Geophysical Equatorial Edge Wave with Underlying Currents in the f-Plane Approximation

I present an exact and explicit solution to the nonlinear governing equations in the equatorial f-plane, describing geophysical edge waves propagating over a plane-sloping beach, in the presence of underlying uniform currents. I also derive the analytical expressions of geophysical edge wave dynamics and the mass transport velocity.

Wave height estimates from pressure and velocity data at an intermediate depth in the presence of uniform currents

Bounds on estimates of wave heights (valid for large amplitudes) from pressure and flow measurements at an arbitrary intermediate depth have been provided. Two-dimensional irrotational steady water waves over a flat bed with a finite depth in the presence of underlying uniform currents have been considered in the analysis. Five different upper bounds based on a combination of pressure and velocity field measurements have been derived, though there is only one available lower bound on the wave height in the case of the speed of current greater than or less than the wave speed. This article is part of the theme issue ‘Nonlinear water waves’.

Comparative Study of Dynamics of Gravity Cages With Different Meshes in Waves and Current

To investigate the dynamics of gravity cage, the finite element program Aqua-FE™, was applied to gravity cages with two different meshes, square-mesh net and diamond-mesh net. Two case studies are chosen to compare the dynamics of cages based on the numerical modeling techniques. The numerical models were developed in Aqua-FE™ to simulate the effects of waves and current. They were validated by comparison with water tank results. The comparison showed good agreement. In both case studies, we consider several loading conditions consisting of different uniform currents and monochromatic waves. Assuming that the system can be modeled as a linear system, we investigated the motion response (heave, surge and pitch) characteristics of the fish cages with square-mesh net and diamond-mesh net, their deformation and the resultant tension in mooring lines. For different wave conditions, we study the storm response of the two cages based on the response amplitude operators (RAOs). In particular, the length of the grid line has significantly effect on the motion of the cage and the tension in mooring lines in wave. In additional, the effect of the mesh shape on the motion of the cage and tension in mooring lines is also analyzed. The comparison results show that the surge motion of the fish cage with square-mesh net is significantly larger than that with diamond-mesh net.

HAM Solution of Nonlinear Wave Interaction With Uniform Current

The interaction of nonlinear progressive waves and uniform currents in water of finite depth is investigated analytically by means of the homotopy analysis method (HAM). In the HAM, the velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The present approach does not depend on any small parameters, thus the solutions are suitable for steep waves and strong currents. To verify the HAM solutions, experiments are conducted in wave-current flume of Education Ministry Key Laboratory of Hydrodynamics at SJTU. It is shown that the HAM solutions are in good agreement with experimental measurements. The present study demonstrated that the great potential of the HAM to solve more complex wave-current interaction problems leading to engineering applications in traditional offshore industry and marine renewable energy sector.

Deformation of Nets With Bending Stiffness Normal To Uniform Currents

The tremendous growth of the fish farming industry in Norway over the past decades was supported by new designs and materials for fish farms, enabling bigger fish cages to be positioned in more exposed sea areas. Today, the nets of most fish cages in Norway are made from nylon, but also new net materials are proposed to better prevent escapes, protect fish from predator attacks, improve the stability of fish cages, and reduce biofouling. Some of these materials are stiff in at least one direction, and there still is a lack of knowledge about the behavior of nets with bending stiffness in currents and waves. The aim of this study was to determine how nets with bending stiffness deform in different currents and how the deformation influences the drag on the nets and to compare the results with predictions from a numerical model. Three types of net (PET, copper, and steel) were clamped to a solid steel bar on the top side but were otherwise unrestricted. The nets were subjected to several flow speeds between 0.1 and 0.9 m/s. The net deformation was determined with an optical tracking system, and the forces on the net panels were measured with a multi-axis force/torque sensor system. It is shown that bending stiffness and density of nets affect net deformation, as both parameters impact the balance between drag and gravitational forces on the nets. Net deformation leads to a decrease of the projected net area. As the rate of deformation with current speed varies greatly between different net types, the discrepancy between measured drag and drag values normalized to the projected net area at different current speeds follows different relationships for different nets. A numerical model, FhSim, was able to predict net deformation of nets with bending stiffness well, and it is shown that FhSim could not only account for the effect of bending stiffness on net deformation, but also that the model captures the structural dynamics of nets with bending stiffness in a current.

On the Torsional Friction of Freely Rotating Short Fairing

Vortex-induced vibrations (VIV) model tests were carried out by Shell on a 38 m flexible pipe at the MARINTEK Ocean Basin in March 2011, Trondheim. As part of the model test campaign, the pipe with short fairings under two different torsional friction conditions between riser and fairings was tested in uniform currents. Test with ‘high’ friction show small responses, tests with ‘low’ friction show distinct large responses, even though, the spectra analysis shows that the responses seem to be dominated by vortex induced forces. Decay tests were carried out on a riser section with fairings to further investigate the torsional friction effect. Friction coefficients were calculated by ‘Coulomb damping model’, which is proved to be a suitable model for fairing-riser friction. The friction coefficients could be directly used to determine the damping ratio and implemented in numerical models. Such decay tests are especially useful to design, manufacture and install fairings in order to achieve a proper friction level and avoid unstable responses such as galloping.

Investigation of the Effects on Benjamin-Feir Instability by Uniform Currents

Systematic experiments focusing on the evolution of wave trains with initially sidebands on uniform currents are carried out in a physical wave-current flume (65m long, 2m wide and 1.8m deep). Wave trains with different initial steepness and perturbed sidebands are generated to propagate on currents with velocity in the range −0.1 < U/c < 0.1 (U is the current velocity, c is the phase velocity of the carrier wave in quiescent water). The experimental results demonstrate that following currents can suppress the modulational instability and reduce the onset criterion. However, opposing currents have the contrary effect. In addition, the estimated experimental initial growth rates of the sidebands are close to the result predicted by the current modified cubic nonlinear Schrödinger equation of Gerber. Furthermore, the development of instability of waves on opposing currents tends to occur in a continuous frequency band rather than in some discrete frequencies.

Deformation of Nets With Bending Stiffness Normal to Uniform Currents

The tremendous growth of the fish farming industry in Norway over the past decades was supported by new designs and materials for fish farms, enabling bigger fish cages to be positioned in more exposed sea areas. Today, the nets of most fish cages in Norway are made from nylon. Nylon nets are lightweight, relatively easy to handle and at the low cost end of proposed net materials. However, nylon nets also have some unfortunate characteristics like low abrasion resistance and limited tensile strength. Thus, new net materials are proposed to better prevent escapes, protect fish from predator attacks, improve the stability of fish cages and reduce bio-fouling. Some of these materials are stiff in at least one direction and there still is a lack of knowledge about the behavior of nets with bending stiffness in currents and waves. The aim of this study was to determine how nets with bending stiffness deform in different currents and how the deformation influences the drag on the nets and to compare the results with predictions from a numerical model. Three types of net (PET, copper and steel) were clamped to a solid steel bar on the top side, but were otherwise unrestricted. Reflective markers were mounted on the nets and an optical tracking system was used to determine the position of the markers during the tests, thus allowing the determination of the deformation of the net panels. The forces on the net panels were measured with a multi-axis force/torque sensor system. The nets were subjected to several flow speeds between 0.1 and 0.9 m/s. It is shown that bending stiffness and density of nets affect net deformation, as both parameters impact the balance between drag and gravitational forces on the nets. Net deformation leads to a decrease of the projected net area. As the rate of deformation with current speed varies greatly between different net types, the discrepancy between measured drag and drag values normalized to the projected net area at different current speeds follows different relationships for different nets. A numerical model, FhSim was able to predict net deformation of nets with bending stiffness well and it is shown that FhSim could not only account for the effect of bending stiffness on net deformation, but also that the model captures the structural dynamics of nets with bending stiffness in a current.