Modified PIC Method for Sea Ice Dynamics

The sea ice cover displays various dynamical characteristics such as breakup, rafting, and ridging under external forces. To model the ice dynamic process accurately, the effective numerical modeling method should be established. In this paper, a modified particle-in-cell （PIC） method for sea ice dynamics is developed coupling the finite difference （FD） method and smoothed particle hydrodynamics （SPH）. In this method, the ice cover is first discretized into a series of lagrangian ice particles which have their own sizes, thicknesses, concentrations and velocities. The ice thickness and concentration at Eulerian grid positions are obtained by interpolation with the Gaussian function from their surrounding ice particles. The momentum of ice cover is solved with FD approach to obtain the Eulerian cell velocity, which is used to estimate the ice particle velocity with the Gaussian function also. The thickness and concentration of ice particles are adjnsted with particle mass density and smooth length, which are adjusted with the redistribution of ice particles. With the above modified PIC method, numerical simulations for ice motion in an idealized rectangular basin and the ice dynamics in the Bohai Sea are carried out. These simulations show that this modified PIC method is applicable to sea ice dynamics simulation.     

Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin

Transport and mixing properties of surface currents can be detected from altimetric data by both Eulerian and Lagrangian diagnostics. In contrast with Eulerian diagnostics, Lagrangian tools like the local Lyapunov exponents have the advantage of exploiting both spatial and temporal variability of the velocity field and are in principle able to unveil subgrid filaments generated by chaotic stirring. However, one may wonder whether this theoretical advantage is of practical interest in real-data, mesoscale and sub-mesoscale analysis, because of the uncertainties and resolution of altimetric products, and the non-passive nature of biogeochemical tracers. Here we compare the ability of standard Eulerian diagnostics and the finite-size Lyapunov exponent in detecting instantaneous and climatological transport and mixing properties in the south-western Mediterranean. By comparing with sea-surface temperature patterns, we find that the two approaches provide similar results for slowly evolving eddies like the first Alboran gyre. However, the Lyapunov exponent is also able to predict the (sub-)mesoscale filamentary processes occurring along the Algerian current and above the Balearic Abyssal Plain. Such filaments are also observed, with some mismatch, in sea-surface temperature patterns. Climatologies of Lyapunov exponents do not show any compact relation with other Eulerian diagnostics, unveiling a different structure even at the basin scale. We conclude that filamentation dynamics can be detected by reprocessing available altimetric data with Lagrangian tools, giving insight into (sub-)mesoscale stirring processes relevant to tracer observations and complementing traditional Eulerian diagnostics.     

Numerical study of sand scour with a modified Eulerian model based on incipient motion theory

Application of the standard Eulerian model to simulations of sand scour results in unrealistic phenomena. Therefore, the present work develops a modified Eulerian model based on sand incipient motion theory. The modified model is applied for simulating a two-dimensional single vertical jet and a moving planar jet. The simulation results generally demonstrate fairly good agreement with published results of scour profiles and the velocity contours of the water and sand phases. In addition, equations to describe self-similar scour profiles for the moving planar jet cases are given. The results demonstrate that the modified model efficiently and accurately simulates the two-dimensional sand scour produced by jets, particularly for the moving jet cases.     

Optimisation of an idealised ocean model,stochastic parameterisation of sub-grid eddies

An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30 km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5 km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model.The system considered is an idealised barotropic double gyre that is chaotic at both resolutions. Using the optimisation scheme, we find and apply the constant in time, but spatially varying, forcing term that is equal to the time integrated forcing of the sub-grid scale eddies. A linear stochastic term, independent of the large-scale flow, with no spatial correlation but a spatially varying amplitude and time scale is used to represent the transient eddies. The climatological mean, variance and 5 day lag-covariance of the velocity from a single high resolution integration is used to provide an optimisation target. No other high resolution statistics are required. Additional programming effort, for example to build a tangent linear or adjoint model, is not required either.The focus of this paper is on the optimisation scheme and the accuracy of the optimised flow. However the forcing can provide insights in the design of deterministic and stochastic parameterisations. In the present study, we found that the stochastic parameterisation correcting the model variance is associated with the spatial pattern of eddy-decorrelation timescales rather than the spatial pattern of the amplitude of the variance. The method can be applied in future investigations into the physical processes that govern barotropic turbulence and it can perhaps be applied to help understand and correct biases in the mean and variance of a more realistic coarse or eddy-permitting ocean model. The method is complementary to current parameterisations and can be applied at the same time without modification.     

Comments on the “shear effect” and diffusion in the Lagrangian framework

We indentify three different types of Lagrangian coordinate systems that are used in oceanography. These are: true Lagrangian coordinates (TLC), Lagrangian coordinates (LC), and averaged Lagrangian coordinates (ALC). The diffusion process is studied in each of these coordinate systems. At large scales the eddydiffusivity is proven to be independent of molecular diffusivity, providing the spectrum of turbulent kinetic energy varies as scale raised to a power less than 4 1/3. The shear effect is examined using solutions to the averaged Lagrangian diffusion equation obtained by Okuboet al. (1983). In Eulerian coordinates both advection and diffusion are necessary for the occurrence of the shear effect, while in ALC timedependent dispersion coefficients are necessary for the process. In TLC we use the method of Taylor (1921) to study the dispersion of material by a velocity field, that from the Eulerian perspective, consists of turbulent motion across a uniform shear. The transformation of the above Eulerian velocity field into TLC results in a uniform deformation field and turbulent motion both along and across the shear. This work shows how dispersion of material is related to the turbulent Eulerian velocity and uniform velocity gradients. The instantaneous rate of change of variance of a spreading patch of material is completely specified by the instantaneous divergence obtained over the area occupied by the patch (Kawai, 1976). This relationship is shown to depend upon the fact that at any particular instant it is possible to define TLC that are equivalent to the Eulerian coordinates. In order to describe patch spreading from divergence measured over longer periods it is also necessary to consider other dispersive processes.Contribution number of the Newfoundland Institute of Cold Ocean Science.     

冰动力学的拉格郎日离散元模式

本文描述一种应用于河冰和海冰动力学研究的平滑质点流体力学的离散元模式。该离散元方法是一种自由拉格郎日方法,和传统的欧拉网格数值方法相比,它具有较小的数值扩散并且能够更加灵活地处理复杂的冰过程等许多优点。本文首先给出海冰动力学的离散元模式的基本方法,并与欧拉有限差分方法和半拉格郎日的质点一网格方法进行了对比,其次,本文还给出了离散元海冰模式在渤海的一个应用。     

Laboratory observation of boundary layer flow under spilling breakers in surf zone using particle image velocimetry

A boundary layer flow under spilling breakers in a laboratory surf zone with a smooth bottom is investigated using a high resolution particle image velocimetry (PIV) technique. By cross-correlating the images, oscillatory velocity profiles within a viscous boundary layer of O(1) mm in thickness are resolved over ten points. Using PIV measurements taken for an earlier study and the present study, flow properties in the wave bottom boundary layer (WBBL) over the laboratory surf zone are obtained, including the mean velocities, turbulence intensity, Reynolds stresses, and intermittency of coherent events. The data are then used to estimate the boundary layer thickness, phase variation, and bottom shear stress. It is found that while the time averaged mass transport inside the WBBL is onshore in the outer surf zone, it changes to offshore in the inner surf zone. The zero Eulerian mass transport occurs at h/h_b ≈ 0.92 in the outer surf zone. The maximum overshoot of the streamwise velocity and boundary layer thickness are not constant across the surf zone. The bottom shear stress is mainly contributed by the viscous stress through mean velocity gradient while the Reynolds stress is small and negligible. The turbulence level is higher in the inner surf zone than that in the outer surf zone, although only a slight increase of turbulent intensity is observed inside the WBBL from the outer surf zone to the inner surf zone. The variation of phase inside and outside the WBBL was examined through the spatial velocity distribution. It is found the phase lead is not constant and its value is significantly smaller than previous thought. By analyzing instantaneous velocity and vorticity fields, a remarkable number of intermittent turbulent eddies are observed to penetrate into the WBBL in the inner surf zone. The size of the observed large eddies is about 0.11 to 0.16 times the local water depth. Its energy spectra follow the − 5/3 slope in the inertial subrange and decay exponentially in the dissipation subrange.     

空间分辨率对海岸线时空演变遥感分析的影响——以渤海湾为例

文章针对中低分辨率遥感影像难以提取海岸线中小尺度变化的实际问题,以渤海湾为例,利用2010—2020年SPOT5、GF-1/6、ZY-3等高分辨率遥感影像,采用数字海岸线分析和分形维数方法获取渤海湾海岸线位置变迁速率和复杂度变化过程;针对目前渤海湾海岸线变迁分析研究多基于中低分辨率遥感影像的问题,结合同时期的Landsat影像,分析遥感影像空间分辨率对渤海湾海岸线变迁速率和分形维数的影响。研究结果表明,遥感影像空间分辨率差异对分形维数的影响较小,但对不同类型的岸线变迁速率影响显著;渤海湾海岸线在2010—2020年的变化呈现出由剧烈过渡至相对稳定的状态,伴随着海岸线位置的变化,岸线的分形维数呈现出先上升再至平稳的趋势。相关研究成果能够为渤海湾地区海洋资源利用优化、海岸线及滩涂湿地等自然资源保护提供数据支持。     

Particle trajectories of nonlinear gravity waves in deep water

The paper presents a numerical method for calculating the particle trajectories of nonlinear gravity waves in deep water. Particle trajectories, mass-transport velocity and Lagrangian wave period can be accurately determined by the proposed method. The high success rate of the proposed method is examined by comparing the present results with those of (a) Longuet-Higgins, M.S., 1986, 1987. Eulerian and Lagrangian aspects of surface waves. Journal of Fluid Mechanics 173, 683-707 and (b) Lagrangian moments and mass transport in Stokes waves. Journal of Fluid Mechanics 179, 547-555. It is shown that the dimensionless mass-transport velocity can exceed 10% for large waves, and the Lagrangian wave period is much larger than the Eulerian wave period for large waves.     

Acoustic imaging of an inhomogeneous sediment matrix

This paper presents and applies a new acoustic imaging approach to quantitatively determine geophysical parameters of complex inhomogeneous sediment layers. The concept is called an Acoustic Sub-seabed Interrogator or ASI and it is based on optimising the criteria of temporal and spatial resolution and of coherence by utilizing broadband, narrow beam calibrated sources and fixed receivers on a stationary platform.The ASI concept was experimentally tested over a complex pseudo-glacial till built at a scale of 20:1. Compressional velocity, attenuation losses and thickness values were easily attained using the ASI's coherent spatial scanning approach and through a discrete application of the Hilbert transform in the post processing of data. The simulations provided indepth insight into the model's physical and spatial variations and by statistical distribution emphasized the depositional processes involved in creating the layer. It is believed that the fundamental internal information elucidated by the ASI for the pseudo-till structure and illustrated in the resultant acoustic core cannot be attained using current marine geophysical and geotechnical techniques.     

Submersible holocamera for detection of particle characteristics and motions in the ocean

A submersible holographic camera has been developed for measuring the particle distributions, characteristics and motions within a sample volume in the ocean. Its main purpose is to provide data on the spatial distribution, size, shape, orientation, inter-particle relationships, turbulence, local shear and relative motion due to swimming and sinking of plankton. This battery powered, modular, self-contained system is remotely operated by a PC through fiber optic links. Data from on-board environmental sensors are used to select locations for recording holograms and relating the images to broader scale physical structures. The holocamera also has a buoyancy control system that allows deployment as a neutrally buoyant drifter or in a slow profiling mode. The instrument is currently configured for in-line holography, but it has been designed to be readily adaptable to off-axis holography. The cylindrical sample volume is 6.3 cm in diameter and its length can be varied from 10 to 68 cm. The light source is a pulsed ruby laser chosen predominantly because zooplankton are typically less sensitive to red light. The laser has independent dual flashlamps for maximum flexibility in selecting delay between exposures. About 300 single or multiple exposure holograms can be recorded during a single deployment. Data such as particle size, shape, orientation, distribution in space and velocity are obtained by reconstructing the holograms, scanning them with a video camera equipped with a microscope objective, digitizing the images and analyzing relevant data. Several recent field tests have demonstrated the system reliability and resolution. Particles with sizes as small as 10 μm and details on cell structures of larger particles in the 3–5 μm range could be identified and used for identifying and categorizing the particles. Sample single and double exposure images, the latter for measuring motion, and sample spatial distributions are provided. Methods for mapping the liquid velocity distribution are addressed briefly. Parameters affecting the image resolution and location in space, such as particle density, distance from the film plane and focus are discussed and demonstrated.     

Dynamics of “critical” trajectories

Two diagnostic dynamic models for flow in hyperbolic and elliptic regions of a geophysical fluid are developed and compared. As the main interest here is in local dynamical processes, these models are used to study trajectories near stagnation points in the flow field. The simplest model presumes a balance between the Coriolis and geopotential accelerations. This model is equivalent to the classic approach that characterizes these regimes by the quadratic equation for the eigenvalues of the velocity gradient. However, since that model imposes geostrophic dynamics, the eigenvalues of the velocity gradient can be replaced by the local curvature or Hessian of the geopotential scaled by Coriolis. The general model adds both local and inertial accelerations to the dynamical balance. In contrast to the classic result the consequent frequency equation is a quartic that involves both the Hessian of the geopotential field, the components of the velocity gradient, and Coriolis. Roots of this equation give two distinct time scales, which are interpreted as Lagrangian time scales. Motion of the geopotential field produces a third Eulerian time scale. Critical trajectories are those whose initial positions and velocities are such that they are independent of the Lagrangian time scales. These simple models establish that within hyperbolic and elliptic regions of the geopotential field there may be trajectories whose time scales differ radically from even their nearest neighbors.A characteristic of critical trajectories in the ocean is that they often are found near stagnation points. These may be hard to identify even in model simulations, but a similar quantity, the null in the geopotential gradient, might be easier to obtain. To analyze the relation between the critical trajectories, stagnation points, and gradient null, evolution models for the later two objects are proposed. For a steady geopotential all three coincide. However with a time varying geopotential, they are distinct even though all have the same time scale. The analysis provides a metric for the separation of all three objects.     

Frictionless Generation of a Tidal Eulerian Residual Flow over a Sill in a Narrow Channel

Using a vertically two-dimensional, two-layer model, we have analytically examined the generation mechanism of a nonzero Eulerian residual flow by strong tide-topography interaction in a narrow channel where the frictional effect is not included. In this case, tidally generated baroclinic disturbances are forced non-uniformly in space and time while being advected by a strong tidal flow over the non-uniform slope of the bottom topography. Consequently, nonzero Eulerian residual flow results when averaged over one tidal period. Although the time average of the velocity field is thus nonzero, the associated Eulerian residual transport in each layer is compensated by a Stokes transport so that no Lagrangian residual transport results in both layers. This warns us that simple time averaging of the velocity data obtained at a fixed mooring station might lead to a spurious material transport. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the effect that the direction of geostrophic wind has on turbulence and quasiordered large-scale structures in the atmospheric boundary layer

The dependence that the structure and intensity of turbulent and large-scale quasiordered eddies in the atmospheric boundary layer (ABL) have on the direction of geostrophic wind has been studied on the basis of a series of numerical experiments with a three-dimensional nonstationary model of high spatial resolution. The presence of the meridional component of the angular velocity of the Earth’s rotation results in a significant intensification of velocity fluctuations in a neutrally stratified turbulent flow during the easterly and northeasterly winds and in their decay during the westerly and southwesterly winds. This, in turn, results in significant variations in the mean velocity profile. It is shown that these variations are associated with the largest scale fluctuations and are comparable (in scale) to the depth of Ekman’s turbulent layer. It is found that, in the neutrally stratified ABL bounded in height and under stable stratification inside the ABL, the wind-direction dependence significantly decreases. The possibilities of parameterizing these effects in locally one-dimensional ABL models are discussed.     

Cluster synchronisation: A mechanism for plankton patchiness and a simulation pitfall

We present a study on the emergence of spatial variability, or patchiness, in biophysical simulations of plankton ecosystems. Using a standard approach to modelling such ecosystems, we represent a distribution of plankton as a lattice of non-identical interacting oscillatory populations. Spatial variation is imposed in population parameters, such as maximum growth rate, leading to a spread in the natural (uncoupled) population properties. Using the methods of synchronisation theory, the emergent spatial structure of the coupled system is investigated as a function of the strength of interaction between populations. Surprisingly, a range of coupling strength is found to induce a tenfold increase in the spread in frequency of oscillation of populations in comparison with the uncoupled level of spatial variation. This apparent desynchronisation corresponds to the formation of temporally evolving clusters of local synchronisation: the interplay of grid-cell scale variability and dispersal between populations leads to patchiness at larger scales. However, the occurrence and length-scale of this patchiness is found to be sensitive to typical simulation parameters such as spatial resolution and strength of dispersal, with emergent spatial structure altering abruptly from patchy to homogeneous as these parameters are varied. These results indicate that whilst cluster synchronisation may be a genuine mechanism for the formation of spatial structure in plankton distributions, biophysical modellers should be aware of the possibility of artificial patchiness arising from the basic physical structure of their model.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

论狭窄潮汐水道中sigma坐标下的余流

在受波动影响的近岸浅水区域,运用sigma坐标是计算平均水位附近的余流的有效途径。本项研究在理论上分析了在狭窄潮汐水道中sigma坐标下的余流的物理意义,并运用一系列的理想化数值模型对分析结果进行了验证。对于浅水波,sigma层和水体中的波动面相一致,因而斯托克斯速度及其分量可以用sigma坐标上的速度来表达。一个sigma层上的余流（即sigma余流）是位于这一sigma层平均深度上的欧拉余流和斯托克斯速度垂向分量的和,可以被看做是半拉格朗日余流。因为斯托克斯速度的垂向分量比其水平分量小一个量级,sigma余流可看做为欧拉余流的近似。在sigma层上的物质输运余流是sigma余流和斯托克斯速度水平分量的和,在大小和方向上和拉格朗日余流近似。     

In situ particle size spectra and density of particle aggregates in a dredging plume

An in situ laser particle sizer, the LISST-100, was used to describe the spatial variation of beam attenuation coefficient, in situ particle size spectra and aggregate densities in a dredging plume in the sound Øresund between Denmark and Sweden. The results proved that the above mentioned parameters varied significantly within the investigated length of the plume (approximately 2 km). It is shown how the small single primary particles aggregate and change the in situ particle size spectra into a slightly better sorted and coarser size distribution, and at the same time how the mean density of particles/aggregates decreases significantly. This shift in the state in which the particles exist in the water effectively changes the optical response of the mass of particles suspended in the water. It is shown that adequate correlations between mass concentrations and beam attenuation coefficients can only be obtained if parameters describing the in situ quality and state of the mass of particles, e.g. standard deviation of the size spectra and volume concentration, is included in the regression. From the spatial variation in mean density and in situ particle size, it was possible to calculate the spatial difference in settling velocity. It was found that the difference in settling velocity was only about a factor of 1.7, because increasing in situ particle size was counter-balanced by decreasing mean density. Furthermore, the time-scale of flocculation within the plume was found to be in the order of 50 min.