Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

On the shear-current effect: Toward understanding why theories and simulations have mutually and separately conflicted

The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient β21 with a favorable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic ($\beta ^u_{21}$) and magnetic ($\beta ^b_{21}$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike $\beta ^b_{21}$, the kinetic SCE $\beta ^u_{21}$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal {O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, $\beta ^b_{21}$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive $\beta ^u_{21}$ can dominate even at energy equipartition urms ≃ brms, resulting in a positive total β21 even though $\beta ^b_{21}<0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-τ closure (STC), for which opposite signs for $\beta ^u_{21}$ have been reported, with the same sign for $\beta ^b_{21}<0$. The results also offer an explanation for the simulations that find $\beta ^u_{21}>0$ and an inconclusive overall sign of β21 for $\mathcal {O}(10)$ Reynolds numbers. The transient behaviour of $\beta ^u_{21}$ is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

Transformation of the Peregrine Breather Into Gray Solitons on a Vertically Sheared Current

In this Brief Research Report, we show, within the framework of the nonlinear Schrödinger equation in deep water and in the presence of vorticity (vor-NLS), that the Peregrine breather traveling at the free surface of a shear current of slowly varying vorticity may transform into gray solitons.

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.

Experimental and Numerical Investigations on VIV Response of a Pipe in Shear Flow

The vortex induced vibration of slender cylindrical structures is common in offshore structures and marine applications such as risers, towing cables, etc. The VIV response of such slender elements in steady uniform current has been investigated in the past using numerical and experimental studies. Though few numerical studies exist for varying current (sheared flow), experimental studies are limited. Hence, the experimental studies are an essential part of VIV investigation, especially for sheared flow. The experiments were conducted using a specially fabricated circular steel tank of diameter 2.4 m with a central hinge to rotate the pipe horizontally in a water pool of depth 0.7 m. Shear current is simulated by rotating the pipe about the hinge. A pipe of diameter 25 mm (= D) and length 1 m (= L) was fixed at one end of the rotating cable support, and the other end was passed over a pulley inside a rotating cylinder. The rotating cylinder is provided with a pulley at the top to tension the pipe. A shear current with a maximum velocity of 1.3 m/s and a minimum velocity of 0.1 m/s is generated using the set up. The VIV response of the pipe was measured using electrical resistance-type strain gauges pasted along the length. The measured axial strain was used to obtain transverse displacements, which was used to determine the response frequency, amplitudes, and forces. The Strouhal number was calculated. The VIV response and the fluid force coefficients obtained from the experiments were compared with Shear7 results.