On hydraulic falls of two-layer flow

Ｏｎｈｙｄｒａｕｌｉｃｆａｌｌｓｏｆｔｗｏ－ｌａｙｅｒｆｌｏｗ￥ＸｕＺｈａｏｔｉｎｇ;ＬｏｕＳｈｕｎｌｉ;ＴｉａｎＪｉｗｅｉａｎｄＳａｍｕｅｌＳｈａｎｐｎＳｈｅｎ（ＩｎｓｔｉｔｕｔｅｏｆＰｈｙｓｉｃａｌＤｅｅａｎｏｐａｐｈｙａｎｄＰｈｙｓｉｃａｌｏｃ...     

An application of a two-layer model to wind driven sub-tidal currents in Puget Sound

A two layer model of an infinitely long channel, with one end closed, is applied to study the sub-tidal response to wind forcing of Puget Sound. The model uses a linear friction parameterization. Data show that the acceleration of current near the surface responds to the wind event almost instantaneously, however, acceleration tends to start decreasing at later times and eventually changes sign even though the wind blows in one direction throughout. Analysis of the model results show that when the forcing frequency is high, the phase lag between forcing and friction causes this phenomena, and as forcing frequency increases, phase lag between forcing and friction approaches /2. When the forcing frequency is low, phase lag between forcing and friction decreases almost linearly with forcing frequency and at extremely low frequency, they almost balance each other. Analysis of the model results show also that the amplitude of baroclinic pressure gradient increases rapidly as forcing frequency decreases and when the forcing frequency is low, the baroclinic pressure gradient becomes important. Effects of baroclinic pressure gradient propagate as a wave from the boundaries and it takes about one day to take effect at the point where the observations were made.     

Velocity distributions of waves and currents in the combined flow

The theoretical model presented here is designed to predict waves and currents velocity profiles in the combined wave and current motion near a fixed bed. It is also valid for the pure wave motion, because the pure wave motion is only a special case of the combined flow. This model has been derived by using the equation of motion and the eddy viscosity assumptions which are somewhat different from those of former authors. Although the model is simple, the predictions are quite good compared with experimental data from Jonsson and Carlsen (1976) No. 1 and No. 2, Van Doorn (1981) V00RA, V10RA and V20RA, Van Doorn (1982) S00RAL, S10RAL and S20RAL, and Jensen (1989) Test-12 and Test-13.     

Modelling of seasonal exchange flows through the Dardanelles Strait

The Dardanelles Strait is a remarkable example of a long, narrow, shallow, and strongly stratified strait with bidirectional exchange that is governed by both baroclinic and barotropic forcing with a wide spectrum of variability. A three-dimensional free surface primitive equation model is applied to study seasonal hydrodynamics variability in this strait. The calculated vertical structure of temperature, salinity, and velocity fields agrees well with available survey data. Seasonal monthly values of the volume exchange at the Aegean and Marmara exits are estimated. It is found that the seasonal exchange dynamics is governed by the turbulent friction and entrainment at the Nara Passage area. The mean annual water transport in the upper layer is increased by 80% after the Nara Passage. About 25% of water entering in the Dardanelles bottom layer reaches the Marmara Sea in winter, and 50% reaches it in summer. The estimate of the Dardanelles hydrodynamics according to hydraulic and viscous–advective–diffusive regime classification shows significant deviation from the two-layer hydraulic asymptotic. However, according to three-layer hydraulic theory, the flow is found to be critical in the Nara Passage area.     

两层简单斜压海洋模式及冬、夏季平均海流模拟

设计了一个两层简单斜压海洋模式(H₁=501,H₁+H₂=250m),利用1月和7月多年平均的海平面气温场、海平面气压场和由该气压场诊断出的海面风场,对此模式的性能进行了检验.结果表明,模拟得出的冬、夏季海洋表层及次表层流与实况较为一致.     

潮流作用下环礁断面的流动特征研究

本文首先通过循环水槽试验测量分析了正向和反向潮流影响下概化环礁断面的流动特性,试验结果表明：在正向流和反向流作用时,礁坪上仅存在亚临界流,并可观察到经典的壁面有界流动流速剖面特征;沿礁的平均水位与各个测线上的流速随潮流幅值的增大而增大。本文随后采用雷诺平均的Navier-Stokes方程并结合标准的k-ωSST湍流模型建立数值水槽,进一步研究了多种水动力与礁型因素影响下前后礁外礁缘处的流速变化规律。数值模拟结果表明：后礁外礁缘处的平均流速均大于前礁外礁缘处;平均流速随潮流幅值的增大而增大,随礁坪水深、礁坪宽度、潟湖宽度和礁前斜坡坡度的增大而减小;最后基于数值模拟结果提出了预测各种因素影响下前后礁外礁缘处流速的幂函数型经验公式。     

Long-period topographic trapped waves in a two-layer ocean with basic flow

The characteristics of free topographic trapped waves are investigated numerically for a two-layer model with basic flow, which is uniform, geostrophically balanced motion flowing parallel to the coast. Six modes are identified for this model with depth variations. They are external and internal Kelvin modes, a topographic Rossby mode, and additional three modes. The two of the additional modes are interesting. The first one is a quasi-geostrophic surface-trapped mode, while the second one is a quasi-geostrophic bottom-trapped mode. It is suggested that baroclinic instability takes place when these two modes take a resonance coupling each other.     

A two-layer simple baroclinic equation ocean model and its simulations of ocean currents in winter and summer

INTRODUCTIONThe world ocean is one of the important components of the human environment. With thedevelopment of marine resource exploit and marine engineering, more and more attention shouldbe paid to the study of ocean current movements by the means of numerical simulation and numerical prediction. It can not only improve our knowledge about the law of ocean circulation but alsocheck the reliability of theoretical research and scientific prediction. On the other hand, it canmake up for t…     

Effect of wave action of a two-layer flow on underwater obstacles

A force action caused by the generation of internal waves in the vicinity of a density jump layer in a marine medium and exerted on underwater obstacles streamlined by a two-layer flow has been studied as part of a theoretical model. A horizontal element of an engineering structure, for example, a transport pipeline, which is modeled by a point dipole, is selected as an underwater obstacle. The integral representations for the wave resistance and the lift force are obtained. The characteristic features of variation in the hydrodynamic reactions to the streamlined obstacle, as well as the conditions of their significant intensification are revealed.     

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。     

In situ modification of modern submarine hyaloclastic/pyroclastic deposits by oceanic currents: an example from the Southern Kermadec arc (SW Pacific)

Submarine volcaniclastic deposits, both modern and ancient, pose a conundrum in distinguishing between syn- and post-eruptive processes. High-standing, submarine volcanic edifices of the late Quaternary southern Kermadec arc (SW Pacific) are point sources of pyroclastic/hyaloclastic deposits that are bathed and modified by a complex current system of the South Pacific gyre flowing southeast along the northern margin of New Zealand, which in part comprises the anticyclonic flow of the warm-cored East Cape Eddy (ECE). Flow of the ECE across the southern Kermadec arc provides a present-day case of extensive and in situ, post-eruptive, textural modification of modern pyroclastic/hyaloclastic deposits on the crests and upper flanks of submarine stratovolcanoes. Photographic observations (and limited textural data) from seven Kermadec volcanoes reveal pervasive evidence of sediment winnowing (including crag and tail structures, scour and moating around volcanic blocks, coarse sand-granule lag deposits, epifaunal deflection, lineated mud streaking, and moulded bioturbation mounds) and asymmetric current-ripple bedforms at water-depths of at least 1500 m. All bedforms indicate increasing current speed at progressively higher elevations (decreasing water-depth) for each volcano. Current-ripples mostly have discontinuous, asymmetric, shorted-crested, linguoid–lunate forms below 1000 m water-depth, progressing to semi-continuous, asymmetric, shorted-crested, linear-sinuous forms above 500 m. Current elutriation of the Kermadec deposits progressively removes fines with decreasing water-depth resulting in relatively fines-depleted, volcaniclastic sands and granules. This post-eruptive process overprints syn-eruptive processes that notionally generate more comminuted fine-grained clasts with decreasing water-depth as phreatomagmatic explosive eruptions become more vigorous. Current-elutriation also modifies volcaniclastic detritus prior to subsequent removal by episodic, mass-gravity flow. In addition the sand-granule traction load, driven by current-flow, moves sediment nearly continuously to gully and rill heads for removal down-slope, independently of syn-eruptive sediment flux. The underlying observation is that volcaniclastic deposits rarely reflect just syn-eruptive processes, and that significant in situ current-elutriation of at the least surficial pyroclastic/hyaloclastic eruption products can occur on submarine volcanoes.Threshold current velocities, derived assuming unidirectional flow over cohesionless sand-lapilli grainsizes, and accounting for bed friction, yield current velocities (at 100 cm above the bed) of ≤15 cm s⁻¹ for water-depths >1500 m through to ∼70 cm s⁻¹ for depths <500 m at the crests of Rumble III and V volcanoes. Estimated velocities are consistent with short-term current velocities of 30–40 cm s⁻¹, measured directly from either acoustic doppler current profile data or relative geostrophic flow, since the latter do not account for seafloor topographic intensification. The variable hydrographic climatology of the ECE, known from sea-surface dynamic heights and repeat CTD surveys, is possibly recorded by seafloor substrates as evinced by worm-trails post-dating ripple formation and differing orientations of winnowed structures and ripples.     

Structure of currents in the soliton of an internal wave

The characteristics of strongly nonlinear solitary internal waves (solitons), which are calculated by the nonlinear numerical model of the Massachusetts Institute of Technology (MITgcm), are studied. The model is verified and adopted on the basis of a laboratory experiment [6]. The field of the vertical and horizontal current in a wave is calculated. The formation of a reversible stream in the near-bottom layer is detected directly behind a soliton.     

Tide-induced flow signature in rip currents on a meso-macrotidal beach

On rip-channelled beaches, intense rip currents are driven by waves due to alongshore variations in breaking-induced wave energy dissipation. This study addresses for the first time the potential development of tidal currents superimposed onto the wave-driven circulation. This phenomenon is observed on a rip-channelled meso-macrotidal beach (Biscarrosse, SW France). Field measurements show 20 to 45% stronger mean rip velocities during ebb than during flood. Numerical experiments reveal that this asymmetry is the signature of tidal currents developing over the rip channel morphology. This asymmetry is found to increase roughly linearly with increasing tidal range. These results are significant to beach safety and lifeguarding and stimulate further numerical exercises.     

Water wave scattering by bottom undulations in an ice-covered two-layer fluid

The scattering of plane surface waves by bottom undulations in an ice-covered ocean modelled as a two-layer fluid consisting of a layer of fresh water of lesser density above a deep layer of salt water, is investigated here by using a simplified perturbation analysis. In such a two-layer fluid there exist waves of two different modes, one with higher mode propagates along the interface and the other with lower mode propagates along the ice-cover. An incident wave of a particular mode gets reflected and transmitted by the bottom undulations into waves of both the modes so that transfer of wave energy from one mode to another takes place. The first-order reflection and transmission coefficients of two different modes are obtained due to incident waves of again two different modes by employing Fourier transform technique in the mathematical analysis. For sinusoidal bottom topography these coefficients are depicted graphically against the wavenumber. These figures show how the transfer of energy from one mode to another takes place.     

Numerical simulations of the Mediterranean sea outflow: impact of the entrainment parameterization in an isopycnic coordinate ocean model

Gravity current entrainment is essential in determining the properties of the interior ocean water masses that result from marginal sea overflows. Although the individual entraining billows will be unresolvable in large-scale ocean models for the foreseeable future, some large-scale simulations are now being carried out that do resolve the intermediate scale environment which may control the rate of entrainment. Hallberg [Mon. Wea. Rev. 128 (2000) 1402] has recently developed an implicit diapycnal mixing scheme for isopycnic coordinate ocean models that includes the Richardson number dependent entrainment parameterization of Turner [J. Fluid Mech. 173 (1986) 431], and which may be capable of representing the gravity current evolution in large-scale ocean models. The present work uses realistic regional simulations with the Miami Isopycnic Coordinate Ocean Model (MICOM) to evaluate ability of this scheme to simulate the entrainment that is observed to occur in the bottom boundary currents downstream of the Mediterranean outflow. These simulations are strikingly similar to the observations, indicating that this scheme does produce realistic mixing between the Mediterranean outflow and the North Atlantic Central Water. Sensitivity studies identify the critical Richardson number below which vigorous entrainment occurs as a particularly important parameter. Some of these experiments also show meddies detaching from the Mediterranean undercurrent at locations that appear to be highly influenced by topographic features.     

Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

Numerical modeling of flow and scour below a pipeline in currents: Part I. Flow simulation

The performance of the standard k–ε, Wilcox high-Reynolds-number k–ω, Wilcox low-Reynolds-number k–ω and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k–ω models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C_s used. The standard k–ε and the Wilcox k–ω models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k–ω models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.     

The rôle of the complete Coriolis force in cross-equatorial flow of abyssal ocean currents

Ocean currents flowing close to or across the equator are strongly constrained by the change in sign of f, the locally vertical component of the Earth’s rotation vector, across the equator. We investigate these currents using a shallow water model that includes both the locally vertical and locally horizontal components of the Earth’s rotation vector, thus accounting for the complete Coriolis force. We therefore avoid making the so-called “traditional approximation” that retains only the part of the Coriolis force associated with the locally vertical component of the rotation vector. Including the complete Coriolis force contributes an additional term to the fluid’s potential vorticity, which may partially balance the change in sign of f as fluid crosses the equator over suitably shaped bathymetry.We focus on the Antarctic Bottom Water, which crosses the equator northwards in the western Atlantic ocean where the local bathymetry forms an almost-zonal channel. We show that this bathymetry facilitates the current’s equatorial crossing via the action of the “non-traditional” component of the Coriolis force. We illustrate this process using both analytical and numerical solutions for flow of an abyssal current over idealised equatorial topography. We also consider the one-dimensional geostrophic adjustment of a body of fluid across the equator, and show that the “non-traditional” contribution to the fluid’s angular momentum permits a larger cross-equatorial transport. These results underline the importance of including the complete Coriolis force in studies of the equatorial ocean, particularly in the weakly-stratified abyssal ocean where the non-traditional component is most pronounced.     

Numerical experiment aimed at modeling the hydrophysical fields in the sea of Marmara with regard for Bosporus and Dardanelles

We performed a long-term prognostic experiment aimed at the investigation of the process of formation of the hydrodynamic structure of the Sea-of-Marmara waters with regard for the influence of Bosporus and Dardanelles. It is shown that the mutual adaptation of hydrophysical fields and their adjustment to the physical and geographical conditions of the sea proceed as a result of the action of rapid (tens of days) and slow (several tens of years) mechanisms of adaptation. An S-like jet current directed from Bosporus to Dardanelles was formed. Two stable anticyclonic formations are well visible in the central part of the sea. In deeper layer, an abyssal jet current was formed as a result of penetration of heavy Mediterranean waters. The established specific features of the circulation of waters in the Sea of Marmara are confirmed by the data of observations. We conclude that the principal features of the dynamics of waters in the Sea of Marmara are formed under the influence of two straits. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 28–41, May–June, 2007.     

Dynamics of Rossby waves in an ocean with inhomogeneous currents

A model for a two-layer ocean is applied to consider, in terms of the geometrical optics approximation, the effect of mean flows propagating within the upper layer upon the dynamics of Rossby waves. The case is theoretically analysed, with the depth of the ocean's upper layer much smaller than that of the underlying layer. In this case, the flow's impact upon the baroclinic mode of Rossby waves is ubiquitous, with the exception of synchronicity. Depending on the parameters, four types of wave packets' behaviour in the vicinity of synchronicity points are singled out, namely, the elimination of the peculiarity, shadowing, and convective/absolute instability. For the mean flow profile simulating cyclonic and anticyclonic gyres, we have obtained wave packet trajectories and have studied the wave packet's interaction with the current. Specifically, it has been demonstrated that, given some modulus of the wave packet, vigorous energy exchange between the wave vector and the flow takes place. Translated by Vladimir A. Puchkin.