numerated papers for last 50 years. In the weakly nonlinear theory, the soliton interaction is inelastic. Here we study more general class of the head-collision of nonlinear waves of various shape (Riemann waves of both polarities, shock waves and solitons) in the shallow water within nonlinear shallow-water theory, Serre-Green-Naghdi and Euler equations. The structure of wave field and induced bottom pressure at the moment of wave interaction is analysed analytically and numerically. It is shown that such an interaction leads to a phase shift and shape deformation in the moment of interaction. Estimates of the height of the Riemann waves as well solitons of moderate amplitudes at the moment of interaction are in agreement with theoretical predictions. The phase shift in the interaction of non-breaking waves is small enough, but becomes noticeable in the case of the shock waves motion. The approximated analytical solution for the wave field and bottom pressure distribution is obtained analytically within Serre-Green-Naghdi system. Computed bottom pressure in dispersive theories has two-bell shape for large amplitude solitary waves in quality agreement with theoretical analysis.

D2884 |
EGU2020-6887
Srinivasa Rao Manam, Ashok Kumar, and Gunasundari Chandrasekar

The problem of normally incident water wave scattering by a flexible membrane is completely solved. The physical problem in a half-plane is reduced to a couple of equivalent quarter-plane problems by allowing incident waves from either direction of the membrane. In the same way, quarter-plane boundary value problems are posed for solid wave potentials that are solutions of the scattering problem involving a rigid structure of the same geometric configuration. Then, two novel integral relations are introduced to establish a link between the required solution wave potentials and few resolvable solid wave potentials. Explicit expressions for the scattering quantities such as the reflection and the transmission wave amplitudes are obtained. Also, the deflection of the flexible vertical membrane and the solution potentials are determined analytically. Numerical results for the scattering quantities and the membrane deflection are presented.

D2885 |
EGU2020-18933
Julien Touboul and Kostas Belibassakis

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.

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).

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).

[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.

[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.

[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.

[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.

[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.

[6] Belibassakis K.A., Touboul J. A nonlinear coupled-mode model for waves propagating in

vertically sheared currents in variable bathymetry-collinear waves and currents, Fluids, 4(2),

61, 2019.

[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.

[8] Ellingsen, S.A., Oblique waves on a vertically sheared current are rotational, Eur. J. Mech. B-Fluid 56, 156–160, 2016.

D2886 |
EGU2020-20307
| Highlight
Clément Le Goff, Alexey Mironov, and Bertrand Chapron

Ocean waves Interacting with large scale ocean currents is a frequent cause of sea-state variability [Ardhuin et al 2017, Quilfen et al 2018, Quilfen and Chapron 2019]. Such situations can lead to sea-state hazards, crucial for shipping security. The Great Agulhas current system is an area of very intensive maritime traffic, where dangerous localized sea-state amplification by the current has quite regularly been reported. 

In absence of wind and wave-induced motions, the heading and drift of every ship along its trajectory can be estimated from the near-surface oceanic current map. This first guess can then be compared with real ship parameters obtained from satellite-collected ship Automatic Identification System (AIS) messages. During Southwestern storm-swell wave conditions, with wind and waves aligned against the current, some ships experience pronounced navigation difficulties, slowing down up to 2 m/s,  and frequently maneuvering to keep their heading perpendicular to dominant waves. Superposed multiple individual ship trajectories can then help map anomalous areas, and to relate them to localized strong wave-current effects such as large refraction of waves by the oceanic current.

[Ardhuin et al 2017] : Ardhuin, F., S. T. Gille, D. Menemenlis,C. B. Rocha, N. Rascle, B. Chapron, J. Gula, and J. Molemaker (2017), Small-scale open ocean
currents have large effects on wind wave heights, J. Geophys. Res. Oceans, 122, 4500–4517, doi:10.1002/2016JC012413.

[Quilfen et al 2018] :Quilfen Yves, Yurovskaya M., Chapron Bertrand, Ardhuin Fabrice (2018). Storm waves focusing and steepening in the Agulhas current: Satellite observations and modeling. Remote Sensing Of Environment, 216, 561-571. Publisher's official version :

[Quilfen and Chapron, 2019] : Quilfen, Y., & Chapron, B. (2019). Ocean surface wave-current signatures from satellite altimeter measurements.
Geophysical Research Letters, 46.

 
D2887 |
EGU2020-20406
Andreas H Akselsen, Andreas Brostrøm, and Simen Ådnøy Ellingsen

Langmuir circulations (LC) in their traditional form are large rolling fluid flow pattern created by the interplay of surface waves and a near-surface shear current, typically both created by the wind. A celebrated theory by Craik and Leibovich (1976) describes two kinematic mechanisms which cause instabilities which grow into Langmuir rolls, both involving only the shear of the flow and the kinematic driving of flow undulations by a wavy surface, but containing no direct reference to the wind as a driving force. The same kinematic processes are present also in boundary layer flow over a wavy bottom topography in almost perfect analogy.

We present a theory of Langmuir-like circulations created by boundary layer flow over a topography in the form of a regular pattern of two monochromatic waves crossing at an oblique angle. Thus, the Craik-Leibovich instability sometimes referred to as CL1 is triggered and the close analogy with surface waves allows us to follow the general procedure of Craik (1970).

A flow of arbitrary shear profile is assumed over the bottom topography. In the opposite limits of transient inviscid flow and steady-state viscous flow simple equations for the stream function in cross-current plane can be derived and easily solved numerically. For the special case of a power-law velocity profile, explicit leading-order solutions are available. This allows us to quickly map out the circulation response to different parameters: wavelength, crossing angle and wave amplitude. The study is supplemented with direct numerical simulations which verify the manifestation of Langmuir-like circulations over wavy geometries with a no-slip boundary condition.

References
Craik, A.D.D., A wave-interaction model for the generation of windrows. J. Fluid Mech. (1970) 41, 801-821.
Craik, A.D.D. & Leibovich, S. A rational model for Langmuir circulations. J. Fluid Mech. (1976) 73, 401-426.