Dynamical cascade generation as basic mechanism of Benjamin-Feir instability

A novel model of discretized energy cascade generated by Benjamin-Feir instability is presented. Conditions for appearance of direct and inverse cascades are given explicitly, as well as conditions for stabilization of the wave system due to cascade termination. These results can be used directly for explanation of available results of laboratory experiments and as basic forecast scenarios for planned experiments, depending on the frequency of an initially excited mode and steepness of its amplitude.Comment: Accepted to EP

Kinematics of the Ship’s Wake in the Presence of a Shear Flow

We present the kinematic model of the ship wake in the presence of horizontal subsurface current linearly varying with the depth of water. An extension of the Whitham–Lighthill theory for calm water is developed. It has been established that the structure of ship waves under the action of a shear flow can radically differ from the classical Kelvin ship wake model. Co propagating ship and shear current lead to increasing the total wedge angle up to full one 180° and decreases for the counter shear current. At relatively large unidirectional values of the shear current, cusp waves in the vicinity of the wedge boundary are represented by transverse waves and, conversely, by diverging waves directed almost perpendicular to the ship track for the opposite shear current. The presence of a shear flow crossing the direction of the ship’s movement gives a strong asymmetry of the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. The limiting value of the shear current corresponds to one or both arms angles equal to 90°. Transverse and divergent edge waves for this limiting case coincide

Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow

The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number Fr (in terms of water depth) and especially on the critical Froude number Frcr, which depends on the magnitude and direction of the shear flow. At its subcritical values FrFrcr two types of waves are presented: long transverse and short divergent waves inside the wedge area with an angle depending on Fr For the supercritical range Fr>Frcr only divergent waves are presented inside the wake region. Critical Froude number Frcr is variable and mostly depends on collinear with the ship path component of the shear flow: it decreases with the unidirectional shear flow and increases on the counter shear current. The wedge angle of the ship wake expands with an increase in the unidirectional shear flow and narrows in the oncoming flow in the subcritical mode of the ship’s motion FrFrcr. Wake angle decreased with Froude number for Fr>Frcr and only divergent waves with the crests almost collinear with ship path are finally presented in the narrow ship wake. For a critical value of the Froude number Fr=Frcr, the ship’s wake has a total wedge angle of 180° with waves directed parallel to the ship’s motion. The presence of a shear flow crossing the path of the ship gives a strong asymmetry to the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms

Streaming flows in a channel with elastic walls

The two-way coupling model for wave motion in a two-phase medium "fluid-elastic walls" accounting for interaction between those phases is considered within the frames of the boundary layer type approximation. An asymptotic linearized model including Navier-Stokes equations for the viscous incompressible fluid and the deformable plate motion equations for elastic walls is analyzed within a wide range of governing parameters variations. The dispersion relationship for different Reynolds numbers shows different oscillation regimes. The structure of the fluid flow is studied in detail for the two asymptotic limit cases of high and low Reynolds numbers. The results show that the intensity of fluid mass transfer induced in a fluid-filled channel with vibrating walls increases when increasing the vibrational Reynolds number. Contrary to the existing opinion, which considers the traveling wave regime of wall oscillations to be the basic mechanism generating the fluid flow, it is proved that the mean flux induced by standing waves could surpass the flux induced by the traveling waves in a range of one order of Reynolds number. © 2002 American Institute of Physics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

An Experimental and Theoretical Study of Wave Damping due to the Elastic Coating of the Sea Surface

Flexible plates or membranes located on the sea surface can be effective for attenuation waves approaching the beach. The most efficient structures should be found through comprehensive research using developed experiments and theory. Our experimental work was focused on the wave propagation and attenuation passing through floating elastic structures. The experiments were conducted at the wave flume of Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan. The experiment mainly analyzes the reflection coefficient, transmission coefficient and energy loss of the regular wave of intermediate water depth after passing through the elastic structure under different wave steepness and other different wave conditions. Our experiments also explore the comparison of energy dissipation effects and the differences in motion characteristics between different elastic plates and different plate fixing methods. Three elastic materials were tested in the experiments: Latex, cool cotton and polyvinyl chloride (PVC). A model of a thin elastic plate covering the sea surface was used to evaluate the effectiveness of the structure of the wave barrier. The results of experiments carried out in the wave flume were compared with theoretical predictions in a wide range of generated waves

OMAE2011-49540 MODULATIONAL INSTABILITY IN DIRECTIONAL WAVE FIELDS, AND EXTREME WAVE EVENTS

ABSTRACT The paper is based on review of research articles by the authors, with the purpose to demonstrate that the modulationalinstability mechanism is active in typical directional wave fields. If so, possible limits for the wave height due to such mechanism can be outlined. The modulational instability can lead to occurrence of very high waves, which either proceed to the breaking or appear as rogue events, but it was derived for and is usually associated with two-dimensional wave trains. There exists argument, both analytical and experimental, that this kind of instability is impaired or even suppressed in three-dimensional (directional) wave systems. The first part of the paper demonstrates indirect experimental evidences which relate the wave breaking in oceanic conditions to features of two-dimensional breaking waves due to modulational instability. The second section is dedicated to direct measurements of such instability-caused breaking in a directional wave tank with directional spread and mean steepness typical of those in the field. The last section provides conclusions on what is maximal height of an individual wave, depending on the mean wave steepness in a wave train/field, that can be achieved due to such non-linear evolution of wave trains. INTRODUCTION Extreme wave events bear apparent significance across the entire range of ocean-engineering applications. Large steep breaking waves can impose enormous loads on vessels and offshore constructions, but even long gently-slopped waves ar

Nonlinear waves on collinear currents with horizontal velocity gradient

Analytical and experimental research of wave dynamics on adverse and following currents with horizontal-velocity gradient, was conducted. Laboratory tests were carried out at the Tainan Hydraulics Laboratory of the National Cheng Kung University of Taiwan, where a special setup aimed at accelerating/decelerating currents was designed, constructed and employed. In the case of accelerating adverse currents, the wave behaviour is strongly nonlinear and leads to downshifting of the wave energy which allows the waves to penetrate the blocking current. For the case of decelerating currents, linear behaviour should lead to amplification of wave amplitude and increase in steepness, which is indeed observed, but downshifting also happens if the initial waves are steep enough. Such results point out to the physics which is presently not accounted for in wave forecast models