Solving the equation for viscous incompressible liquid in a rectangular domain for small reynolds numbers

An algorithm is given for an analytical solution to the problem of the eigenvalue and eigenfunction for the Navier-Stokes equation within a rectangle under the adherence condition at its boundaries. The resulting system of orthonormal functions can be used for correctly deriving the divergence-free component of flow at the free surface of laboratory currents. This system makes it possible to apply the spectral approach to the solution of the Navier-Stokes equation, strictly calculate the primary regimes, investigate their stability, and calculate the secondary currents for small above-criticalities for the conditions of a laboratory experiment on simulating geophysical flows.     

非均匀风影响下风力机三维气动粘性流场的数值模拟

基于面向对象的开源软件OpenFOAM,选择美国国家新能源实验室(NREL)Phase VI风力机为对象,对以往研究较少的非均匀来流风速作用下风力机三维气动粘性流场进行数值模拟。采用较为接近于真实情况的指数型风剖面,计算了轮毂处风速分别为5、10、15和25 m/s四种工况下的叶片表面压力分布、叶片的推力、尾涡等气动力数据,并与均匀来流风速下的风力机气动力学性能进行详细的对比,探讨非均匀风剖面对风力机流场结构和流动特性影响的物理现象和规律。     

Vertical velocity and transport in the South China Sea

Deep water in the South China Sea is renewed by the cold and dense Luzon Strait overflow. However, from where and how the deep water upwells is poorly understood yet. Based on the Hybrid Coordinate Ocean Model reanalysis data, vertical velocity is derived to answer these questions. Domain-integrated vertical velocity is of two maxima, one in the shallow water and the other at depth, and separated by a layer of minimum at the bottom of the thermocline. Further analysis shows that this two-segmented vertical transport is attributed to the vertical compensation of subsurface water to the excessive outflow of shallow water and upward push of the dense Luzon Strait overflow, respectively. In the abyssal basin, the vertical transport increases upward from zero at the depth of 3 500–4 000 m and reaches a maximum of 1.5×106 m3/s at about 1 500 m. Deep water upwells mainly from the northeastern and southwestern ends of the abyssal basin and off the continental slopes. To explain the upward velocity arising from slope breaks, a possible mechanism is proposed that an onshore velocity component can be derived from the deep western boundary current above steep slopes under bottom friction.     

Plane incompressible flow under a periodic force and its geophysical application

Plane incompressible flow under an external spatially doubly periodic force is numerically simulated. It is shown that the stationary point of the system loses stability when the Reynolds number crosses the first critical value and a periodic solution appears from the resonant interaction of modes. Self-oscillation parameters in the structural element of the flow are calculated and compared with the results obtained in a laboratory cell. It is assumed that the phenomenon of a quasi-two-year cycle of the atmospheric circulation is connected with the parametric resonance resulting from seasonal variations of the absolute vortex on hemispheres like in a unified hydrodynamic system.     

完全非线性孤立波的直墙反射

报道了应用边界积分方法模拟完全非线性孤立波的传播与直墙反射,给出了波形演变过程。结果表明,本模型对计算孤立波的传播与直墙反射是有效的。三阶Boussinesq方程的孤立波解比低阶方程的孤立波解更接近完全非线性的数值解.当来波波高增大时,孤立波直墙反射的相位滞后变小。若考虑大波高孤立波的直墙反射或波——波相互作用,一阶理论预报的相位滞后往往低估实际情况。     

Simulation of free surface flow around a VLCC hull using viscous and potential flow methods

Numerical simulations have been carried out to determine the incompressible free surface flow around a VLCC hull form for which experimental results are available. A commercial viscous flow finite volume code using the two-phase Eulerian–Eulerian fluid approach and a potential flow code based on the Rankine source method have been used in this study. The simulation conditions are the ones for which experimental results exist. The shear stress transport (SST) turbulence model has been used in the viscous flow code. A tetrahedral unstructured grid was used with the viscous flow code for meshing the computational domain, while quadrilateral structural patches were used with the potential flow code for meshing the VLCC hull surface and the water surface around it. The results compare well with the available experimental data and they allow an understanding of the differences that can be expected from viscous and potential flow methods as a result of their different mathematical formulations, which make their complementary application useful for determining the total ship resistance.     

均匀流中直立圆柱体绕流三维数值模拟

研究直立贯底圆柱体的三维粘性绕流问题。以不可压缩Navier-Stokes方程为控制方程,采用有限体积法和SIMPLE算法,建立了数值模拟方法。考察在不同水平和垂直断面上,圆柱体绕流产生的尾涡和流动速度场的分布特性,成功地数值模拟了直立贯底圆柱体绕流场的三维特性。结果表明,在考虑重力影响的情况下,直立圆柱体周围的流动具有明显的三维特性,而且沿圆柱体轴向不同断面上的尾涡分布是不相同的。     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Average velocity field of the air flow over the water surface in a laboratory modeling of storm and hurricane conditions in the ocean

Laboratory experiments on studying the structure of the turbulent air boundary layer over waves were carried out at the Wind-Wave Channel of the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS), in conditions modeling the near-water boundary layer of the atmosphere under strong and hurricane winds and the equivalent wind velocities from 10 to 48 m/s at the standard height of 10 m. A modified technique of Particle Image Velocimetry (PIV) was used to obtain turbulent pulsation averaged velocity fields of the air flow over the water surface curved by a wave and average profiles of the wind velocity. The measurements showed that the logarithmic part of the velocity profile of the air flow in the channel was observed in the immediate vicinity from the water surface (at a distance of 30 mm) and could be detected only using remote methods (PIV). According to the measured velocity profiles, dependences of aerodynamic drag factors of the water surface on the wind velocity at a height of 10 m were retrieved; they were compared with results of contact measurements carried out earlier on the same setup. It is shown that they agree with an accuracy of up to 20%; at moderate and strong wind velocities the coincidence falls within the experimental accuracy.     

Trajectory and drift velocity of a sounding instrument in the field of nonuniform currents

We present a method for the determination of the trajectory of a sounding instrument and its drift velocity in the field of currents nonuniform in depth and develop special software for IBM/PC compatible computers. The proposed method and software are checked by using the well-known analytic solution of a similar problem given by Academician A. N. Krylov. We also consider some special examples of application of the developed method to the processing of the data of an OLT profilometer. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Vertical structure of the tidal current ellipse in a rotating basin

Tidal current ellipses formed by the Coriolis effect are investigated theoretically, taking account of the effect of horizontal boundaries. This study reveals that even in a narrow bay, the tidal current ellipse appears in the inside of the bottom boundary layer, although the ellipticity cannot be recognized in the outside of the boundary layer. In a wide bay, the ellipticity is observed even in the outside and it is larger in the inside. The rotation direction of these ellipses is counterclockwise in the northern hemisphere. And also, the Coriolis force has an effect to deflect the major axis of the ellipse in the inside of the boundary layer. These nature of the tidal current ellipse is well explained by the consideration of the formation mechanism of the ellipse.     

两层粘性流体中圆柱体受迫振荡数值模拟

研究两层粘性流体中无限长水平圆柱体的受迫振荡问题。在湍流模式下,采用VOF方法追踪两层流体的内界面,基于动网格技术模拟圆柱体的运动边界,对均匀流中横向振荡圆柱体的绕流场进行了数值模拟。计算受迫振荡圆柱体的升力系数、阻力系数随时间的演化曲线和圆柱体的尾涡分布,以及圆柱体的受迫振荡激发两层流体内界面的扰动,并与均匀流体的情况进行了比较分析。研究表明,流体的两层分层效应对受迫振荡圆柱体的升阻力系数和尾涡分布特性都有显著影响,在水下输油气管道涡激振动特性的工程评估中,应考虑流体的密度分层效应。     

A model for the propagation of nonlinear surface waves over viscous muds

The effect of a thin viscous fluid–mud layer on nearshore nonlinear wave–wave interactions is studied using a parabolic frequency-domain nonlinear wave model, modified to incorporate a bottom dissipation mechanism based on a viscous boundary layer approach. The boundary-layer formulation allows for explicit calculation of the mud-induced wave damping rate. The model performed well in tests based on laboratory data. Numerical tests show that damping of high frequency waves occurs, mediated by “difference” nonlinear interactions. Simulations of 2-dimensional wave propagation over a mud “patch” of finite extent show that the wave dissipation causes significant downwave diffraction effects.     

Nonlinearity of the horizontal velocity field under wind-waves

Using the data from a wind-tunnel experiment, bispectra of orbital-motions of wind-waves and of turbulence are calculated, and nonlinear interaction of wind-waves with turbulence in water are discussed. The wind-waves or the orbital motions of them, at first, produce the turbulence coherent with themselves, and then this coherent turbulence changes to the turbulence noncoherent with wind-waves. Nonlinearity of the velocity fluctuations in the surface layer in water under wind-waves is almost due to the nonlinear energy transfer from the orbital motions of wind-waves to the coherent turbulence. The vertical variations of the power spectra and of the normalized bispectra suggest that the wind driven currents near the surface play an important role in the process from orbital motion of wind-waves to noncoherent turbulence.     

Occurrence probability of a freak wave in a nonlinear wave field

The Edgeworth’s form of a cumulative expansion of the probability density function (PDF) of surface elevation expands the maximum wave height distribution to predict the occurrence probability of freak waves. This study investigated the enhancement of the occurrence probability of freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for a small number of waves N=250. The statistical theory was compared with field data, and freak waves sometimes appear when not expected by the Rayleigh theory, but they were predicted by the proposed theory.     

An investigation of the velocity field under regular and irregular waves over a sand beach

Near-bed horizontal (cross-shore) and vertical velocity measurements were acquired in a laboratory wave flume over a 1:8 sloping sand beach of finite depth. Data were acquired using a three-component acoustic Doppler velocimeter to measure the velocity field close to, but at a fixed distance from the bed. The near-bed velocity field is examined as close as 1.5 cm above a trough and crest of a ripple under three different types of wave forcing (Stokes waves, Stokes groups, and irregular waves). Although both horizontal and vertical velocity measurements were made, attention is focused primarily on the vertical velocity. The results clearly indicate that the measured near-bed vertical velocity (which was outside the wave-bottom boundary layer) is distinctly nonzero and not well predicted by linear theory. Spectral and bispectral analysis techniques indicate that the vertical velocity responds differently depending on the location over a ripple, and that ripple-induced effects on the velocity field are present as high as 4–8 cm above the bed (for vortex ripples with wavelengths on the order of 8 cm and amplitudes on the order of 2 cm). At greater heights above the bed, the observed wave-induced motion is adequately predicted by the linear theory.     

The electromagnetic method and horizontal sections in the velocity field

In this paper a modified electromagnetic current meter (ECM) is presented which, in contrast to the old model, permits us to perform continuous measurements of the velocity field and to acquire the data immediately in a vector form at one direction of towing of the device. To prove that the new current meter can be produced, the relationship between the recorded electric signal and the velocity field, with two transducers being towed across the areas of variable currents, is examined. Analysis of the errors allows a deduction regarding possible utilization of the modified ECM to study the horizontal variability of the current velocity field practically without any restrictions in the deep sea and with some restrictions in the continental shelf zone.Translated by V. Puchkin.     

Acoustic measurements of the velocity field beneath shoaling and breaking waves

An acoustic current meter attached to a servo-hydraulic surface-following device was used to obtain near-surface velocity measurements beneath breaking and near breaking surface gravity waves shoaling on a 1:40 beach. The data are compared to velocities predicted by two adaptations of linear theory: superposition and stretching. For unbroken and near breaking waves, the predictions are in close agreement with the measurements. For breaking and broken waves, near surface crest velocity measurements are influenced by air entrainment; trough velocities are relatively well predicted. The problems associated with the acoustic measurement of near-surface velocities are highlighted.     

PN断面黑潮流速垂直分布特征及机制分析

基于全球海洋再分析模拟GLORYS2(Global Ocean Reanalysis Simulation 2)结果,分析了PN断面(126.0°E-128.2°E,1 000 m以浅)黑潮流速垂直结构的季节和年际变化,探讨了黑潮流速垂直结构形成的动力学机制。结果表明:1)PN断面黑潮夏季流量最大,春季次之,秋、冬季节最小;气候态平均的冬、夏季流速最大值都位于次表层,春、秋季节流速最大值位于表层;夏季相对流速较大、最大值深度较浅;等密线在黑潮主轴区下凹,冬季更为明显。流速最大值深度和密度水平梯度为零的深度均表现出了较大的年际差异,该年际变化甚至超过季节差异;2)流速与密度符合热成风关系。黑潮通量由太平洋大尺度风场及中尺度运动两者共同决定,但局地的热通量和环流对温盐的输运共同影响密度场,调节黑潮流速的垂直分布,影响水通量的分配及营养盐输运;3)有些年份夏季流速最大值出现在表层,可能是夏季西南季风诱导陆架水离岸输运进入黑潮上层导致的结果。非线性、非地转物理过程的影响没有考虑在本研究中,热成风关系能够解释黑潮流速垂直分布形成的部分原因。     

Stationary waves in the flow of a homogeneous fluid with vertical shear of the velocity

A plane problem of free stationary gravitational waves in a horizontal current with vertical shear of the velocity is studied in the linear statement. The determination of the parameters of waves is reduced to the solution of the Sturm–Liouville boundary-value problem. For some vertical distributions of current velocity, we obtain analytic solutions. We propose a numerical algorithm for finding the parameters of waves. On the basis of the performed analysis, we establish the possibility of existence of stationary surface waves in currents for certain ranges of the Froude number. As the Froude number decreases, the waves become shorter, which leads to a faster attenuation of waves disturbances with depth. Under the actual conditions, the waves are short and suffer the influence of shear currents only in the subsurface layer of the ocean.