Transport properties of entrained topographic waves during their interaction with turbulence

In the Boussinesq approximation, topographic waves entrained by a sloping bottom are considered with allowance for turbulent viscosity and diffusion. The mean flows induced by a wave through nonlinearity are determined. The turbulent exchange coefficients are expressed in terms of the density of turbulent energy by using the relations of the semiempirical theory of turbulence. The equation for boundary-layer wave solutions and the equation of turbulent energy balance are solved jointly, which makes it possible to determine the vertical distribution of the density of turbulent energy in the area of the given wave. In the diffusion approximation, the vertical distribution of the concentration of wave-suspended sediments is obtained for the case when the tangential bottom stress exceeds the critical values corresponding to the start of sediment motion.     

Structure of the Wave Bottom Boundary Layer over Smooth and Rough Bottoms

The comparison of six well-known models of the wave bottom boundary layer shows that they are identical in the case of a smooth bottom but exhibit serious differences for the other types of conditions. The thickness of the wave bottom boundary layer and the coefficient of vertical diffusion of momentum are studied by using the relations of the k-ε-model. The validity of these estimates is checked by comparing the measured and computed values of the friction velocity. This comparison demonstrates fairly good agreement between the results characterized by a coefficient of correlation equal to 0.851. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 54–67, November–December, 2005.     

Transport Properties of Trapped Topographic Waves

In the Boussinesq approximation, we study weakly nonlinear topographic waves trapped by a flat slope of arbitrary orientation. We compute the mean currents induced by the waves due to the nonlinearity in the quadratic approximation with respect to the wave amplitude in the presence of dissipation of the wave energy into the turbulent motion. In the diffusion approximation, we determine the vertical distribution of the concentration of wave-suspended sediments. It is shown that the consumption of sediments across the isobaths is directed downward along the slope. At the same time, the consumption of sediments along the isobaths has the same direction as the projection of the horizontal wave vector.     

Experimental estimation of the coefficient of vertical turbulent exchange in a stratified layer of the black sea near the continental slope

On the basis of the data of field measurements, we present the results of numerical analysis of the intensity of vertical turbulent exchange in stratified layers of the Black Sea in the region of the shelf–continental-slope boundary depending on the local stratification. The experiments were carried out within the framework of the GEF/BSERP and Black Sea-2004 international projects. The data were obtained by using a probing version of the Sigma-1 measuring complex. In processing the data of measurements, we apply a procedure of evaluation of the coefficient of vertical turbulent diffusion depending on the external conditions based on the analysis of the spectra of the gradient of temperature fluctuations. For the two studied regions of the shelf, the coefficients of turbulent exchange turn out to be much higher (by about an order of magnitude) than for the open sea under similar conditions. This can be explained by the specific features of the bottom topography affecting the dynamics of quasiinertial waves playing to role of the main causes of small-scale mixing and vertical diffusion. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 14–24, November–December, 2008.     

Currents and turbulent diffusion in the bottom boundary layer of the Barents Sea

The numerical analysis of the stationary field of current velocity on the upper boundary of the bottom boundary layer in the Barents Sea is performed on the basis of a simplified model taking into account the fields of wind velocity and density of water for the principal periods of the seasonal cycle and the bottom topography. The analysis is based on the climatic BarKode database and the data on the wind velocity over the Barents Sea for the last 50 yr. The numerical results demonstrate that the field of bottom currents is fairly nonuniform and the current velocities vary from several fractions of 1 cm/sec to 5 cm/sec in the zones with noticeable slopes of the bottom. The estimates of the thickness of the bottom boundary layer are obtained for the constant coefficient of bottom friction C _f = 0.04. In the major part of the water area of the Barents Sea, the thickness of the bottom boundary layer is close to 1 m. In the regions with significant slopes of the bottom, it increases to 2–2.5 m and, in the two zones of intensification of the bottom currents, becomes as large as 5 m. The maximum estimate of the coefficient of turbulent viscosity is close to 5 cm²/sec. The mean value of the coefficient of vertical density diffusion K _S is equal to 2.34 cm²/sec and its standard deviation is equal to 1.52 cm²/sec. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 31–49, September–October, 2007.     

Investigation of the fields of concentration of the suspension on the northwest shelf of the Black Sea in the case of roiling of the bottom sediments by a moving cyclone

The processes of roiling of the bottom sediments, diffusion transport of the suspension, and its repeated sedimentation on the northwest shelf of the Black Sea caused by a moving cyclone are studied by using a numerical sigma-coordinate model. It is supposed that bottom sediments are formed by particles of the same type. We determine the regions of the most intense rise of the suspension, directions of its transport by the flows of water, and the vertical profiles of concentration of suspended bottom sediments in different regions. In particular, it is shown that the distribution of suspended substances at a distance of 1 m from the bottom reflects the location of the active and inactive centers of erosion. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 3–20, January–February, 2007.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

Vertical structure of the M<Subscript>2</Subscript> tidal current in the Yellow Sea

The vertical structure of the M₂ tidal current in the Yellow Sea is analyzed from data acquired using an acoustic Doppler current profiler. The observed vertical profiles of the M₂ tidal current are decomposed into two rotating components of counter-clockwise and clockwise, and restructured using a simple one-point model with a constant vertical eddy viscosity. The analyzed results show that the internal fictional effect dominates the vertical structure of the tidal current in the bottom boundary layer. In the Yellow Sea, the effect of the bottom friction reduces the current speed by about 20–40% and induces the bottom phase advance by about 15–50 minutes. In the shallower coastal regions, the effects of bottom topography are more prominent on the vertical structure of tidal currents. The vertical profile of the tidal current in summer, when the water column is strongly stratified, is disturbed near the pycnocline layer. The stratification significantly influences the vertical shear and distinct seasonal variation of the tidal current.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

Investigation of Transformations of the Local Regions of Pollution in the Northwest Part of the Black Sea Caused by the Motion of a Cyclone

By the method of mathematical simulation, we study the evolution of local discharges of pollutants on the northwest shelf of the Black Sea induced by the motion of a cyclone. We use the nonlinear equations of motion of a homogeneous viscous fluid in the hydrostatic approximation and the equation of turbulent diffusion. A cyclonic formation is represented by a moving axisymmetric area of low pressures. The discharges of pollutants are caused by the action of instantaneous sources located on the sea surface. We perform the analysis of dependences of the paths of motion of polluted regions, the periods of their dissipation, and the depths of penetration of pollutants on the bottom topography and the intensity of diffusion processes. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 17–27, November–December, 2005.     

A model of the bottom turbulent layer in the shallow-water region

We present a semiempirical model of the bottom turbulent boundary layer aimed at the application as one of the components of the procedure of evaluation of the vertical distribution of the concentration of suspensions in the coastal region of the sea. The model is based on data of laboratory experiments and is suitable for the sand bottom in a broad range of amplitudes of the bottom velocities of the wave origin.     

The key features of the bottom sediment composition in the anoxic Lake Mogil’noe

In the summer 2006, integrated geological, geochemical, hydrological, and hydrochemical studies were performed on the relict anoxic Lake Mogil’noe (down to 16 m depths) located on Kil’din Island in the Barents Sea. The chemical and grain-size composition of the bottom sediments were compared for the lake (a permanently anoxic basin) and the Baltic Sea Deeps (periodically anoxic basins). The vertical location of the hydrogen sulfide layer boundary in the lake (9–11 m depths) was practically the same from 1974 up to now. The concentrations of suspended particulate matter in the lake in June and July 2006 appeared to be close to its summer concentrations in the seawaters of the open part of the Baltic Sea. The mud from Lake Mogil’noe compared to those of the Baltic Sea Deeps are characterized by fluid and flake consistency and by pronounced admixtures of sandy and silty fractions probably of eolic origin. The lacustrine mud contain much plant remains; iron sulfides and vivanite were also found in ooze. The concentrations of 22 elements determined in the lacustrine bottom sediments were of the same levels as those found here 33 years ago. The concentrations also appeared to be close to those in the corresponding grain-size types of the bottom sediments in the Baltic Sea. The low C_org/N value (5% on average) in the mud of Mogil’noe Lake compared to the values for the mud of the Baltic Sea Deeps (10% on average) points to the considerable planktogenic component in the organic matter composition of the lacustrine mud. No indications were reveled for anthropogenic contaminations of the lacustrine bottom sediments with toxic metals.     

Dependence of seafloor boundary layer thickness on the overlying flow direction: a large eddy simulation study

Using large eddy simulation (LES) incorporating the effect of the horizontal component of the earth’s rotation vector, we studied the seafloor turbulent boundary layer to investigate the dependence of the boundary layer thickness on the overlying geostrophic flow orientation. The thickest boundary layer appears for the westward geostrophic flow: it is almost twice that of the eastward flow. The turbulent disturbances in the boundary layer are elongated slightly leftward relative to the geostrophic flow. Linear stability analysis for the Ekman’s spiral flow showed that the growth rate is maximum for the westward geostrophic flow and the unstable roll-like mode appears, which points slightly leftward relative to the geostrophic flow. These properties correspond to the feature near the bottom of the developed turbulent layer.     

底床粉质土液化下波动水体含沙量垂向L型分布特征试验研究

根据现场大风浪条件下的实测资料,粉质土海岸水体中的含沙量沿垂向具有上部均匀、近底突增的分布特点,即呈L型分布特征。利用黄河三角洲粉质土作为试验底床开展波浪水槽试验研究,揭示了底床粉质土在波浪作用下产生液化情况的水体含沙量沿垂向存在L型分布特征。根据试验现象以及悬沙粒度变化,分析认为底部高含沙层的形成主要受粉质土液化后细颗粒析出的影响,上部水体中悬沙由湍流脉动维持。对粉质土海岸大风天气期间水体含沙量剧烈增加采用波致粉质土液化的观点进行了初步解释。     

Preliminary results of measurements of atmospheric turbulence over the sea

We perform the experimental verification of the applicability of the theory of similarity to the wave boundary layer and the assessment of wave-induced perturbations of the air flow depending on various conditions of stratification of the atmosphere and the state of the sea. The measurements were carried out from a stationary platform located in the coastal part of the Black Sea. The experimental procedure is based on the simultaneous measurements of the profile and fluctuations of the wind speed at 5–6 levels in the 1.3–21-m layer, the elevations of the sea surface, the directions of waves and winds, and the mean gradients of temperature and humidity of air. The structure of the boundary layer in the region of measurements depends on the direction of the wind. For weak and moderate onshore winds (< 9 m/sec), the approximate balance is preserved between the production and dissipation of turbulent energy in the cases of unstable and neutral stratification. On the average, the estimates of friction velocity according to the profiles are higher than the dissipative estimates by 10% mainly due to the deficiency of dissipation near the surface. For the offshore wind, the structure of the boundary layer abruptly changes and is determined not by the local parameters but by strong turbulent eddies formed over the dry land. The intensity of low-frequency turbulent fluctuations and the gradient of wind velocity near the surface in the coastal zone are 1.5–2 times higher than for the open sea. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 42–61, May–June, 2007.     

Effect of surface wave breaking on the surface boundary layer of temperature in the Yellow Sea in summer

Near-surface enhancement of turbulent mixing and vertical mixing coefficient for temperature owing to the effect of surface wave breaking is investigated using a two-dimensional (2-D) ocean circulation model with a tidal boundary condition in an idealized shelf sea. On the basis of the 2-D simulation, the effect of surface wave breaking on surface boundary layer deepening in the Yellow Sea in summer is studied utilizing a 3-D ocean circulation model. A well-mixed temperature surface layer in the Yellow Sea can be successfully reconstructed when the effect of surface wave breaking is considered. The diagnostic analysis of the turbulent kinetic energy equation shows that turbulent mixing is enhanced greatly in the Yellow Sea in summer by surface wave breaking. In addition, the diagnostic analysis of momentum budget and temperature budget also show that surface wave breaking has an evident contribution to the turbulent mixing in the surface boundary layer. We therefore conclude that surface wave breaking is an important factor in determining the depth of the surface boundary layer of temperature in the Yellow Sea in summer.     

夏季长江口及其邻近海域湍流特征分析

利用2019年7月在长江口科学考察实验研究夏季航段(NORC2019-03-02)中获得的MSS90L湍流剖面仪的直接观测数据,本文计算并分析了该断面的湍动能耗散率ε和垂向湍扩散系数K_Z的分布情况。湍动能耗散率的大小为1.72×10?10～2.95×10?5 W/kg;垂向湍扩散系数的大小为3.24×10?7～4.55×10?2 m2/s。湍动能耗散率和垂向湍扩散系数的分布相似,均为上层最强,底层次之,中层最弱。上层由于风应力的作用,使得湍动能耗散率和垂向湍扩散系数较大;温跃层处层化较强,抑制了湍动能的耗散和垂向上的湍混合。盐度锋面的次级环流会促使低盐水团脱离,锋面引起的垂向环流会加强海洋的湍混合。低盐水团与外界的能量交换较少,湍动能耗散率较弱。长江口海区存在明显的上升流和下降流,它们是由锋面的次级环流产生的;上升流和下降流的存在促进湍动能的耗散与湍混合。     

Effect of bottom slope in northeastern North Pacific on deep-water upwelling and overturning circulation

Hydrographic data show that the meridional deep current at 47°N is weak and southward in northeastern North Pacific; the strong northward current expected for an upwelling in a flat-bottom ocean is absent. This may imply that the eastward-rising bottom slope in the Northeast Pacific Basin contributes to the overturning circulation. After analysis of observational data, we examine the bottom-slope effect using models in which deep water enters the lower deep layer, upwells to the upper deep layer, and exits laterally. The analytical model is based on geostrophic hydrostatic balance, Sverdrup relation, and vertical advection–diffusion balance of density, and incorporates a small bottom slope and an eastward-increasing upwelling. Due to the sloping bottom, current in the lower deep layer intensifies bottomward, and the intensification is weaker for larger vertical eddy diffusivity (K _V), weaker stratification, and smaller eastward increase in upwelling. Varying the value of K _V changes the vertical structure and direction of the current; the current is more barotropic and flows further eastward as K _V increases. The eastward current is reproduced with the numerical model that incorporates the realistic bottom-slope gradient and includes boundary currents. The interior current flows eastward primarily, runs up the bottom slope, and produces an upwelling. The eastward current has a realistic volume transport that is similar to the net inflow, unlike the large northward current for a flat bottom. The upwelling water in the upper deep layer flows southward and then westward in the southern region, although it may partly upwell further into the intermediate layer.     

Nonlinear effects in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion

By the method of asymptotic multiscale expansions in the Boussinesq approximation, we study nonlinear effects observed in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion. We determine the decrement of attenuation of waves and the boundary-layer solutions at the bottom and on the free surface. The wave-induced mean current is found in the second order of smallness in the wave steepness. The coefficients of the nonlinear Schr?dinger equation are obtained for the envelope of the wave packet. It is shown that a weakly nonlinear plane wave is stable under longitudinal modulation in the long-wave limit. If the wavelength is smaller than a certain critical value, then the wave is unstable under modulation.     

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。