A note on modeling double diffusive mixing in the global ocean

Though ubiquitous in the global oceans, double diffusive mixing has been largely ignored or poorly represented in the models of turbulent mixing in the ocean and in 3-D ocean models, until recently. Salt fingers occur in the interior of many marginal seas and ocean basins, the Tyrrhenian Sea and the subtropical Atlantic being two examples. Diffusive convection type of double diffusion occurs in the upper layers of many sub-polar seas and polar oceans due to cold melt water from sea ice. Consequently, it is important to be able to properly parameterize double diffusive mixing in basin scale and global ocean models, so that the water mass structure in the interior of the ocean can be properly simulated. This note describes a model for double diffusive mixing in the presence of background shear, based on Mellor–Yamada type second moment closure, more specifically Kantha, 2003, Kantha and Clayson, 2004 second moment closure models of resulting turbulence, following Canuto et al. (2008a) but employing a different strategy for modeling the pertinent terms in the second moment equations. The resulting model is suitable for inclusion in ocean general circulation models.     

Validating a turbulence closure against estuarine microstructure measurements

A simple k–ε turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates (ε) and turbulent length scales (l_th) in regions of strong mean shear and small gradient Richardson number (R_g) to within factors of 2–3. It fails in regions of small shear and large R_g, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k–ε closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413–1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505–512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ε and l_th requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18–0.25, while flux Richardson numbers are constrained to the range of 0.1–0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production–dissipation balance. The time rate of change and vertical diffusion of TKE are small, of the same order of magnitude, and vary in magnitude relative to each other systematically across the water column.     

Assessment of mixed layer models embedded in an ocean general circulation model

The atmospheric mixed layer obtained using the Mellor–Yamada model grows slower and becomes shallower than observed, which motivated Nakanishi and Niino (J Meteorol Soc Jpn 87:895–912, 2009) to present a modified version of the Mellor–Yamada model. In this study, incorporating each of the Mellor–Yamada and the Nakanishi–Niino models into an ocean general circulation model, we evaluate its performance in the ocean. Comparing the numerical results with the observed ones in the western North Pacific, the Nakanishi–Niino model is shown to exhibit a better performance than the Mellor–Yamada model under strong wind forcing and sea surface cooling during winter and after passage of typhoons during summer.     

Assessment of turbulence closure models for resonant inertial response in the oceanic mixed layer using a large eddy simulation model

Large eddy simulation (LES) of the resonant inertial response of the upper ocean to strong wind forcing is carried out; the results are used to evaluate the performance of each of the two second-order turbulence closure models presented by Mellor and Yamada (Rev Geophys Space Phys 20:851–875, 1982) (MY) and by Nakanishi and Niino (J Meteorol Soc Jpn 87:895–912, 2009) (NN). The major difference between MY and NN is in the formulation of the stability functions and the turbulent length scale, both strongly linked with turbulent fluxes; in particular, the turbulent length scale in NN, unlike that in MY, is allowed to decrease with increasing density stratification. We find that MY underestimates and NN overestimates the development of mixed layer features, for example, the strong entrainment at the base of the oceanic mixed layer and the accompanying decrease of sea surface temperature. Considering that the stability functions in NN perform better than those in MY in reproducing the vertical structure of turbulent heat flux, we slightly modify NN to find that the discrepancy between LES and NN can be reduced by more strongly restricting the turbulent length scale with increasing density stratification.     

厦门海域浅水三维潮流场动力学模型

基于Casulli的三维浅水模型,改进浅滩处理方法,并入简化的紊流闭合模型,形成完整的海洋动力学基本方程组,改进了紊流闭合模型的求解方法,动力学模拟结果与实测结果符合良好,海域中大量浅滩的干出与淹没的面积和位置与实际情况吻合良好.本模型是厦门海域海洋动力学理论研究中第一个完全的三维斜压潮流场模型,全部程序用FORTRAN语言独立开发和编写.     

Extending the k–ω turbulence model towards oceanic applications

Four different two-equation turbulence models for geophysical flows are compared: The k–ϵ model, two new versions of the k–ω model, and the Mellor–Yamada model. An extension of the k–ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k–ϵ model fail. It is illustrated that only one version of the k–ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k–ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.     

近海区域二阶紊流封闭模型的比较研究

将雷诺应力方程不同封闭方式归结为稳定函数的差异,并以此作为区分标准,总结了6种国内外采用过的稳定函数并以统一的形式列出,分析不同紊流模型稳定函数的分布和影响因素,并且通过实验资料进行了比较分析,发现(1)2000年后提出的3种稳定函数得到的临界理查德森数大于2000年前的3种,更符合实际情况,这与其在压强应变相关项和浮力相关项中增加了旋转效应和重分布效应有关;(2)尽管这3种模型考虑的因素更加全面,但在某些特定场合下,如边界层,与实验的吻合程度反不如前3种较早的稳定函数,反映了封闭模型本身存在的缺陷。最后,提出了二阶紊流封闭模型还待解决的问题。     

悬对沙Mellor-Yamada海洋边界层模型计算结果的影响

为了分析海洋水体垂向水流紊动及紊动交换情况而采用了一维的海洋边界层模型(Mellor-Yamada)并利用数值实验的方法对悬沙、盐度、温度等数据进行分析。原模型未将悬沙考虑在内，本文试将它引入进去探讨由于它的存在对紊动混合特性的影响。2000年4月，Mellor将最初的模型引入了依赖于Richardson数的紊动动能耗散率。本文通过比较具有悬沙和不具有悬沙两种情况下的速度、温度和盐度垂向分布随时间的变化，分析讨论由于悬沙的存在所引发的密度层化对紊动混合作用的影响，并发现悬浮泥沙抑制了部分模拟时间的紊动混合作用。     

潮汐汊道均衡断面面积计算与稳定性分析中的问题 ——以海南陵水新村为例

通过对潮汐汊道稳定性与均衡断面面积定义的探讨,明确了O Brien等、Kreeke与Bruun对潮汐汊道稳定性定义的差异。通过不同方法求解一维水力学与连续方程,计算了海南陵水新村潮汐汊道的封闭曲线,并采用华南沿海A-P关系得出的均衡流速曲线及Soulsby临界流速曲线,计算了新村潮汐汊道的均衡断面面积,根据O Brien等与Kreeke的稳定性定义对新村潮汐汊道的稳定性进行了判别。结果表明,在大、小潮期用不同方法及不同的断面变化方式得出的稳定均衡断面面积(A2)在同样的均衡流速曲线下基本一致,而小潮期的稳定均衡断面面积要小于大潮期,最大流速处的断面面积(Acc)要大于大潮期。A2、Acc及饱满系数为0.8时对应的断面面积三者之间具有较大的差异。用封闭曲线求取潮汐汊道均衡断面面积并进行稳定性判断,在概念上有一定意义,可以作为潮汐汊道稳定性判断的一个依据,但通过求解一维水力学与连续方程以获取均衡断面面积则具有较大的局限性与不确定性。应通过中长期的野外观测、数值模拟与物理模型,以确定潮汐汊道的水动力特征以及地形演变规律,得出A-P关系进而求出均衡断面面积,并结合Bruun方法判定潮汐汊道的稳定性。     

在大洋环流模型中对应于惯性内波破碎的垂直混合的一个参数化方案

Based on the theoretical spectral model of inertial internal wave breaking(fine structure) proposed previously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior below the surface mixed layer in the ocean general circulation model(OGCM) is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes(including inertial internal wave breaking product) on oceanic interior mixing is emphasized. We suggest that adding the inertial internal wave breaking mixing scheme(F-scheme for short) put forward in this paper to the turbulence mixing scheme of Canuto et al.( T-scheme for short) in the OGCM, except the region from 15°S to 15°N. The numerical results of F-scheme by using WOA09 data and an OGCM(LICOM, LASG/IAP climate system ocean model) over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation(AMOC) by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.     

Numerical simulation of micro-bubble drag reduction using population balance model

The phenomenon of drag reduction by the injection of micro-bubbles into turbulent boundary layer has been investigated using an Eulerian-Eulerian two-fluid model. Multiple-size group (MUSIG) based on population balance models, which resolve a wide range of bubble sizes taking into account the bubble break-up and coalescence have been used for this purpose. The simulated results are compared against the experimental findings of Madavan et al. [1984. Reduction of turbulent skin friction by micro-bubbles. Physics of Fluids 27, 356-363] and also other numerical studies explaining the sophisticated phenomena of drag reduction. For the two Reynolds number cases considered, the buoyancy with the plate on the bottom configuration is investigated, as from the experiments it is seen that buoyancy seem to play a role in the drag reduction. Numerical model employed in the investigation comprises of a micro-bubble laden flow wherein two independent sets of Reynolds averaged Navier-Stokes (RANS) transport equations were used to describe both the phases of the flow. The shear stress transport (SST) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. Change in the mean streamwise velocity profiles, void fraction, turbulence modification and other results are presented and discussed with corresponding change in the gas injection rates. The complex mechanism of drag reduction are scrutinised and explained in context to our numerical findings. Special attentions have been also devoted to divulge the effect of bubble coalescence and break-up caused by random collision and turbulent impact. Numerical results showed good agreement for the skin-friction coefficients against experimental data throughout various air injection rates. The MUSIG model was found to be one of the best candidates to resolve the bubble dynamics in micro-bubble-induced drag reduction problems.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅱ. Simulation of SAR signatures of internal solitary waves

A new model developed from the full-spectrum model of Lyzenga and Bennett （ 1988 ） is built up by us preliminarily through considering the impact of the ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves. In the partial differential equation of the action spectral density of the surface gravity-capillary waves the source function representing the contribution of the turbulence is added besides the usual source function representing the contribution of the wind. The source function is determined by applying the κ - ε model and adopting the Nasmyth spectrum of oceanic turbulence （ Nasmyth, 1970; Oakey, 1982; Fan, 2002） on the basis of the previous simulation results of internal tide transformation obtained in the companion paper （Fan et al. ,2008）. Either under relatively high wind speed, or under low wind speed, our model predicts significant large modulations of radar backscatter at all three bands （ L, C and X bands） for both VV and HH polarization. These results prove that considering the impact of ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves is reasonable and appropriate for settlement of the well-known problem of contemporary radar imaging models.     

渤海夏季潮致-风生-热盐环流的数值诊断计算

基于正交曲线坐标的ECOMSED三维水动力模式,并考虑了潮汐、风和实测温盐场,诊断计算了渤海夏季三维潮致-风生-热盐环流,分析了渤海夏季潮致余流、风生和热盐环流的分布结构。结果显示,在夏季,渤海中部海区明显存在一个顺时针向的涡旋,同时渤海还存在着多个逆时针向的涡旋。通过分析和比较各个分量在总环流中的作用,认为夏季潮致余流是相对弱的;热盐环流在夏季总环流中占主要成分。     

Mechanism of local scour around submarine pipelines based on numerical simulation of turbulence model

1 IntroductionSubmarine pipelines are important ocean engi-neeringequipm ents, especiallyfortheoiland gasin-dustries. M anyresearchershavebeendedicatedtotheproblem of local scour around the submarinepipelines, butmostoftheirwork arelaboratory testsand foc…     

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).     

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds.     

Parameterization of vertical mixing in the Weddell Sea

A series of vertical mixing schemes implemented in a circumpolar coupled ice–ocean model of the BRIOS family is validated against observations of hydrography and sea ice coverage in the Weddell Sea. Assessed parameterizations include the Richardson number-dependent Pacanowski–Philander scheme, the Mellor–Yamada turbulent closure scheme, the K-profile parameterization, a bulk mixed layer model and the ocean penetrative plume scheme (OPPS). Combinations of the Pacanowski–Philander parameterization or the OPPS with a simple diagnostic model depending on the Monin–Obukhov length yield particularly good results. In contrast, experiments using a constant diffusivity and the traditional convective adjustment cannot reproduce the observations. An underestimation of wind-driven mixing in summer leads to an accumulation of salt in the winter water layer, inducing deep convection in the central Weddell Sea and a homogenization of the water column. Large upward heat fluxes in these simulations lead to the formation of unrealistic, large polynyas in the central Weddell Sea after only a few years of integration. Furthermore, spurious open-ocean convection affects the basin-scale circulation and leads to a significant overestimation of meridional overturning rates. We conclude that an adequate parameterization of both wind-induced mixing and buoyancy-driven convection is crucial for realistic simulations of processes in seasonally ice-covered seas.     

海浪破碎对海洋上混合层中湍能量收支的影响

海浪破碎产生一向下输入的湍动能通量,在近海表处形成一湍流生成明显增加的次层,加强了海洋上混合层中的湍流垂向混合。为了研究海浪破碎对混合层中湍能量收支的影响,文中分析了海浪破碎对海洋上混合层中湍流生成的影响机制,采用垂向一维湍封闭混合模式,通过改变湍动能方程的上边界条件,引入了海浪破碎产生的湍动能通量,并分别对不同风速下海浪破碎的影响进行了数值研究,分析了混合层中湍能量收支的变化。当考虑海浪破碎影响时,近海表次层中的垂直扩散项和耗散项都有显著的增加,该次层中被耗散的湍动能占整个混合层中耗散的总的湍能量的92.0%,比无海浪破碎影响的结果增加了近1倍;由于平均流场切变减小,混合层中的湍流剪切生成减小了3.5%,形成一种存在于湍动能的耗散和垂直扩散之间的局部平衡关系。在该次层以下,局部平衡关系与壁层定律的结论一致,即湍动能的剪切生成与耗散相平衡。研究结果表明,海浪破碎在海表产生的湍动能通量影响了海洋上混合层中的各项湍能量收支间的局部平衡关系。