Numerical modeling of turbulent flows over an urban-type surface: Computations for neutral stratification

Computations of turbulent flows over surfaces with explicitly specified roughness elements that imitate an urban built-up area have been performed using a large-eddy simulation (LES) model. Results are presented for neutral stratification. Some statistics of the flow over an inhomogeneous surface are compared with those over a flat surface. Results of spectral analysis performed to identify characteristic length scales are discussed. A relation is established between the Prandtl mixing length and the turbulence scale defined through the cospectrum-weighted-mean wave number. Values of the roughness parameter and displacement height are determined for three different configurations of objects on the surface.     

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。     

Effect of three-dimensional structures on the dynamics of turbulence in thin layers of fluid in a laboratory experiment

The results of experiments on turbulent flows excited by the Ampere force in a thin layer of a conducting fluid over a solid surface upon the passage of a current and the action of a spatially periodic magnetic field are considered. Third-order longitudinal structure functions of the velocity field are shown to be approximately linear in the spatial shift and negative even at horizontal scales that exceed the layer thickness by an order of magnitude. This is how the three-dimensional dynamics is manifested as a result of the dominant contribution of energy dissipation when the no-slip boundary condition is satisfied on the lower surface. Dissipation and the main summands of energy production have been estimated for the energy-balance equation.     

一种近岸区波浪破碎模型

从波浪破碎的能量关系入手,以紊流能量方程为基础,考虑破碎区内单个波在不同破碎阶段所提供的紊动能量强度的变化过程,提出了一种波浪破碎模式.通过将这一模型引入Boussinesq方程中,初步建立了一种近岸区波浪变形数学模型,并用波浪水槽实验资料对模型模拟波高和平均水位的情况进行了初步验证,得到了良好的结果.     

A nearshore wave breaking model

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Estimates of the characteristics of the horizontal turbulent exchange in the northwestern part of the Pacific Ocean

Estimates of the characteristics of the horizontal turbulent exchange (coefficients of horizontal exchange, scales of deviations of the velocity of geostrophic currents from the background flows, and horizontal scales of perturbations) in the upper ocean layer were obtained on the basis of the data of expeditions held in 1978 and 1980 in the northwestern part of the Pacific Ocean. It is shown that the characteristics of the horizontal turbulent exchange strongly depend on the structure of the background flows, and one of the causes of their variability is related to tropical cyclones. A tendency to a decrease (to different degrees) of the turbulent coefficients in the wake of a tropical cyclone is noted.     

Statistics from Lagrangian observations

We review statistical analyses of Lagrangian data from the ocean. These can be grouped into studies involving single particles and those with pairs or groups of particles. Single particle studies are the most common. The prevalent analysis involves binning velocities geographically to estimate the Eulerian means and lateral diffusivities. However single particle statistics have also been used to study Rossby wave propagation, the influence of bottom topography and eddy heat fluxes. Other studies have used stochastic models to simulate dispersion, calculated Lagrangian frequency spectra and examined the relation between Lagrangian and Eulerian integral scales. Studies involving pairs of particles are fewer, and the results are not well-established yet. There are indications that pair separations grow exponentially in time below the deformation radius, as is also the case in the stratosphere. The behavior at larger scales is less clear, indicating either a turbulent cascade or dispersion by the sheared large-scale circulation. In addition, three or more particles can be used to measure relative vorticity and divergence.     

海面对风应力的非定常响应

针对常垂直湍流系数和变垂直湍流系数两种情况，给出了开阔静止海面对风应力的非定常响应的解析表达式，并讨论了水深，风应力强弱对响应过程的影响，尽管没有考虑风场的非定常性，但本文的结果对理解海洋对风应力的非定常响应过程具有一定的帮助，对分析海面停风后的消衰过程也具有实际意义。通过与实测资料比较，认为垂直湍流系数模式要比常垂直湍流系数模式更为合理。     

Wavelet-based vortical structure detection and length scale estimate for laboratory spilling waves

Turbulent flow fields under spilling breaking waves are measured by particle image velocimetry and analyzed using the wavelet techniques in a laboratory surf zone. The turbulent vortical structures and corresponding length scales in the flow are detected through the eduction of the most excited mode with local intermittency measure that is found to correlate with the passage of the structure. Distributions and evolution of the educed vortical structures are presented and discussed. Packets of vortical structures with high intermittency is observed to stretch downward below the initially low-intermittency trough level, indicating these structures play a crucial role in turbulent mixing below the trough level. It is found that the probability density functions of the intermittent energy of the educed structures, vorticity and swirl strength display an exponential decay. Ensemble-averaged length scales of the educed vortical structures are found to be about 0.1 to 0.2 times the local water depth, close to the turbulent mixing length reported in the surf zone. The Kolmogorov microscale is evaluated and the turbulent mixing length is estimated using the k − ε relation and mixing length hypothesis. The k − ε relation may overestimate the mixing length scale for energetic descending eddies.     

Numerical study on the characteristics of flow field and wave propagation near submerged breakwater on slope

In this study,characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical twodimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propa-gates over breakwater. When wave crest propagates over breakwater,the anticlockwise vortex may generate. On the contrary,when wave hollow propagates over breakwater,the clockwise vortex may generate. Meanwhile,the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy,turbulent dissi-pation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.     

Large-wave simulation of three-dimensional,cross-shore and oblique,spilling breaking on constant slope beach

In this work, the large-wave simulation (LWS) method is adapted for application in spilling wave breaking over a constant slope beach. According to LWS, large scales of velocities, pressure and free-surface elevation are numerically resolved, while the corresponding unresolved scale effects are taken into consideration by a subgrid scale (SGS) model for wave and eddy stresses. The model may be not fully applicable in very shallow water, close to the shoreline, where the unresolved, turbulent, free-surface oscillation is of the same order with the water depth. Time integration of the Euler equations is achieved by a two-stage fractional scheme, combined with a hybrid scheme for spatial discretization, consisting of finite difference and pseudospectral approximation methods. Model parameters are calibrated by comparison to available experimental data of free-surface elevation and velocities in the surf zone for cross-shore incoming waves. The action of the wave SGS stresses in the outer coastal and surf zones initiates breaking and generates appropriate vorticity, in the form of an eddy structure (surface roller), at the breaking wavefront. At incipient breaking, both advection and gravity contribute to the vorticity flux at the free surface, while only after the full development of the surface roller, the effect of advection becomes stronger. The SGS model is also utilized to simulate propagation, refraction and breaking of oblique incoming waves. The gradual breaking and dissipation of wave crestlines and the surface roller structure along the breaking wavefront are automatically captured without any empirical input, such as data for the roller shape or the wave propagation angle at breaking.     

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.     

Features of turbulent momentum and heat transfer in a stably stratified boundary layer over a rough surface

The features of the structure of a stable boundary layer over an urbanized surface are studied using a nonlocal model for the turbulent momentum and heat fluxes, which physically adequately takes into account the effect of buoyancy on turbulent transfer. The transformation of the structure of the boundary layer during transition from a state of convective mixing to a stable state is described by unified expressions for the turbulent momentum and heat fluxes. In some known schemes, different models are used for unstable and stable states. The model reproduces a stable dependence of the Prandtl number on the Richardson number and countergradient heat transfer in a strongly stable boundary layer. The results of numerical simulation are compared to the data of a laboratory experiment and the data obtained using the large-eddy simulation (LES) method.     

Numerical simulation of breaking waves by a multi-scale turbulence model

In this paper, a two-dimensional multi-scale turbulence model is proposed to study breaking waves. The purpose of developing this model is to produce a relatively accurate model with moderate computer requirements. The free surface is tracked by the VOF technique, the log-law profile for the mean velocity is applied at the bottom. Comparing with the Reynolds-Averaged Navier-Stokes models (RANS), the present model shows improving agreement with experimental measurements in terms of surface elevations, particle velocities, wave height distributions and undertow profiles. The subgrid scale (SGS) turbulent transport mechanism is also discussed in the paper. It is found that turbulent production and dissipation are of the same order, but turbulent production is primarily located at the wavefront and above the wave trough, whereas turbulent dissipation is primarily located at the back face of a wave, indicating that in these regions, the assumption of equilibrium is not correct. Below the trough level, the local equilibrium assumption is reasonable. Turbulent convection and diffusion are of the same order at the trough level. Above the trough level, turbulent convection dominates. Under the spilling breaking wave, turbulent kinetic energy is continue to dissipate in the bore region, whereas under the plunging breaking wave, the turbulent kinetic energy is dissipated very rapidly within one wave period.     

Theoretical models of the height of the atmospheric boundary layer and turbulent entrainment at its upper boundary

The planetary boundary layer (PBL), which directly interacts with the underlying surface, differs significantly in its nature from the low-turbulent stably stratified free atmosphere. Fluctuations of the Earth’s surface heat balance immediately affect the PBL and assimilate there owing to the effective mechanism of turbulent heat transfer. In this case the upper boundary of the PBL plays the role of a cover, preventing the direct penetration of thermal effects and contaminants into an overlying atmospheric layer. In view of this, air pollution is especially dangerous when associated with shallow PBL. In addition, local peculiarities of climate change are mainly determined by the PBL height due to the high sensitivity of thin stably stratified PBLs to the thermal effects. Deep convective PBLs are not very sensitive to weak thermal effects, but they significantly affect the formation of convective cloudiness and the climate system as a whole by means of the turbulent entrainment of the thermal energy, humidity, aerosols, and other admixtures through the upper boundary. The PBL height and turbulent entrainment must be calculated when simulating and forecasting air pollution, abnormal frosts and heat, and other hazardous phenomena. In this paper we discuss the state-of-the-art knowledge in the area of PBL height simulation and suggest a new model of turbulent entrainment for convective PBLs.     

Modelling of the upper turbulent layer in the ocean

A differential model of the upper turbulent layer in the ocean is considered. A closed system of equations includes equations of motion, balance, and dissipation of kinetic turbulence energy. Boundary conditions at the surface are determined using a solution of the atmospheric problem taking into account the interaction between the two media. The formulated algorithm allows for a relationship between turbulent energy dissipation and flux and the parameters of wind disturbance. The vertical profiles of turbulence and drift current characteristics are presented as well as parameters of the ocean-atmosphere interaction for various values of impulse jump within the limits of the wave layer with waves collapsing and not collapsing.UDK 551.456.152     

Mathematical modeling of turbulent jets of deep-water sewage discharge into coastal basins

The basic properties of the dynamic model of a turbulent jet formed by a deep-water sewage discharge into the stratified environment of coastal regions are considered. The model developed was used to estimate the parameters of a floating-up jet of deep wastewater discharge from Sand Island into the basin of Mamala Bay (Hawaii) depending on the season and discharge operation mode. The estimates of the float-up depths of the jet and the initial dilution of the jet were estimated on the basis of model calculations using experimental data on the vertical profiles of the water temperature and salinity under the actual conditions of stratification in the study region. It is shown that the further propagation of the wastewater jet depends on tidal events and internal waves generated by tides. The appearance of turbulent jets at the sea surface was recorded. The model estimates of the parameters of the wastewater discharge were compared with the results of experimental measurements. Good agreement was found, which indicates that the physical mechanisms of the propagation of turbulent jets in a stratified medium are adequately described by the model.     

湍流局地平衡假设的新推论--齐次湍流动能输运方程封闭模型与应用(Ⅱ)

在湍流局地平衡假设下 ,建立了齐次湍能输运方程封闭模型 (HKE) ,并在平板边界层的两种经典流动中加以检验 ,给出 HKE封闭下的流速、湍流动能和湍流混合系数剖面的形式解。结果表明 ,HKE可以避免在流速剪切为零时的无湍流混合问题 ,其解与 L aufer湍流实验吻合 ,因而HKE模型比混合长理论有更合理的内涵。文中还给出 HKE封闭的浅海动力学模型 ,以湍应力和水位梯度力的平衡为运动的基本受力平衡 ,进行了模型的量阶分析和运动分析 :当阻尼频率和运动频率同量阶时 ,惯性运动不可忽略 ;在潮振荡占优的浅海中 ,对流非线性相对于惯性运动为小量 ;当阻尼频率足够大时 ,科氏力项相对于湍应力也可能为小量。