Aerial observations of sea ice break-up by ship waves

We provide the first in situ observations of floe size distributions (FSD) resulting from wave-induced sea ice break-up. In order to obtain such data, an unmanned aerial vehicle was deployed from the Canadian Coast Guard Ship Amundsen as it sailed in the vicinity of large ice floes in Baffin Bay and in the St. Lawrence Estuary, Canada. When represented as probability density functions weighted by the surface of ice floes, the FSDs exhibit a strong modal shape which confirms the preferential size hypothesis debated in the scientific community. Both FSDs are compared to a flexural rigidity length scale, which depends on ice properties, and with the wavelength scale. This comparison tends to show that the maximal distance between cracks is preferentially dictated by sea ice thickness and elasticity rather than by the wavelength. Temporal analysis of one fracture event is also done. Results show that the break-up advances almost as fast as the wave energy and that waves responsible for the break-up propagate following the mass loading dispersion relation. Moreover, our experiments show that thicker ice can attenuate wave less than thinner ice. This method thus provides key information on the wave-induced FSD, clarifies theoretical aspects from the construction of the FSD to its implementation in models and brings new knowledge regarding the temporal evolution of sea ice break-up.

Bending-gravity waves in the sea with an ice cover from moving disturbances

В статье проводятся исследования колебаний плавающего ледяного покрова под действием движущихся возмущений. В основу колебаний плавающего ледяного покрова положены линеаризованные уравнения гидромеханики и линейная классическая теория колебаний пластин. Ледяной покров рассматривается как тонкая упругая изотропная пластинка. Анализируются образующиеся при этом трехмерные изгибно-гравитационные волны. Показано, что при движении источника возмущений со скоростью 0<v<v0 изгибно-гравитационные волны не образуются, а наблюдается статический прогиб. Здесь v0 – минимальное значение фазовой скорости. При скорости движения v0<v<v1 образуется одна система изгибно-гравитационных волн. Эти волны распространяются как впереди, так и за источником возмущений. Волны, бегущие впереди источника, обусловлены упругими и массовыми силами пластинки. Волны, распространяющиеся за источником, имеют характер гравитационной волны для чистой воды. При v1<v<(gH)1/2 образуется три системы волн. Упругие волны распространяются впереди источника. Две другие волны распространяются за источником и носят характер поперечной и продольной корабельных волн. При v>(gH)1/2 образуются впереди источника упругие волны, а за источником продольные корабельные волны. Исследовано влияние скорости перемещения нагрузки на амплитуды образующихся волн. The article studies the fluctuations of the floating ice cover under the action of moving perturbations. The vibrations of the floating ice cover are based on the linearized equations of hydro-mechanics and the linear classical theory of plate vibrations. The ice sheet is considered as a thin elastic isotropic plate. The resulting three-dimensional bending-gravity waves are analyzed. It is shown that when the source of disturbances moves at a speed of 0<v<v0, bending-gravitational waves are not formed, but a static deflection is observed. Here v0is the minimum value of the phase velocity. At the speed of motion v0<v<v1, a single system of bending-gravitational waves is formed. These waves propagate both ahead and behind the source of the disturbances. The waves traveling ahead of the source are caused by the elastic and mass forces of the plate. The waves propagating behind the source have the character of a gravitational wave for pure water. At v1<v<(gH)1/2, three wave systems are formed. Elastic waves propagate ahead of the source. The other two waves propagate behind the source and have the character of transverse and longitudinal ship waves. At v>(gH)1/2, elastic waves are formed in front of the source, and longitudinal ship waves are formed behind the source. The influence of the load displacement velocity on the amplitudes of the generated waves is investigated.

OPTIMIZED ROCK GROYNE DESIGN FOR LONG-PERIODIC SHIP WAVE LOADS

Increased severity of damage to estuarine rock structures have been observed across the major German estuaries during the past two decades. These damages are predominantly caused by long-period primary ship waves, which can result in load cases that are particularly erosive to the rock armour layer. To date no design methods exists to dimension structures for long-period ship wave loads. This study presents an innovative groyne design optimized for resistance to ship-induced waves. During a field trial data were collected which allow for the characterisation of wave-structure-interaction as well as loads and damage parameters for the future development of validated design methods.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/FnrU8AKBITo

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.

The Influence of Ship Waves on Sediment Resuspension in the Large Shallow Lake Taihu, China

Sediment resuspension induces endogenous nutrient release in shallow lakes, which has been demonstrated to be associated with eutrophication. In addition to natural wind-driven resuspension, navigable shallow lakes (such as Lake Taihu, China) also experience resuspension from human activities, such as ship waves. Both processes determine the intensity, frequency, and duration of sediment resuspension, and may consequently affect the pattern of cyanobacteria blooms in the lake. In this study, acoustic Doppler Velocimeter (ADV), Optical Backscatter Sensor (OBS), and temperature wave tide gauge (instrument model :RBR duo TD|wave) were placed in an observation platform in the lake to obtain high-frequency flow velocities, suspended sediment concentration (SSC), and wave parameters before, during, and after a cargo ship passed by. We found that the ship wave disturbance intensity is greatly influenced by the draft depth. The movement generated by ship disturbance is primarily horizontal rather than vertical. Compared with the wind-induced wave, the disturbance caused by the ship waves has a high intensity, short duration, and narrow range of influence. The maximum total shear stress under ship disturbance can reach 9~90 times the critical shear stress under a natural state. Therefore, the effect of ship waves on sediment resuspension near the channel of Lake Taihu is much greater than that of wind-induced waves. These findings represent an important step towards understanding the quantitative relationship between ship wave disturbance and sediment resuspension, and lay the foundation for future research in order to understand and control the eutrophication of shallow lakes.

Measurements and Analysis of Primary Ship Waves in the Stockholm Archipelago, Sweden

Primary ship waves generated by conventional marine vessels were investigated in the Furusund fairway located in the Stockholm archipelago, Sweden. Continuous water level measurements at two locations in the fairway were analyzed. In total, 466 such events were extracted during two months of measurements. The collected data were used to evaluate 13 existing predictive equations for drawdown height or squat. However, none of the equations were able to satisfactorily predict the drawdown height. Instead, a new equation for drawdown height and period was derived based on simplified descriptions of the main physical processes together with field measurements, employing multiple regression analysis to derive coefficients in the equation. The proposed equation for drawdown height performed better than the existing equations with an R2 value of 0.65, whereas the equation for the drawdown period was R2 = 0.64. The main conclusion from this study is that an empirical equation can satisfactorily predict primary ship waves for a large data set.