Observations of the energy-containing oceanic Eddies,and theoretical models of waves and turbulence

Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascade of energy to small scales isnot occurring. The way is left open for interpretation as a mixture of geostrophic turbulence and waves.Detailed models are given which yield plausible behavior of various parts of the wave-number and frequency spectra, and illustrate the workings of nonlinearity and wave dispersion: (i) simple dispersion of linear, wind-generated internal waves gives at depths an inertial peak and a steeply sloping high-frequency spectrum (the inertial peak at the very top of the ocean is a direct response of the mixed layer to the wind); (ii) at longer periods,two-dimensional turbulence subjected to the beta effect produces well-ordered motions from a chaotic initial state, with dominant length and time-scale independent of initial conditions. The turbulence evolves quickly and naturally into Rossby waves, leaving a peaky, quasi-stationary spectrum; (iii) inone dimension, the Korteweg de Vries equation again shows how waves may sharpen and fix the wave-number spectrum while dispersing the energy in physical space; (iv) possible application of the ideas tothree-dimensional turbulence and waves is discussed.The most general result is that the scale-dependent boundary, at which the wave steepness is about unity, often divides energy-frequency/wave-number space into regions in which the mobility of energy is vastly different; depending on the direction and speed of nonlinear migration within these regions, energy may pile up at this boundary. Thus, wave-restoring forces can concentrate spectra at certain wave numbers while dispersing the fields in physical space.Now at Woods Hole Oceanographic Institution.     

Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance

Atmospheric cyclones with strong winds significantly impact ocean circulation, regional sea surface temperature, and deep water formation across the global oceans. Thus they are expected to play a key role in a variety of energy transport mechanisms. Even though wind-generated internal gravity waves are thought to contribute significantly to the energy balance of the deep ocean, their excitation mechanisms are only partly understood.The present study investigates the generation of internal gravity waves during a geostrophic adjustment process in a Boussinesq model with axisymmetric geometry. The atmospheric disturbance is set by an idealized pulse of cyclonic wind stress with a Rankine vortex structure. Strength, radius and duration of the forcing are varied. The effect upon wave generation of stratification with variable mixed-layer depth is also examined.Results indicate that internal gravity waves are generated after approximately one inertial period. The outward radial energy flux is dominated by waves having structure close to vertical mode-1 and with frequency close to the inertial frequency. Less energetic higher mode waves are observed to be generated close to the sea floor underneath the storm. The total radiated energy corresponds to approximately 0.02% of the wind input. Deeper mixed-layer conditions as well as weaker stratification reduce this fraction.The low energy transfer rates suggest that other processes that drive vertical motion like surface heat fluxes, turbulent motion, mixed region collapse and storm translation are essential for significant energy extraction by internal gravity waves to occur.     

三维静力适应过程中声重力波的特性和能量转换研究

为了研究三维静力适应过程的机理,推导三维静力适应方程组并导出声重力波的频散特征、解析解和能量转换关系以及位涡方程。结果表明,三维静力适应过程实际上就是三维声重力波和重力内波的频散过程,声重力波和重力内波的频率在水平方向上可以区分开来。声重力波的频率随着水平波数和垂直波数的增大而增大。取近轴近似,其解析解在空间上呈螺旋曲面,为大气中热通量和动量从一个区域向另一个区域的输送提供了一种机制,从而为研究大气提供了新的视角。垂直速度在动能与有效势能的转换、有效势能与有效弹性势能的转换中发挥着重要的作用,并且只发生在垂直方向上。在静力适应过程中总能量和位涡是守恒的。适应终态中有效势能比有效弹性势能大一个数量级。      

梅雨锋中尺度系统及其与大尺度运动相互作用的能量学研究

本文导出了二维非均匀介质中重力惯性波的频散方程、波列传播路径方程和考虑了中尺度与天气尺度运动之间相互作用的动能收支方程,并用于讨论了一个典型的梅雨锋过程。研究发现,由一条中尺度雨带强迫产生的重力惯性波的能量频散可能成为另一条中尺度雨带生成和维持的机制;中尺度与天气尺度运动之间相互作用所产生的动能交换是中尺度系统发展的一个非常重要的动能来源,在中尺度系统的维持中也有重要作用。      

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。     

风速垂直切变下非均匀层结大气中重力惯性内波的稳定性

本文应用WKB方法研究了在弱非均匀层结大气中,当基本气流具有弱垂直切变时,重力惯性内波的稳定性问题.由导得的波能量方程出发,分析了风速垂直切变及非均匀大气层结对重力惯性内波波能变化率的影响.     

Inertial oscillations near the coast of Nova Scotia during CASP

Abstract

Analysis of current, temperature and salinity records in the nearshore region of the Scotian Shelf during the Canadian Atlantic Storms Program (CASP), reveals that the inertial wave field is highly intermittent, with comparable amplitudes in the surface and deep layers. Clockwise current energy in the surface layer is concentrated at a frequency slightly below inertial, consistent with Doppler shifting by the strong mean current and/or straining by the mean flow shear, whereas the spectral peak in deep water is at the local inertial frequency. Clockwise coherence is high (γ² ≥ 0.8) horizontally over the scale of the array (60 km × 120 km) and in the vertical, with upward phase propagation rates of 0.15–0.50 × 10^?12 ms^?1, inversely proportional to the local value of the Brunt Väisälä frequency. Clockwise current energy decreases in the onshore direction and appears to be completely inhibited on the 60‐m isobath.

A case study of the response to the CASP IOP 14 storm indicates that the inertial waves may be generated by a strong wind shift propagating onshore at a speed of 10 ms^?1. On the eastern side of the array (Liscomb line), clockwise current oscillations propagate onshore in the surface layer at a rate (8.1 ± 0.9 m s^?1) comparable with the speed of the atmospheric front, while waves in the pycnocline move offshore at a lower (internal wave) speed (1.8 m s^?1). Furthermore the temperature and salinity fluctuations are in (out) of phase with longshore current in the deep (surface) layer. However, on the western side of the array (Halifax line), the inertial waves are more complex. A sharp steepening of phase lines at the coast indicates that the phase speed of clockwise current oscillations is considerably reduced and the evidence for offshore propagation of internal waves is less clear. The discrepancies between observations on the two lines suggest that the internal wave field is three‐dimensional.

Results of simple mixed‐layer models indicate that the inertial response near the surface is sensitive to the accurate definition of the local wind field, but not to certain model physics, such as the form of the decay term. The observations also show some qualitative similarities with models for two‐dimensional response to a moving front (e.g. Kundu, 1986), but the actual forcing terms are more complicated, based on IOP 14 wind measurements.     

基于秒级探空资料分析四川重力波统计特征

利用2014年6月-2017年9月的秒级探空资料,选取四川地区5个代表性站点研究重力波在对流层（2~10 km）和平流层（18~25 km）的时空特征。选取结果表明:重力波能量在四川地区各个高度均存在明显的季节变化,冬季强,夏季弱;在对流层由于地形影响,川西和川北高原地区的能量小于其他地区。垂直波长没有明显的时空变化,在对流层和平流层分别集中分布于1.5~3 km和1.5~3.5 km;水平波长则差别较大,分别分布于0~300 km和100~700 km,平均值分别为100 km和350 km。重力波固有频率在对流层有较大的区域差异,表现为在四川西北部的高原地区固有频率平均值为3f（f为地转参数）,其他地区则仅为2.4f;平流层则没有明显的差异存在,均约为2f。四川地区重力波的垂直传播方向特征基本相同,在对流层约有50%的波动向上传播,平流层则有90%以上的波动向上传播。水平传播则存在明显的不确定性,特别是对流层;平流层水平传播方向存在明显的季节变化,表现为夏季重力波多向偏东方向传播,而其他季节则向偏西方向传播。     

Propagation and Effects of a Mesoscale Gravity Wave Over a Weakly-Stratified Nocturnal Boundary Layer During the SABLES2006 Field Campaign

During the SABLES2006 (Stable Atmospheric Boundary Layer Experiment in Spain 2006) field campaign, a gravity-wave episode was observed on the night of July 11 by the microbarometers deployed at the surface and on the 100-m tower. The high-amplitude, low-frequency periodic pressure fluctuations were very well correlated with the wind speed and direction. Data from neighbouring automatic stations showed that the gravity wave was not local, but long-lived and mesoscale. The propagation of the wave over the experimental site had significant effects on the structure of the weakly-stratified nocturnal boundary layer that developed that night: the stability increased, turbulent vertical motions were suppressed, the nocturnal low-level jet was disrupted, and periodic temperature fluctuations of amplitude up to 3–4 K were observed. In this work we analyse the different available data sources (tower data, RASS-SODAR, microbarometric, satellite imagery, automatic stations) to describe the phenomena in depth and to find a suitable explanation for the generation and propagation of the wave. The linear wave theory explains remarkably well most of the observations, and the wave parameters could be estimated by applying a wavelet-based technique to surface microbarometric measurements. We also analyse the vertical structure of the wave and find wave ducting conditions above the surface. Finally, by means of the multi-resolution flux decomposition, we analyse in detail the changes in vertical turbulent fluxes and the spectra of turbulent motions produced by the interaction between the gravity wave and the local flow.     

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.     

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.

     

Numerical experiments on internal gravity waves in an accelerating shear flow

The influence of an accelerating shear flow on the propagation of an internal gravity wave in a continuously stratified fluid is studied by means of two-dimensional numerical simulations. These are motivated by earlier laboratory experiments [Thorpe, S.A. 1978b. On internal gravity waves in an accelerating shear flow, Vol. 88. J. Fluid Mech. pp. 623–639]. In these experiments the mean flow is an accelerated Couette flow and the mean density profile is linear. The laboratory experiments revealed the striking effect of the unsteady shear flow in the evolution of an internal gravity wave leading to the wave focusing in a region where the flow is extremum. This phenomenon is associated with the growth of small scale density fluctuations. As a result density overturns are sometimes observed. This behaviour is well reproduced by the numerical simulations. We provide insights on the flow dynamics in particular on the possible occurrence of wavebreaking. We show that the dynamics is characterized by two competitive mechanisms that is a damping of the wave and a local enhancement of its steepness leading sometimes to density overturns. The budget for the energy of the wave reveals that the initial damping of the wave results from wave-mean flow interactions. These interactions lead to the development of a fine scale vertical density structure which is associated with high vertical shear. We find that in some cases wavebreaking occurs as a result of shear instability. The value of the acceleration of the mean flow is very likely to influence the onset of the instability. The scaling laws of the wave evolution, in particular the rate of decrease of its energy, are determined. From these laws the lifetime of the wave is found as a function of the acceleration of the shear. It may be expected that, in the ocean, this development will result in the largest fluctuations derived from wave-flow interactions occurring where the mean flow in the wave direction is greatest. Waves travelling normal to a two-dimensional shear flow will be unchanged. Waves travelling parallel will be damped. This may have particular application at the continental shelf where flow, mainly parallel to the isobaths, will damp waves travelling along-slope, but allows waves travelling normal to the isobaths (e.g., directly across the shelf-break) to be transmitted without attenuation. Similar effects are expected for the evolution of a high frequency wave interacting with a lower frequency (e.g., near inertial) motion.     

Wavy Vertical Motions in the ABL Observed by Sodar

Some characteristics of wavelike motions in the atmospheric boundary layer observed by sodar are considered. In an experiment carried out in February 1993 in Milan, Italy, Doppler sodar measurements were accompanied by in situ measurements of temperature and wind velocity vertical profiles using a tethered balloon up to 600 m. The oscillations of elevated wavy layers containing intense thermal turbulence, usually associated with temperature-inversion zones, were studied by using correlation and spectral analysis methods. The statistics of the occurrence of wavelike and temperature-inversion events are presented. The height distributions of Brunt–Vaisala frequency and wind shear and their correlation within elevated inversion layers were determined, with a strong correlation observed between the drift rate of the wavy layers and the vertical velocity measured by Doppler sodar inside these layers. Spectral analysis showed similarities regarding their frequency characteristics. The phase speed and propagation direction of waves were estimated from the time delay of the signals at three antennae to provide estimates of wavelength. Moreover, wavelengths were estimated from the intrinsic frequency obtained from sodar measurements of the Doppler vertical velocity and oscillations of wavy turbulent layers. The two wavelength estimates are in good agreement.     

Wave-Modified Flux and Plume Dispersion in the Stable Boundary Layer

The effects of a pressure jump and a following internal gravity wave on turbulence and plume diffusion in the stable planetary boundary layer are examined. The pressure jump was accompanied by a sudden increase in turbulence and plume dispersion. The effects of wave perturbations on turbulence statistics are analysed by calculating fluxes and variances with and without the wave signal for averaging times ranging from 1 to 30 min. The wave signals are obtained using a band-pass filter. It is shown that second-order turbulence quantities calculated without first subtracting the wave perturbations from the time are greater than those calculated when the wave signal is separated from the turbulence. Estimates of the vertical dispersion of an elevated tracer plume in the stable boundary layer are made using an elastic backscatter lidar. Plume dispersion observed 25 m downwind of the source increases rapidly with the arrival of the flow disturbances. Measured plume dispersion and plume centreline height correlate with the standard deviation of the vertical velocity but not with the wave signal.     

Properties and stability of a meso-scale line-form disturbance

By using the 3D dynamic equations for small- and meso-scale disturbances, an investigation is performed on the heterotropic instability (including symmetric instability and traversal-type instability) of a zonal line-like disturbance moving at any angle with respect to basic flow, arriving at the following results: (1) with linear shear available, the heterotropic instability of the disturbance will occur only when flow shearing happens in the direction of the line-like disturbance movement or in the direction perpendicular to the disturbance movement, with the heterotropic instability showing the instability of the internal inertial gravity wave; (2) in the presence of second-order non-linear shear, the disturbance of the heterotropic instability includes internal inertial gravity and vortex Rossby waves. For the zonal line-form disturbance under study, the vortex Rossby wave has its source in the second-order shear of meridional basic wind speed in the flow and propagates unidirectionally with respect to the meridional basic flow. As a mesoscale heterotropic instable disturbance, the vortex Rossby wave has its origin from the second shear of the flow in the direction perpendicular to the line-form disturbance and is independent of the condition in the direction parallel to the flow; (3) for general zonal line-like disturbances, if the second-order shear happens in the meridional wind speed, i.e., the second shear of the flow in the direction perpendicular to the line-form disturbance, then the heterotropic instability of the disturbance is likely to be the instability of a mixed Rossby–internal inertial gravity wave; (4) the symmetric instability is actually the instability of the internal inertial gravity wave. The second-order shear in the flow represents an instable factor for a symmetric-type disturbance; (5) the instability of a traversal-type disturbance is the instability of the internal inertial gravity wave when the basic flow is constant or only linearly sheared. With a second or nonlinear vertical shear of the basic flow taken into account, the instability of a traversal-type disturbance may be the instability of a mixed vortex Rossby – gravity wave.     

Determination of parameters of low-frequency internal waves in the coastal zone of a fringing sea using field measurements and basing on the nonlinear theory

A method is presented to determine the quadratic nonlinearity parameter and amplitude of low-frequency internal gravity waves in the coastal zone of a fringing sea, based upon their propagation rate dependence on local value of pycnocline vertical displacement produced by the waves. To test the method, the internal wave field observations in the coastal zone of the Sea of Japan are used. The testing results show that the internal wave parameters calculated using the proposed method and the experimental data are in a good agreement with those calculated from theoretical formulas.     

Internal Gravity Waves Generated by a Local Thermal Source in an Irrotational Zonal－Vertical Plane：Numerical Analysis

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Anemobaric low-frequency waves in the Chukchi Sea

The characteristics of currents and sea level wave perturbations of synoptic scale in the Chukchi Sea are compared with well-known dispersion relations of low-frequency waves of different types. This comparison allowed identifying the currents and sea level wave perturbations as internal Kelvin waves and barotropic and baroclinic topographic waves. Assessments of statistical relations between wave perturbations of currents and different meteorological characteristics showed that the energy supply of low-frequency waves is provided sporadically by various components of anemobaric (wind-induced) forces in the local areas of the Chukchi Sea and the Bering Strait.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

Atmospheric Disturbances that Generate Intermittent Turbulence in Nocturnal Boundary Layers

Using the unprecedented observational facilities deployed duringthe 1999 Cooperative Atmosphere-Surface Exchange Study (CASES-99),we found three distinct turbulent events on the night of 18October 1999. These events resulted from a density current,solitary wave, and internal gravity wave, respectively. Our studyfocuses on the turbulence intermittency generated by the solitarywave and internal gravity wave, and intermittent turbulenceepisodes associated with pressure change and wind direction shiftsadjacent to the ground. Both the solitary and internal gravitywaves propagated horizontally and downward. During the passage ofboth the solitary and internal gravity waves, local thermal andshear instabilities were generated as cold air was pushed abovewarm air and wind gusts reached to the ground. These thermal andshear instabilities triggered turbulent mixing events. Inaddition, strong vertical acceleration associated with thesolitary wave led to large non-hydrostatic pressure perturbationsthat were positively correlated with temperature. The directionaldifference between the propagation of the internal gravity waveand the ambient flow led to lateral rolls. These episodic studiesdemonstrate that non-local disturbances are responsible for localthermal and shear instabilities, leading to intermittentturbulence in nocturnal boundary layers. The origin of thesenon-local disturbances needs to be understood to improve mesoscalenumerical model performance.