A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

Spectrum Analysis of Wind Profiling Radar Measurements

Unlike previous studies on wind turbulence spectrum in the planetary boundary layer, this investigation focuses on high-altitude （1-5 km） wind energy spectrum and turbulence spectrum under various weather conditions. A fast Fourier transform （FFT） is used to calculate the wind energy and turbulence spectrum density at high altitudes （1-5 km） based on wind profiling radar （WPR） measurements. The turbulence spectrum under stable weather conditions at high altitudes is expressed in powers within a frequency range of 2 × 10-5-10-3 s-1, and the slope b is between -0.82 and -1.04, indicating that the turbulence is in the transition from the energetic area to the inertial sub-range. The features of strong weather are reflected less obviously in the wind energy spectrum than in the turbulence spectrum, with peaks showing up at different heights in the latter spectrum. Cold windy weather appears over a period of 1.5 days in the turbulence spectrum. Wide-range rainstorms exhibit two or three peaks in the spectrum over a period of 15-20 h, while in severe convective weather conditions, there are two peaks at 13 and 9 h. The results indicate that spectrum analysis of wind profiling radar measurements can be used as a supplemental and helpful method for weather analysis.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

On the Time Evolution of the Turbulent Kinetic Energy Spectrum for Decaying Turbulence in the Convective Boundary Layer

Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z _i at a convective surface-layer height z = 0.05z _i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.     

The Theoretical Model of Atmospheric Turbulence Spectrum in Surface Layer

It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv-Burgers equation lies between -5/3 and -2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov’s isotropic turbulence and Frisch’s intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the equation, the 1 / Re, corresponds to dissipative coefficient v, to dispersive coefficient β, then (v/ 2β)2 corresponds to .We prove that the wave number corresponding to maximum energy spectrum decreases with the decrease of stability (i.e., the increase of in eddy-containing region. And the spectrim amplitude decreases with the increase of (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.     

多年月平均500毫巴图上60°N和30°N纬圈的波谱分析

本文对北半球多年月平均500毫巴图上60°N和30°N纬圈的高度和纬圈平均的经向运动动能进行了波谱分析,探讨了前3个波幅和位相角的季节变化,以及在高低纬度之间的差异。主要结果如下:1位势场的高度主要贡献,集中在准静止长波范围内,并具有明显的季节变化。2波数为1的波在高低纬度性质有显著的不同,其分界线大约在50°-60°N之间。此外,准静止的长波愈向低纬度去逐渐有向西偏移的现象。例如,在30°N上准静止的长波比60°N上要偏西(1/4)-(1/2)波长。360°N纬圈平均的经向运动动能主要部分亦集中在准静止长波范围内。虽然峰值有明显的季节变化,但最大的极值都出现在波数n=2-4之间。30°N纬圈平均的经向运动动能谱有着明显的季节变化,大致可分成如下3个类型:(1)冬季型:纬圈平均的经向运动动能谱存在着两个极值,最大的极值稳定于准静止长波范围内(n=3附近),次极植位于移动性行星波范围内(n=5-8)。(2)夏季型:纬圈平均的经向运动动能谱只有一个极值,稳定于波数为6-7的波内。(3)过渡型:纬圈平均的经向运动动能谱分布较平坦,没有稳定的极值存在。     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

Stability Dependence of Canopy Flows over a Flat Larch Forest

The dependence on atmospheric stability of flow characteristics adjacent to a very rough surface was investigated in a larch forest in Japan. Micrometeorological measurements of three-dimensional wind velocity and air temperature were taken at two heights above the forest, namely 1.7 and 1.2 times the mean canopy height h. Under near-neutral and stable conditions, the observed turbulence statistics suggest that the flow was likely to be that of the atmospheric surface layer (ASL) at 1.7h, and of the roughness sublayer (RSL) at 1.2h. However, in turbulence spectra, canopy-induced large coherent motions appeared clearly at both heights. Even under strongly stable conditions, the large-scale motions were retained at 1.2h, whereas they were overwhelmed by small-scale motions at 1.7h. This phenomenon was probably due to the enhanced contribution of the ASL turbulence associated with nocturnal decay of the RSL depth, because the small-scale motions appeared at frequencies close to the peak frequencies of well-known ASL spectra. This result supports the relatively recent concept that canopy flow is a superimposition of coherent motions and the ASL turbulence. The large-scale motions were retained in temperature spectra over a wider region of stability compared to streamwise wind spectra, suggesting that a canopy effect extended higher up for temperature than wind. The streamwise spacing of dominant eddies according to the plane mixing-layer analogy was only valid in a narrow range at near neutral, and it was stabilised at nearly half its value under stable conditions.     

Inertial ranges in three-dimensional quasi-geostrophic turbulence

A theory is presented both for spectral energy transfer and for the transfer of spectral components of pseudo-potential enstrophy in a homogeneous quasi-geostrophic turbulent field which is rendered anisotropic by the distortion caused by a random collection of vortices superimposed on the principal motions. The fluid is, thus, subjected to an almost irrotational distortion. The random vortices cause straining effects on turbulent velocity and temperature fluctuations and modify the energy spectrum in the spectral ranges of interest. The strain imposed by the distortion is assumed to be homogeneous. For three-dimensional quasi-geostrophic turbulence that conserves pseudo-potential enstrophy as well as energy, this theory predicts –8/3 and –4 power inertial-range energy spectra.The predictions favourably corroborate the observed spectrum of energy in the atmosphere in the region of hemispheric wave-numbers 10–16 with a –8/3 slope and at higher wave-numbers with –4 slope on a log-log energy-wave-number diagram. The transfer rates of pseudo-potential enstrophy in the range 10n16 and of energy in the rangen>16 are identically zero, while the transfer of energy in the first range is from higher to lower wave-numbers and that of the pseudo-potential enstrophy in the second range is from lower to higher wave-numbers.As compared with the earlier two-dimensional turbulence theory of Kraichnan and the quasigeostrophic turbulence theory of Charney, the present theory predicts more realistic shapes of the energy spectra of atmospheric motions at scales shorter than the baroclinic excitation scales.     

Impact of the Nocturnal Low-Level Jet and Orographic Waves on Turbulent Motions and Energy Fluxes in the Lower Atmospheric Boundary Layer

The nocturnal low-level jet (LLJ) and orographic (gravity) waves play an important role in the generation of turbulence and pollutant dispersion and can affect the energy production by wind turbines. Additionally, gravity waves have an influence on the local mixing and turbulence within the surface layer and the vertical flux of mass into the lower atmosphere. On 25 September 2017, during a field campaign, a persistent easterly LLJ and gravity waves were observed simultaneously in a coastal area in the north of France. We explore the variability of the wind speed, turbulent eddies, and turbulence kinetic energy in the time–frequency and space domain using an ultrasonic anemometer and a scanning wind lidar. The results reveal a significant enhancement of the turbulence-kinetic-energy dissipation (by?50%) due to gravity waves in the LLJ shear layer (below the jet core) during the period of wave propagation. Large magnitudes of zonal and vertical components of the shear stress (approximately 0.4 and 1.5 m² s^?2, respectively) are found during that period. Large eddies (scales of 110 to 280 m) matching the high-wind-speed regime are found to propagate the momentum downwards, which enhances the mass transport from the LLJ shear layer to the roughness layer. Furthermore, these large-scale eddies are associated with the crests while comparatively small-scale eddies are associated with the troughs of the gravity wave.

     

On the effects of vertical eddy viscosity on rossby and eady waves in the ocean

The effects of vertical eddy viscosity on simple mesoscale waves in the ocean are studied. The decay of Rossby waves is investigated by one-dimensional depth-dependent linear stability problems which are derived for the interior non-viscous or viscous quasigeostrophic flow using parameterizations of the top and bottom boundary layers corresponding to Ekman suction, no-stress and bottom-stress boundary conditions.The non-slip condition at the bottom yielding an O(E_v^1/2)-Ekman layer causes very short damping times for the 0th Rossby mode. This suggests that this boundary condition is not suitable for mesoscale wave studies, because a Rossby wave fit for the MODE eddy can be done satisfactorily without any damping. Reasonable results for damping times of Rossby waves are obtained by prescribing the bottom stress, resulting from the constant-stress layer at the bottom, and the free-slip condition at the surface. The growth rates of Eady waves are reexamined using this bottom-stress condition.Vertical viscosity in the interior of the ocean, e.g. internal wave induced viscosity, may have a significant influence on the dynamics of the mesoscale motions, comparable to that of the boundary layers in some cases. The results are compatible with the sparse observations available.     

斜压切变基流中横波型扰动的特征波动──Ⅰ:谱点分析

文中对谱点的分布作了定性分析和数值计算。结果发现：当基流存在切变时,无论是重力惯性波还是涡旋波都存在连续谱。在通常的环境下,对天气尺度的扰动,3支波动的连续谱不重叠,3支波动明显可分;当扰动尺度小于临界波长l0时,可出现涡旋波和一支重力惯性波的两波连续谱区的重叠,当扰动尺度小于l0／2时,可出现涡旋波和一对重力惯性波的三波连续谱区的重叠,此时两种波动不可分。当出现重叠谱时,若出现不稳定扰动,其频率的实部落在重叠谱区。     

Some evidence of organized flow over natural waves

Measurements of the flow characteristics at 2 m over unobstructed wave surfaces on Lake Michigan were made using an anemometer-bivane as a velocity sensor. During one 40-min period of measurement, significant energy concentration was observed at the frequency of dominant surface waves in the vertical and cross wind spectra. Cross spectra between the surface elevation and vertical motions in the flow indicate that the surface lags the vertical motions by about 55 ° at the frequency of dominant waves.     

Numerical simulation of the boundary layer above waves

A new approach to investigations of the structure of the boundary layer above waves is discussed. The approach is based on direct numerical simulation of wave motions in the boundary layer produced by a moving curved surface. Model equations are derived, which are the Reynolds equations in a curvilinear nonstationary system of co-ordinates, evolution equations for turbulent kinetic energy, and Kolmogorov's approximate similarity formulae relating the coefficient of turbulent viscosity to the dissipation of turbulent energy; the length scale is assumed to grow linearly with increasing distance from the surface. Principles of constructing the model numerical scheme are described. Results are given of modelling the structure of the boundary layer above a nonsteady surface, which, in a general case, is a superposition of progressive waves with assigned dispersion relations and amplitudes. Mechanisms of energy and momentum transfer to the surface, effects of density stratification and energy structure in the boundary layer are studied. Merits and demerits of the approach are discussed.     

Turbulence and mixing in the boundary layer generated by shoaling internal waves

Over a range of incidence angles the energy of an internal wave propagating onto a sloping boundary is concentrated in a boundary layer on the slope. As a wave propagates upslope the change in its amplitude and interaction with the downslope flow remaining from previous waves results in the wave breaking and the generation of turbulence and mixing in the boundary layer. Measurements of the overturning and buoyancy scales on the slope show that turbulence is generated and decays during each wave cycle and that much of the energy input to mixing scales is extracted from density inversions generated by the wave-induced mean flow. A comparison with decaying turbulence behind a grid in a stratified water tunnel suggests that the criterion for the extinction of the buoyancy flux is similar in the two cases.     

Thermal plumes and turbulence spectra in the atmospheric boundary layer

Experimental observations on the temperature and wind fields above flat grassy terrain have been obtained with an instrumented 92-m tower during intervals of strong insolation about midday. The turbulence characteristics of the air confirm that free convection prevailed at heights between 16 and 48 m, with some tendency for departure at higher levels. The spectra of temperature and vertical velocity contain gaps at wave numbers in the range 0.01–0.025 m^–1. These are attributed to natural thermal plumes that act as sources of extra energy input to the Kolmogorov-Obukhov-Corrsin scheme of turbulence in or at the low-wave number limit of the inertial subrange. Modified forms of the K-O-C spectral laws for thermally unstable air are derived which agree with the observed spectra over the whole range of wave numbers examined, and which contain the spectral gap at wave numbers corresponding to the thermal plume diameters.     

中尺度大气波动的波谱和谱函数——数学模型和计算方法

作者得到了准二维Boussinesq方程组，并用其研究了中尺度大气波动的波谱和谱函数。在一定条件下对该方程组线性化并取标准模后，可将其初边值问题转化为矩阵的广义特征值问题来进行数值求解，这样就可知原问题波谱和谱函数的性质。当无基本流且取地转参数、层结参数为常数时，可求得其波谱和谱函数的解析解。此时该模式中仅包含有一对重力惯性内波模态，且各模态均是简谐波；模态越高，垂直波数越大则波动传播得越慢，所有的模态均为离散谱，并存在聚点。对此作者用数值解作了验算，结果表明，该数值求解方案合理可行，对不太高的模态其精度也令人满意。在无基本流然而考虑层结的垂直变化后，则一般无法求取解析解，为此进行了数值求解。这时该模式仍仅包含有一对重力惯性内波的离散谱模态，不过由于层结参数的变化，各模态结构与简谐波出现了偏差。     

Spectra and Cospectra of Turbulence in an Internal Boundary Layer over a Heterogeneously Irrigated Cotton Field

During the Energy Balance Experiment, patch-to-patch irrigation generated gradients in soil moisture in a north-south oriented cotton field. An internal boundary layer (IBL) developed as a result of strong horizontal advection from relatively dry upstream patches to relatively wet downstream patches associated with the prevailing northerly winds. This generated large eddies of multiple sizes, which had significant influences on the structure of turbulence in the IBL. The power spectra and cospectra of wind speed, temperature, humidity, and energy fluxes measured at two heights within the IBL are presented and used to investigate the influence of the IBL on surface layer turbulence. The spectra and cospectra were greatly enhanced by external disturbances at low frequencies. The peak frequencies of these disturbances did not change with height. The spectra and cospectra typically converged and were parallel to the Kansas spectrum at high frequencies (in the inertial subrange). A clear gap in the spectra of horizontal wind velocity existed at intermediate frequencies when the surface layer was stable. The results indicate that large eddies that originated in the upstream convective boundary layer had considerable impacts on the spectra and cospectra of surface layer turbulence. The influence of these large eddies was greater (1) when the IBL was well-developed in the near surface layer than when the IBL did not exist, (2) at higher levels than at lower levels, and (3) when the atmospheric surface layer (ASL) was unstable than when the ASL was stable. The length scales of these large eddies were consistent with the dominant scales of surface heterogeneity at the experiment site.     

On Wind Forces in the Forest-Edge Region During Extreme-Gust Passages and Their Implications for Damage Patterns

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.