Trapped internal waves over undular topography in a partially mixed estuary

The flow of a stratified fluid over small-scale topographic features in an estuary may generate significant internal wave activity. Lee waves and upstream influence generated at isolated topographic features have received considerable attention during the past few decades. Field surveys of a partially mixed estuary, the Rotterdam Waterway, in 1987, also showed a plethora of internal wave activity generated by isolated topography, banks and groynes. Additionally it revealed a spectacular series of resonant internal waves trapped above low-amplitude bed waves. The internal waves reached amplitudes of 3–4 m in an estuary with a mean depth of 16 m. The waves were observed during the decreasing flood tide and are thought to make a significant contribution to turbulence production and mixing. However, while stationary linear and finite amplitude theories can be used to explain the presence of these waves, it is important to further investigate their time-dependent and non-linear behaviour. With the development of advanced non-hydrostatic models it now becomes possible to further investigate these waves through numerical experimentation. This is the focus of the work presented here. The non-hydrostatic finite element numerical model FINEL3D developed by Labeur was used in the experiments presented here. The model has been shown to work well in a number of stratified flow investigations. Here, we first show that the model reproduces the field data and for idealised stationary flow scenarios that the results are in agreement with the resonant response predicted by linear theory. Then we explore the effects of non-linearity and time dependence and consider the importance of resonant internal waves for turbulence production in stratified coastal environments.Responsible Editior: Hans Burchard     

Statistics and spectra of turbulence under different roughness in the near-neutral atmospheric surface layer

Accurate knowledge of the contacts between surface roughness and the resultant wind speed are important for climatic models, wind power meteorology, agriculture and erosion hazards especially on sand saltation in arid and semi-arid environments, where vegetation cover is scarce. In this study, synchronous measurements of three-dimensional wind speed below 5 m are carried out in three different surface roughness conditions in Minqin, China, and the difference in the turbulence statistics and the structure of the very large-scale motions (VLSMs) were revealed. The results show that the slope of the mean wind profile (MVP), the turbulent kinetic energy (TKE) and Reynolds stress increase with the surface roughness. The roughness seems to suppress the ejection events and the surface roughness will not only weaken the energy of the VLSMs, but also reduce the scale values of VLSMs near the wall. These influences may cause some changes regarding the dust transportation in streamwise and vertical directions during the sand and dust storm (SDS). That is, the decrease of the mean velocity near the ground will reduce the dust transportation in the streamwise direction and influence of the roughness on the ejection and sweep events will change the dust transportation in the vertical direction. Furthermore, the increase of roughness will weaken the scale and energy of VLSMs, which will lead to the decrease of the capacity of dust transportation. © 2019 John Wiley & Sons, Ltd.     

近地层能量闭合度对陆面过程模式影响

大量近地层观测试验表明,利用涡动相关法观测的湍流通量小于近地层可利用能量,即近地层能量是不闭合的,这种不闭合度一般为20%甚至更高.而陆面过程模式是基于地气间能量平衡建立,并且模式中的湍流边界层参数化方案通常根据实际观测的湍流通量来确定,因此能量不闭合必将对陆面过程模式造成一定的影响.本文利用2007年春季SACOL站的近地层观测资料,依据能量守恒将能量不闭合中的残余能量通过波文比分配到观测的湍流通量中,即修正涡动相关法观测的湍流通量使得近地层能量达到平衡;之后分别利用观测和修正的湍流通量,建立了能量不闭合和闭合情形下的湍流参数化方案,借助陆面过程模式SHAW,通过数值模拟和对比分析方法考察近地层能量闭合度对陆面过程模式的影响.研究结果表明近地层能量闭合对陆面过程模式有显著的影响:在陆面过程数值模拟中,当应用近地层能量不闭合的湍流通量形成的湍流参数化方案时,陆面过程模式会明显高估地表长波辐射及土壤温度;但当应用修正湍流通量使得近地层能量达到闭合形成的湍流参数化方案后,在不改变任何地表土壤物理生化属性的情况下,陆面过程模式能较好地模拟地表长波辐射和土壤温度.     

近地层能量闭合度对陆面过程模式影响

大量近地层观测试验表明,利用涡动相关法观测的湍流通量小于近地层可利用能量,即近地层能量是不闭合的,这种不闭合度一般为20%甚至更高.而陆面过程模式是基于地气间能量平衡建立,并且模式中的湍流边界层参数化方案通常根据实际观测的湍流通量来确定,因此能量不闭合必将对陆面过程模式造成一定的影响.本文利用2007年春季SACOL站的近地层观测资料,依据能量守恒将能量不闭合中的残余能量通过波文比分配到观测的湍流通量中,即修正涡动相关法观测的湍流通量使得近地层能量达到平衡;之后分别利用观测和修正的湍流通量,建立了能量不闭合和闭合情形下的湍流参数化方案,借助陆面过程模式SHAW,通过数值模拟和对比分析方法考察近地层能量闭合度对陆面过程模式的影响.研究结果表明近地层能量闭合对陆面过程模式有显著的影响:在陆面过程数值模拟中,当应用近地层能量不闭合的湍流通量形成的湍流参数化方案时,陆面过程模式会明显高估地表长波辐射及土壤温度;但当应用修正湍流通量使得近地层能量达到闭合形成的湍流参数化方案后,在不改变任何地表土壤物理生化属性的情况下,陆面过程模式能较好地模拟地表长波辐射和土壤温度.     

Internal waves,baroclinic energy fluxes and mixing at the European shelf edge

The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200 m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139 W m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8 W m⁻¹. However, the waves propagating onshelf transported up to 200 W m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153–425 W m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100–200 W m⁻¹, but these waves could only propagate ∼20–30 km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180 km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.     

太湖湍流动能耗散率的廓线分布及其可能机制

湍流不仅是导致物质、动量等在水-气交界面的交换、水柱内部输送的关键过程,也是促进浅水湖泊中底泥再悬浮及水生生态系统演变的驱动力;其中湍流动能耗散率（ε）不仅是描述湍流动能变化的关键物理量,也是刻画水体中湍流产生机制的关键过程.基于2017年10月29日-11月2日位于太湖梅梁湾采集的高频三维流速廓线和水温廓线观测资料,结合东山气象站同期的风场和辐射等气象资料,探讨太湖中ε的分布特征及其变化的可能机制.结果表明,0.7 m深度以下水平方向上ε介于10^-8~10^-7 m²/s³之间,比垂直方向大一个数量级左右.尽管大型浅水湖泊几何深度浅,但其ε的深度廓线依然存在典型的3层：ε随深度递减的风浪直接作用层,深度从水面至1.0 m左右;ε基本不随深度变化的常数层,分布区间为水深1.0~1.9 m;随后是ε随深度递减的底边界混合层.热力分层的强弱（垂向温差）、位置对常数层和底部边界中ε的贡献显著,甚至造成ε的常数层起始深度下移.本研究有利于进一步理解大型浅水湖泊的动力学过程及其对水生生态系统演变的驱动效应.     

On the instability of internal gravity waves propagating at small but finite angles to the vertical

The question of the instability of internal gravity waves (IGWs) propagating at small angles to the vertical is re-visited. The case of an IGW of finite-amplitude propagating at a very small but finite angle to the vertical is considered. This angle serves as a small parameter in the problem, and the instability of such an IGW is investigated by using the Fourier method and the Sivashinsky integral relations. The analysis undertaken confirms the existence of short-wave instability for small IGW amplitudes and for an arbitrarily small value of their propagation angle to the vertical. For small viscosity and thermal conductivity of the fluid medium, the growth rate of the most unstable mode is proportional to the square of the amplitude of the IGW. The results obtained may be of interest for interpreting the results of observations and confirming the existence of turbulence in the middle atmosphere.     

On the effect of subinertial phenomena on the internal lee waves generation in the Strait of Gibraltar

The generation of internal lee waves (ILW) in the Strait of Gibraltar takes place in the main sill where the tidal flow interacts with a submarine obstacle. The tidal flow is perturbed by subinertial phenomena of different nature summarized in the subinertial currents that can inhibit the ILW generation. The authors present an attempt to randomize the problem by the introduction of a Gaussian noise in the Taylor–Goldstein equation. The random number sets are generated from the statistical distribution of the previously isolated random part of the subinertial currents from experimental data taken in the area during the Gibraltar Experiment 94–96. The effect of the noise is translated into a continuous spreading of the spectrum around the solution of the noise-free problem. A stability analysis is carried out in order to determine the single neutral modes of oscillations and the phase space is divided onto regions of stability and instability as a function of the inflowing subinertial current. The methodology and results could be useful for the design and timing of oceanographic surveys in straits where the ILWs occur.     

Effects of shear in the convective boundary layer: analysis of the turbulent kinetic energy budget

Effects of convective and mechanical turbulence at the entrainment zone are studied through the use of systematic Large-Eddy Simulation (LES) experiments. Five LES experiments with different shear characteristics in the quasi-steady barotropic boundary layer were conducted by increasing the value of the constant geostrophic wind by 5 m s^-1 until the geostrophic wind was equal to 20 m s^-1. The main result of this sensitivity analysis is that the convective boundary layer deepens with increasing wind speed due to the enhancement of the entrainment heat flux by the presence of shear. Regarding the evolution of the turbulence kinetic energy (TKE) budget for the studied cases, the following conclusions are drawn: (i) dissipation increases with shear, (ii) the transport and pressure terms decrease with increasing shear and can become a destruction term at the entrainment zone, and (iii) the time tendency of TKE remains small in all analyzed cases. Convective and local scaling arguments are applied to parameterize the TKE budget terms. Depending on the physical properties of each TKE budget contribution, two types of scaling parameters have been identified. For the processes influenced by mixed-layer properties, boundary layer depth and convective velocity have been used as scaling variables. On the contrary, if the physical processes are restricted to the entrainment zone, the inversion layer depth, the modulus of the horizontal velocity jump and the momentum fluxes at the inversion appear to be the natural choices for scaling these processes. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.     

A note on Stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea

Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.     

黄土高原复杂地形上边界层低空急流对近地层湍流的影响

利用中尺度气象数值模式（Weather Research and Forecasting Model,WRF）模拟风场,结合兰州大学半干旱气候与环境观测站（Semi-Arid Climate and Environment Observatory of Lanzhou University,SACOL）湍流观测资料,分析了黄土高原复杂地形上稳定边界层低空急流对近地层湍流活动的影响.黄土高原复杂地形上稳定边界层低空急流的形成与地形作用引发的局地环流有关.低空急流对近地层湍流活动有强烈影响,剪切作用使小尺度湍涡活动加剧,湍动能增大,同时非平稳运动被压制.低空急流发生时,观测数据有87.3%是弱稳定情形（梯度理查森数小于0.25）;而无低空急流时,对应时段的观测表明65.4%属于强稳定层结（梯度理查森数大于0.3）,非平稳运动造成湍流功率谱在低频端迅速增大.与无低空急流和弱低空急流情形相比,强低空急流发生时,近地层湍动能增大1倍,湍动能在垂直方向上的传递增大1个量级,且方向向下,约为-3 × 10-3 m3·s-3,湍流在上层产生并向下传递.     

Generation and evolution of internal solitary waves in the southern Taiwan Strait

ABSTRACT

The generation processes and potential energy sources of internal solitary waves (ISWs) in the southern Taiwan Strait are investigated by driving a high resolution non-hydrostatic numerical model with realistic background conditions. Two main types of ISWs are clarified according to their different energy sources. One is generated by the nonlinear disintegration of remote internal tides emanating from Luzon Strait, and the other type is generated by local tide-topography interaction at the continental slope. The basic properties and evolution processes differ between these two kinds of ISWs. The waves originated from the remote internal tides at Luzon Strait have amplitudes comparable to previous field observations. In contrast, the ISWs generated locally are much weaker than observed waves, even in the presence of a steady offshore background current, which intensifies the generation of onshore ISWs. The ISWs induced by remotely generated M₂ internal tides are stronger than those induced by K₁ internal tides, and the fraction of internal wave energy transmitted onto the shelf is not significantly influenced by the intensity of remotely generated internal tides.     

Variation of Froude number versus depth during the passage of internal solitary waves from the in-situ observation and a numerical model

There are few studies on the variation of Froude number versus depth during the passage of internal solitary waves (ISWs). In this paper, according to the limited observational data of the ISWs near the Dongsha Islands in the northern South China Sea (SCS), it is found that, during the passage of an ISW, the local Froude number near the main thermocline gets maximum and the flow is supercritical, with the Froude number decreasing gradually upward and downward, whilst before and after the passage of the ISW, the local Froude number is less than 1 and the flow is subcritical in the entire water column. Since the observational current data are only available in the upper ocean, a two-dimensional continuously stratified nonlinear model is employed here to study the variation of Froude number versus depth during the passage of an ISW. The modeled ISW induced current field agrees well with that observed during the passage of the observational ISW. It is found that, even during the passage of the ISW, although the Froude number is larger than 1 in the upper layer, it is less than 1 in the lower layer, and the duration when the Froude number is larger than 1 also changes with depth. Thus, it is suggested that, once the Froude number near the main thermocline is larger than 1, the passage of ISWs could be identified. Moreover, it would be better to choose a sampling interval of no more than 1/4 passage period of the ISW during an in-situ observation of ISWs.     

A note on the approximate determination of the dispersion of Love waves in a laterally nonhomogeneous layer lying over a homogeneous half-space

Rayleigh's principle and the concept of the local wave number have been utilised for the approximate determination of the dispersion of Love waves propagating in a laterally heterogeneous layer lying over a homogeneous half-space. The shear wave velocity and the rigidity in the surface layer have been assumed to decrease with the increase of the lateral distance from the origin. The range of validity of the dispersion equation obtained by this method has been examined critically. It was found that: (a) for existence of Love waves the minimum value of shear wave velocity in the layer must be less than that in the matter below, and (b) the phase velocity of Love waves decreases with the increase of the lateral distance from the origin.     

Experimental study of near-bed concentration and sediment vertical mixing parameter for vertical concentration distribution in the surf zone

Two formulae for the near-bed concentration(C_a) and the sediment vertical mixing parameter(m) are established based on a large scale wave flume experiment.The advantage of the new formulae is that the turbulent kinetic energy induced by wave breaking can be taken into account;the formula for C_a is in terms of the near-bed,time-averaged turbulent kinetic energy,and the formula for m is in terms of depth-and time-averaged turbulent kinetic energy.A new expression for suspended sediment load also is established by depth integration of the vertical distribution of the suspended sediment concentration obtained on basis of the new formulae.Equation validation is done by comparing the predicted C_a and m to measurements for different types of waves(regular wave,wave group,and irregular wave),and good agreement is found.The advantages of the proposed formulae over previous formulae also are discussed.     

Statistical model on the surface elevation of waves with breaking

In the surface wind drift layer with constant momentum flux, two sets of the consistent surface eleva- tion expressions with breaking and occurrence conditions for breaking are deduced from the first in- tegrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the func- tions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite func- tion and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.     

南海东北部海洋内波的反射地震研究

已有的内波研究多来自单点的垂直剖面观测资料,但研究内波水平特征的实测资料却非常缺乏．利用反射地震方法研究海水温盐结构,具有高水平分辨率和短时间内对整个海水垂直剖面进行成像的优势,能够弥补传统物理海洋学观测方法的缺陷,为研究海洋内波提供有前景的新手段．本文通过对南海东北部地震剖面的重新处理、分析,认为地震叠加剖面上同相轴呈现的起伏变化反映了内波的总体形态．计算的水平波数能量密度谱与GM76模型谱基本一致,但在低波数段和高波数段中,两者的振幅及斜率存在着一定差异,经分析认为这种差异主要与内潮波和复杂海底地形的强烈非线性相互作用以及内波破碎等因素有关