Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow, the nonlinear potential flow and the viscous fluid flow models. The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined, by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated. The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed, including the increased focused wave crest, delayed focused time and downstream shift of focused position with the increase of input amplitude. It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models. However, only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed, implying the insignificant effect of fluid viscosity on focused wave behavior. Therefore, the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.     

Nonlinear Model of the Ekman Boundary Layer in the Generalized Vorticity Equation

Izvestiya, Atmospheric and Oceanic Physics - Approximations are proposed for the Ekman thickness scale, in which the Coriolis parameter is replaced by absolute vorticity to consider the variability...     

Study of the Neutral Ekman Flow Using an Algebraic Reynolds Stress Model

A recently developed fully explicit algebraic model of Reynolds stress and turbulent heat flux in a thermally stratified planetary atmospheric boundary layer without stratification has been used for a numerical study of the Ekman turbulent boundary layer over a homogeneous rough surface for different dimensionless surface Rossby numbers. A comparative analysis has been conducted for a closure model of the transport term in the prognostic equation of turbulent kinetic energy dissipation including third-order moments. Dependences of the total wind rotation angle on the Rossby number have been obtained. The calculated vertical profiles of mean velocity, turbulent stress, turbulent kinetic energy, surface-friction velocity, and boundary-layer height agree satisfactorily with observational and earlier obtained LES data.     

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.     

并列双圆柱绕流的水动力特性研究

多柱体系统在石油开采逐渐向深海发展的过程中得到广泛的应用,由于波浪、流对多柱体的影响易导致其破坏。因此研究多柱体系统绕流具有重大价值。目前多不等直径多柱体绕流的研究还有待深入。本文利用Fluent模拟雷诺数Re=3 900,G/D为0.1~2.5,d/D为0.5、1.0情况下并列双圆柱的绕流过程,并根据模拟结果分析G/D和d/D的变化对大、小柱体涡脱落形态、升力系数Cl、阻力系数Cd和St值的影响。结果表明,随着G/D变化,涡脱落形态会呈现出不同的形式,绕流参数值也随之发生变化。当0G/D≤0.2时,柱后只有一个涡脱落,为单一涡脱落区,升、阻力系数值存在突变,St值小于单柱St值;当0.2G/D≤0.5~1.0时,柱后出现交替的偏斜流,为偏斜流区,升、阻力系数随着G/D的增大而减小,St值在两个极值之间变化;当0.5~1.0G/D≤2.5时,柱后有成对的涡旋,为双旋涡脱落区,升阻力系数值趋于稳定,St值稳定在0.2左右。偏斜流区与双旋涡脱落区之间的临界间距比G/D随着d/D的增大而增大;不等直径情况下,间隙流偏斜对大柱的影响小于对小柱的影响。     

Linear Approximations of the Second Turbulent Moments of the Atmospheric Convective Surface Layer in a Forced-Convection Sublayer

The Monin–Obukhov similarity theory for the convective surface layer distinguishes two limiting cases: a dynamic limit and a free-convection limit. The dynamic limit for the convective surface layer is defined as a flow with a logarithmic profile of wind and a zero buoyancy flux at the underlying surface. The free-convection limit is characterized by a zero wind speed and a positive buoyancy flux at the underlying surface. The limits of the generalized Monin–Obukhov similarity theory are able to describe the higher order turbulent moments. In this paper, it is assumed that the convective surface layer consists of two sublayers: the lower dynamic sublayer adjacent to the surface and the upper forced-convection sublayer. The turbulent moments can be approximated separately for each sublayer. Linear approximations are suggested for the turbulent moments of the vertical velocity and the potential temperature variance in the forced-convection sublayer. The first-order expansion terms of them correspond to the free-convection limits of the Monin–Obukhov theory under no-wind conditions. The second-order expansion terms describe profiles of the turbulent moments in under convective conditions with a moderate wind. A comparison between the proposed approximations and experimental data strongly suggests that the linear approximation is correct within a forced-convection range.     

Steady Response of a Ventilated Thermocline to Enhanced Ekman Pumping

The steady response of the ventilated thermocline to an increase in Ekman pumping is investigated, focusing on the effect of the mixed layer depth distribution on the subsurface density anomaly. We consider only the subtropical gyre, and the mixed layer is assumed to be deep in the northwest and shallow elsewhere with a narrow transition zone separating the deep and shallow mixed layer regions. At the intersection of this narrow transition zone and the outcrop line, low potential vorticity fluid is subducted into and ventilates the thermocline. In such a situation, an enhancement of the Ekman pumping confined to the northern subtropical gyre leads to pronounced subsurface cold anomalies in the southern subtropics, which is free of anomalous forcing. These density anomalies are much greater than those that occur when either the mixed layer depth is zonally uniform or the Ekman pumping is enhanced in the whole subtropical gyre. They are caused by anomalous changes in the trajectory of the low potential vorticity fluid in response to anomalous Sverdrup flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calculation Methods of Added Resistance and Ship Motion Response Based on Potential Flow and Viscous Flow Theory

To improve the energy efficiency of ships and to predict ship motion response under actual sea conditions, the far-field theory, strip theory, and Fujii and Takahashi’s modified semi-empirical method are based and studied to calculate the wave-induced added resistance. Firstly, a new modified formula based on the Maruo method is presented to calculate the radiation added resistance for the ship with a complex surface. Meanwhile, some calculation details such as the Green function, the shape of the sections (shape below the still water level or shape below the wave level) in the strip theory, and so on are discussed. Finally, the CFD method is used to simulate the motions of the hull and the added resistance, and the results of the CFD method and those of other numerical methods are analyzed and compared with the experiment results. The modified method in the paper can predict the added resistance in waves for the complex-hull-surface ships well and quickly.

     

Ekman螺线的动力学结构

介绍了Ekman螺线的动力学结构 ,分析研究了风应力及海水内部的动量传递形式 .结果表明 :动量传递方向与海流方向成 45°左偏 .这对于研究海洋内部的动力结构是有意义的 .     

不等直径串列双圆柱体绕流的数值模拟

利用Fluent软件模拟雷诺数为200时不同间距比G/D和直径比d/D情况下的圆柱绕流现象。根据模拟结果分析G/D和d/D对圆柱体的涡脱落形态,大、小柱体的升力,阻力系数和St数的影响,结果表明涡脱落形态随着G/D和d/D的变化呈现不同的形式,在G/D小于临界间距比时呈现单一涡脱落形态,在G/D大于临界间距比时,呈现双旋涡脱落形态;临界间距比随着d/D增大而增大。在临界间距比附近大、小柱体的升力和阻力系数值及St数变化较大,大、小柱体的St数具有相同的变化规律,St随着d/D的增大而减小。     

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from lO0 to lO00. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.     

Effect of the Planetary Boundary Layer Horizontal Inhomogeneity in the Two-Dimensional Fluid Motion Model

The generalized two-dimensional vortex equation is derived for an incompressible viscous fluid in a rotating system for a vertically averaged flow taking into account the variability of the boundary layer characteristics. The resulting equation contains parameters and their spatial derivatives determined by the second moments of functions describing the vertical profiles of the flow components. Numerical experiments demonstrate the influence of the boundary-layer horizontal inhomogeneity on the evolution of the vorticity field of a pair of atmospheric vortices.     

Ekman Friction and the Formation of Upper Tropospheric Zonal Flows

Izvestiya, Atmospheric and Oceanic Physics - The influence of the Ekman friction on the dynamics of zonal flows (ZFs) has been studied within the framework of a quasigeostrophic model of the...     

Resonant Excitation of Baroclinic Waves in the Presence of Ekman Friction

The quasi-geostrophic dynamics of disturbances of a flow with a vertical shear is described by a transfer equation for potential vorticity. Wave solutions of this equation are represented by edge baroclinic waves (modes in a discrete spectrum) and singular modes in a continuous spectrum. When frequencies of these modes coincide, the effect of resonant excitation occurs in which the amplitude of baroclinic waves increases linearly. This paper studies this effect in the presence of Ekman bottom friction. It is shown that friction suppresses linear wave growth and gives rise to baroclinic waves of finite amplitude.     

河北省一次强对流天气机理分析

利用常规天气资料、气象自动站加密观测资料及乡镇加密雨量站资料、其它物理量资料及卫星云图资料等,对2009-06-08河北省的强降水及强对流天气进行了分析。研究表明,蒙古低涡携带强的正涡度平流和冷空气,为强对流天气提供了良好的动力条件;南风与偏东风急流为大暴雨提供了良好的水汽,同时,低涡底部的西北风急流与2支暖风急流汇合,为暴雨、冰雹、大风等强对流的形成提供了条件。暴雨落区处于低层次大值能量场的顶部,能量场剖面具有鞍形场结构,高层、低层具有大值能量,中层为中性结构,为深对流的发展提供了初始热力条件。自动气象站加密风场资料分析表明,长时间的中小尺度风场辐合增强了地面空气的辐合抬升,同时也是造成此次局地大暴雨的中尺度系统和触发条件。     

Sinking of less dense water in the bottom Ekman layer formed by a coastal downwelling current over a sloping bottom

Laboratory experiments on the dynamics of a downwelling coastal current over a sloping bottom were conducted in a tank on a rotating platform. The current was generated by a source of stable water flow of the same density (barotropic case) or of lesser density (baroclinic case) compared with the surrounding water in the tank. It was found that even in the case of the baroclinic current, a less dense water downflow in the bottom Ekman layer was formed under certain conditions. At some moment, this downflow undergoes convective instability. Taking into account the results of the experiment, the parameters of the bottom Ekman layer on the continental shelf/slope of the Black Sea were preliminarily estimated and the possible sinking depth of less dense water was calculated.     

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift.     

The effect of Stokes drift on Ekman transport in the open sea

By introducing the wave-induced Coriolis-Stokes forcing into ageostrophic motion equation,the Eulerian transport is modified by the wave-induced Stokes drift.The long-term mean contributions of the Stokes transport with remotely generated swells being included to the ageostrophic transport are analyzed using the ECMWF(European Centre for Medium-Range Weather Forecasts) reanalysis data.The ratio of Stokes transport to Ekman transport in north-south(N-S) direction can reach a maximum of over 50% in the subtropical region.The preliminary influence of the Stokes transport on the North Pacific gyre is all year persistent,while the effect on the North Atlantic gyre is only obvious in boreal winter and early spring.     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。