Discussion on the “Numerical simulation of wave-induced laminar boundary layers”

The effect of the shear and normal stress free surface boundary conditions on the laminar flow induced by wave propagation is discussed. The approximate form of the boundary conditions, as used by (Lin, P., Zhang, W., 2008. Numerical simulation of wave-induced laminar boundary layers. Coast. Eng. 55, 400–408), is valid only when the free surface slope is mild.     

A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.     

波浪运动在底边界层的湍流结构数值研究

本文基于$ k $-$ \varepsilon $ 模型研究了波流边界层内湍流结构特征。研究结果表明,时均流速分布数值解与实验结果高度吻合。一个波周期内湍流结构特征（如：涡量、湍动能、湍动能耗散率等）呈周期性变化规律,波浪作用引起涡量、湍动能及湍动能耗散率均在减速阶段减小,在波谷处达到最低值,而后在加速阶段增大,并在波峰处达到最大值。近壁面处湍流结构变化幅值较大（湍动能耗散率变化可达53%）,远离壁面处变化幅值较平均值较小（仅3%）。波流边界层厚度在减速阶段增加,在加速阶段减小。本文所建立的数值模型克服了现有模型因采用“高雷诺数方法”引起的近壁区精度不高问题,可较好地描述波浪作用下湍流结构演变过程的物理机制,为河口海岸地区泥沙运动、岸滩演变及海洋可再生能源的开发利用提供一些指导意义。     

Modification of the damping function in the k–ε model to analyse oscillatory boundary layers

A simple relationship has been developed between the wall coordinate y⁺ and Kolmogorov's length scale using direct numerical simulation (DNS) data for a steady boundary layer. This relationship is then utilized to modify two popular versions of low Reynolds number k–ε model. The modified models are used to analyse a transitional oscillatory boundary layer. A detailed comparison has been made by virtue of velocity profile, turbulent kinetic energy, Reynolds stress and wall shear stress with the available DNS data. It is observed that the low Reynolds number models used in the present study can predict the boundary layer properties in an excellent manner.     

Tests and applications of an approach to absorbing reflected waves towards incident boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

台风期间厦门湾潮流边界层特征研究

本文基于2007年8月圣帕台风影响台湾海峡期间的厦门湾垂向海流流速剖面观测资料,运用Karman-Prandtl模型统计和分析了流速对数剖面的出现频率和边界层参数（摩阻流速与粗糙长度）．结果表明流速剖面满足对数分布出现频率都超过50％,但进行内部一致性原则分析后,流速剖面满足对数分布情况均不足30％．造成流速剖面偏离对数分布的因素主要有：台风、径流、流速加减速、水体分层、底床结构、海底悬沙浓度等等．台风期间的摩阻流速和粗糙长度都大于非台风期间的数值．     

Full-range equation for wave boundary layer thickness

Full-range equation covering all the flow regimes in a wave boundary layer is proposed for the boundary layer thickness. The results are compared with the available experimental data and good agreement has been found. In case of wave boundary layers, there are three definitions of boundary layer thickness in use. Therefore, the full-range equation is derived for three of the definitions. The findings of this study may be useful in calculating suspended sediment transport in coastal environments and studying wave–current combined motion.     

江苏大丰潮滩潮流边界层特征研究

2003年7月中小潮期间使用MIDAS-400用户化数据采集系统在江苏大丰潮滩上进行了垂向多层位同步的流速和悬沙浓度观测。根据观测资料研究了潮流作用下的潮滩底部边界层过程,结果表明,观测地点的潮汐不对称现象十分明显,落潮流速、历时和输水输沙量皆明显大于涨潮;在潮周期内的多数时间里流速剖面符合对数分布,但在风力较强、水流快速增加和流速缓慢的情况下,流速剖面常偏离对数分布;悬沙颗粒垂向混合均匀,悬沙浓度剖面符合Rouse公式;落潮时的底部切应力和摩阻流速明显大于涨潮,摩阻流速与各水层流速通常有较好的线性关系;滩面糙度主要与沙纹形态和推移质运动强度有关,它与摩阻流速存在密切关系;悬沙浓度具有明显的减阻效应,受其影响,摩阻流速和底部切应力分别减小了28%~41%和40%~62%。     

强潮环境下悬沙对底部边界层的影响

对杭州湾金山深槽附近两个定点站位的大潮期间同步水文、泥沙观测结果进行了粉砂分布区再悬浮效应的分析,提出了根据再悬浮过程反演底床切应力的新方法。研究结果表明,在强潮动力、高悬沙质量浓度环境下,即使无密度成层性,悬沙质量浓度对底部边界层的影响仍然存在,表现为底部切应力的减小。在这一条件下,如仍然采用卡门-普朗特模型(κ=0.4),则估算的底部切应力将大大高于实际的数值。     

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.     

Non linear shallow water modelling of bore-driven swash: Description of the bottom boundary layer

The paper presents a simple approach to estimate the bottom shear stress in the swash zone by coupling the Non Linear Shallow Water Equations with the momentum integral equation for the bottom boundary layer. The approach allows not only the computation of the frictional dissipation term in the equations but also to have an insight into the flow structure in the water column during a swash event. The numerical results have been compared with a new set of experiments involving a single dam-break generated swash event. Three different grain sizes, ranging from coarse sand to gravel, have been tested in the laboratory.     

基于新型高频声学多普勒流速剖面仪的河口近底部边界层观测初探

河口物质输运、能量交换与底边界层内的水动力过程密切相关,底边界层参数(如切应力、拖曳系数)的确定至关重要。挪威Nortek公司生产的新型声学多普勒流速剖面仪AD2CP相比传统ADCP具有高频、低噪的优点,可用于高频(16Hz)流速剖面观测,而被广泛应用于底边界层观测的ADV只能测量单点高频流速。本文采用AD2CP在长江口南槽最大浑浊带区域进行座底式观测,并与同步近底部三脚架上ADV的观测结果进行对比。结果表明,使用AD2CP测得的近底部平均流速与ADV的测量结果吻合良好;使用惯性耗散法计算了底切应力,基于ADV的单点高频流速数据计算结果为2.16×10~(-2)～5.69×10~(-1)N/m~2,基于AD2CP的结果为2.09×10~(-2)～4.26×10~(-1)N/m~2,二者范围大致相当。在此基础上,基于AD2CP数据计算出摩阻流速为4.55×10~(-3)～2.06×10~(-2)m/s、底拖曳系数范围为1.84×10~(-4)～2.49×10~(-3),与ADV的计算结果基本一致。此外,由于AD2CP可以获得高频的流速剖面数据,优于单点ADV,具备观测近底部边界层参数和边界层内湍流剖面的潜力。     

Comparison of the nonlocal transport characteristics of a series of one-dimensional oceanic boundary layer models

Seven one-dimensional oceanic boundary layer models are investigated to assess the possible nonlocal transport characteristics of mass and heat in the upper ocean. The dynamical models have been chosen from the diffusion and bulk types currently in use plus two modifications of the transilient type that have been used extensively for atmospheric work by Stull. The models are forced using wind speed and insolation conditions recorded during a 9-day oceanographic cruise near Bermuda in March 1993 during the decline of the spring bloom. The attenuation of sunlight in the upper ocean is calculated using a full spectral model for downwelling irradiance. The vertical heat transport characteristics are reported and compared. A series of spectral diagnostic tests (Green's function analysis, process spectra, and overall mixing lengths) reveal significant differences in the vertical transport characteristics of the models that are not observed in commonly used diagnostics such as sea surface temperature or mixed layer depth. Age spectra (or modal time since last surface contact) are calculated from Green's functions and reveal how a water mass can be cut off from the surface within a short time period. The large differences in the vertical mixing characteristics of the upper ocean boundary layer models have potential implications on the vertical distributions of short-lived chemical tracers and phytoplankton.     

An assessment model for the fate and environmental effects of offshore drilling mud discharges

The benthic boundary layer transport (bblt) model was developed to assess potential impact zones from drilling mud discharges from offshore oil and gas drilling. The model focuses on the drift, dispersion and concentration levels of the suspended fraction of the drilling mud fines in the benthic boundary layer with the assumption of a spatially homogeneous environment. The current version of the model includes a wave boundary layer, a breakup module for drilling mud flocs, a dose–response module for scallops, and a graphical user interface (GUI). The GUI was written in Java which makes the code largely platform independent. Simulations of suspended barite concentration near Sable Island on the Scotian Shelf during drilling in the fall of 1999 reproduce the very low concentrations (generally less than 1 μg L⁻¹) observed during the Environmental Effects Monitoring program. However, the simulations also exhibited concentrations in excess of the no-effects concentration for scallops (100 μg L⁻¹) prior to the sampling program. The model estimates that the potential impact on scallops in the vicinity of the drilling is a few days of lost growth over scales of a few kilometers.