Hydrodynamic Analysis of Elastic Floating Collars in Random Waves

As the main load-bearing component of fish cages, the floating collar supports the whole cage and undergoes large deformations. In this paper, a mathematical method is developed to study the motions and elastic deformations of elastic floating collars in random waves. The irregular wave is simulated by the random phase method and the statistical approach and Fourier transfer are applied to analyze the elastic response in both time and frequency domains. The governing equations of motions are established by Newton＇s second law, and the governing equations of deformations are obtained based on curved beam theory and modal superposition method. In order to validate the numerical model of the floating collar attacked by random waves, a series of physical model tests are conducted. Good relationship between numerical simulation and experimental observations is obtained. The numerical results indicate that the transfer function of out-of-plane and in-plane deformations increase with the increasing of wave frequency. In the frequency range between 0.6 Hz and 1.1 Hz, a linear relationship exists between the wave elevations and the deformations. The average phase difference between the wave elevation and out-of-plane deformation is 60° with waves leading and the phase between the wave elevation and in-plane deformation is 10° with waves lagging. In addition, the effect of fish net on the elastic response is analyzed. The results suggest that the deformation of the floating collar with fish net is a little larger than that without net.

Evolution of stress fields during the supercontinent cycle

We investigate the evolution of stress fields during the supercontinent cycle using the 2D Cartesian geometry model of thermochemical convection with the non-Newtonian rheology in the presence of floating deformable continents.In the course of the simulation,the supercontinent cycle is implemented several times.The number of continents considered in our model as a function of time oscillates around 3.The lifetime of a supercontinent depends on its dimension.Our results suggest that immediately before a supercontinent breakup,the over-lithostatic horizontal stresses in it(referring to the mean value by the computational area)are tensile and can reach-250 MPa.At the same time,a vast area beneath a supercontinent with an upward flow exhibits clearly the over-lithostatic compressive horizontal stresses of 50-100 МРа.The reason for the difference in stresses in the supercontinent and the underlying mantle is a sharp difference in their viscosity.In large parts of the mantle,the over-lithostatic horizontal stresses are in the range of±25 MPa,while the horizontal stresses along subduction zones and continental margins are significantly larger.During the process of continent-to-continent collisions,the compressive stresses can approximately reach 130 MPa,while within the subcontinental mantle,the tensile over-lithostatic stresses are about-50 MPa.The dynamic topography reflects the main features of the su-percontinent cycle and correlates with real ones.Before the breakup and immediately after the disin-tegration of the supercontinent,continents experience maximum uplift.During the supercontinent cycle,topographic heights of continents typically vary within the interval of about±1.5 km,relatively to a mean value.Topographic maxima of orogenic formations to about 2-4 km are detected along continent-to-continent collisions as well as when adjacent subduction zones interact with continental margins.

Effect of Marangoni Number on Thermocapillary Convection and Free-Surface Deformation in Liquid Bridges

Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.