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.     

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.     

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.     

Wind-Tunnel Experiments for Gas Dispersion in an Atmospheric Boundary Layer with Large-Scale Turbulent Motion

Large-scale turbulent motions enhancing horizontal gas spread in an atmospheric boundary layer are simulated in a wind-tunnel experiment. The large-scale turbulent motions can be generated using an active grid installed at the front of the test section in the wind tunnel, when appropriate parameters for the angular deflection and the rotation speed are chosen. The power spectra of vertical velocity fluctuations are unchanged with and without the active grid because they are strongly affected by the surface. The power spectra of both streamwise and lateral velocity fluctuations with the active grid increase in the low frequency region, and are closer to the empirical relations inferred from field observations. The large-scale turbulent motions do not affect the Reynolds shear stress, but change the balance of the processes involved. The relative contributions of ejections to sweeps are suppressed by large-scale turbulent motions, indicating that the motions behave as sweep events. The lateral gas spread is enhanced by the lateral large-scale turbulent motions generated by the active grid. The large-scale motions, however, do not affect the vertical velocity fluctuations near the surface, resulting in their having a minimal effect on the vertical gas spread. The peak concentration normalized using the root-mean-squared value of concentration fluctuation is remarkably constant over most regions of the plume irrespective of the operation of the active grid.     

Ondes de gravite interfaciales marginalement instables dans la couche limite planetaire

Wavelike motions within a strong morning inversion of the planetary boundary layer were investigated experimentally using two atmospheric research aircraft: an Aerocommander 280FL and a Cessna 206. The Aerocommander aircraft, instrumented for the measurement of rapid fluctuations of temperature, water vapour density and air velocities, was flown horizontally at different levels within the inversion layer in order to document adequate data on the wave motion. An example of such motions observed on 8 June, 1974 is described and analyzed in the present paper. The aircraft records obtained within the inversion layer at about 600 m above the ground show large fluctuations of the meteorological variables with well-defined amplitudes and wavelengths.Spectra and cross-spectra of temperature, water vapour density and air velocities were computed and analyzed to determine characteristics of gravity waves according to the method described by Metcalf (1975). These spectra exhibit a sharp maximum associated with high coherences at a particular wavelength. In this narrow spectral band, phase angles ±90 ° are obtained between vertical velocity and temperature as well as between vertical and horizontal velocities. These features suggest that observed motions are horizontally propagating trapped or evanescent waves. They enable us to estimate true wavelengths (500 m), wave vector azimuths, intrinsic frequencies and phase velocities of these waves. These results appear to be mutually consistent. Furthermore, it is possible to confirm these latter with the detailed vertical profiles of the boundary layer provided by the Cessna aircraft making spiral soundings. In this regard, the vertical structure of the Brunt-Väisälä frequency confirms that the waves are everywhere evanescent except within a thin highly stable layer between the diurnal mixed layer and the overlapping inversion. Moreover, examination of the wind profiles reveals that the interfacial vertical wind shear might be a relevant parameter reducing phase velocities. Such a conclusion is also supported by the observed wave vector directions which appear to be closely parallel to the wind shear vectors at the 600-m level. Additional confirmation is found by comparing the observed wavelengths to those predicted by applying the hydrodynamical stability model of Hazel (1972) to the measured profiles. Although the wind shear clearly plays a role in wave development, local heat flux and temperature variance values show that in this case the instability is only a marginal and sporadic event embedded in nearly neutral waves. Accordingly, it is argued that the observed motions are interfacial waves at the inversion base level, the amplitude and wave vector azimuth of which are controlled by the vertical wind shear.

---

Ondes de gravite interfaciales marginalement instables dans la couche limite planetaire

Résumé Des ondes de gravité interfaciales progressives sont étudiées à l'aide de deux avions dans la couche limite planétaire. Les spectres des vitesses et de la température fournissent les directions et vitesses de propagation. La comparaison des résultats aux profils verticaux du vent et de la température montre que ces ondes sont marginalement instables sous l'effet du cisaillement vertical du vent.

---

---

IOPG, 12, avenue des Landais - 63001 Clermont-Ferrand Cedex.

---

Complexe Scientifique des Cézeaux BP 45 - 63170 Aubiere.     

Internal gravity waves in a stably stratified boundary layer

Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.     

On the failure of Laplace's tidal equations to model subinertial motions at a discontinuity in depth

Infinitesmal amplitude, inviscid, subinertial oscillations over a discontinuity in depth are considered distinguishing three ocean models: (i) the Laplacian model in which the flow is governed by Laplace's tidal equations (LTE); (ii) the more realistic geophysical model in which the Vaisala frequency is assumed to be much greater than the inertial frequency; and (iii) the laboratory model in which the fluid is homogeneous with the Vaisala frequency equal to zero. The Laplacian model supports free waves perfectly trapped at the step while the laboratory model supports no perfectly trapped waves. The two approximations nevertheless predict similar behavior, because in the presence of forcing, the surface mode of the laboratory model is highly excited at frequencies and wavenumbers close to those of the perfectly trapped solutions predicted by LTE. Only in the limit of very long, low-frequency motions does the Laplacian model describe the barotropic modes of the geophysical model well, qualitatively, and even here the quantitative disagreement in predicted phase speeds and group velocities is substantial. At shorter wavelengths, LTE qualitatively misrepresent the dispersion properties by erroneously predicting topographically trapped motions with vanishing group velocity at a subinertial upper limit to the frequency of free oscillation. In particular, the results indicate that, for the step topography, there is in general no trapped, barotropic mode (double-Kelvin wave) in the geophysical model. Thus, LTE fail in modeling even the barotropic parts of subinertial motions at a depth discontinuity and should not be used in such calculations.     

Island-trapped waves,with application to observations off Bermuda

A theory is presented for linear island-trapped waves around a circular island with stratification and bottom relief. The free waves propagate clockwise in the northern hemisphere and are quantized azimuthally and in the radial–vertical plane. A formalism is derived for low frequency (subinertial frequency) motions forced either by winds or by ambient oceanic motions. The present model results appear to reproduce four observed (from moored array data) resonances to within less than 9% in frequency. Observations and results of the wind-forced theory suggest that subinertial sea level fluctuations off Bermuda are driven by ambient oceanic fluctuations. As long as the oceanic motions have scales large relative to the island, they ought to appear in island coastal sea level records without distortion.     

青藏高原红原站平流层下部重力波观测特征分析

利用位处青藏高原的红原探空站2008年5月垂直高分辨率的无线电探空资料分析了其上空下平流层(19～26 km)重力波的波动特性.结果表明:重力波的垂直波长主要集中在2～4 km之间,平均值约为2.9 km;水平波长主要集中在100～600 km之间,平均值约为311 km;固有频率主要集中在1.5f～3.5f(f为科氏...     

The vertical structure of concentration fluctuation statistics in plumes dispersing in the atmospheric surface layer

This paper describes a study of the vertical structure of concentration fluctuations in a neutrally buoyant plume from an elevated point source in slightly convective to moderately stable meteorological conditions at ranges of between 12.5 and 100 m for a range of source heights between 1 and 5 m. Observations were made of concentration fluctuations in a dispersing plume using a vertical array of sixteen very fast-response photoionization detectors placed at heights between 0.5 and 16 m. Vertical profiles of a number of concentration statistics were extracted, namely, mean concentration, fluctuation intensity, intermittency factor, peak-to-mean concentration ratio, mean dissipation rate of concentration variance, and various concentration time and length scales of dominant motions in the plume (e.g., integral macro-scale, in-plume mid-scale and Taylor micro-scale). The profiles revealed a similarity to corresponding crosswind profiles for a fully elevated plume, but showed greater and greater departure from the latter shapes once the plume had grown in the vertical so that its lower dege began to interact progressively more strongly with the ground. The evolution of the concentration probability density function at a fixed range, but with decreasing height from the ground, is similar to that obtained at a fixed height but with increasing distance from the source. Concentration power spectra obtained at different heights all had an extensive inertial-convective subrange spanning at least two decades in frequency, but spectra measured near the ground had a greater proportion of the total concentration variance in the lower frequencies (energetic subrange), with a correspondingly smaller proportion in the higher frequencies (inertial-convective subrange). It is believed that these effects result from the increased mean shear near the surface, and blocking by the surface. The effect of enhanced shear-induced molecular diffusion on concentration fluctuations is examined.     

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.     

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.     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves

An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler–Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.     

Diagnostic Analysis of the Quasi-Balanced Flow of a Mesoscale Vortex During the 12 June 2008 Guangxi Rainstorm

By using the high-resolution observation data and MM5 model simulation data, the analysis on the 12 June 2008 Guangxi flash-flood rainstorm shows that the associated major mesoscale weather system of this event is a quasi-stationary mesoscale vortex, which resulted from the interaction between the midlatitude synoptic-scale waves in the westerly belt and the low-latitude warm-moist flow under the terrain effect. The genesis, development, and movement of the mesoscale vortex have significant impacts on the intensity and persistence of the severe precipitation from the Guangxi flash-flood rainstorm. This vortex is characterized by the coexistence of strong vorticity and divergence with the same order of magnitude. Well organized, deep, and moist convection was observed for a long period of time, and was produced by the interaction between the mesoscale vortex and the gravity waves. The latter was generated by the terrain effect and the ageostrophic effect of high winds in the low-level jet. According to the quasi-balanced dynamical theory, quasi-balanced flow must have existed in the mesoscale motions with both divergent and rotational winds. Thus, based on the diagnosis of the quasi-balanced flow, the PV-ωinversion method is employed to analyze the organized moist convection. The results show that 50%-70% of the vertical circulation in the rainstorm areas was quasi-balanced, so the quasi-balanced flow could well reflect features of the strong vertical motions associated with the coexistence of vorticity and divergence during this event.     

Observations of Coherent Turbulence Structures in the Near-Neutral Atmospheric Boundary Layer

Turbulence structures of high Reynolds number flow in the near-neutral atmospheric boundary layer (ABL) are investigated based on observations at Shionomisaki and Shigaraki, Japan. A Doppler sodar measured the vertical profiles of winds in the ABL. Using the integral wavelet transform for the time series of surface wind data, the pattern of a descending high-speed structure with large vertical extent (from the surface to more than 200-m level) is depicted from the Doppler sodar data. Essentially this structure is a specific type of coherent structure that has been previously shown in experiments on turbulent boundary-layer flows. Large-scale high-speed structures in the ABL are extracted using a long time scale (240 s) for the wavelet transform. The non-dimensional interval of time between structures is evaluated as 3.0–6.2 in most cases. These structures make a large contribution to downward momentum transfer in the surface layer. Quadrant analyses of the turbulent motion measured by the sonic anemometer (20-m height) suggest that the sweep motion (high-speed downward motion) plays a substantial role in the downward momentum transfer. In general, the contribution of sweep motions to the momentum flux is nearly equal to that of ejection motions (low-speed upward motions). This contribution of sweep motions is related to the large-scale high-speed structures.     

Coupling effect diagnoses of quasi-stationary mesoscale vortex in Guangxi rainstorm process of China

The mesoscale weather system which affected the Guangxi flash-flood-producing rainstorm of China in June 2008 is a quasi-stationary mesoscale vortex. Its genesis and development is closely related to the coupling effects of weather systems in different scales and different latitudes. On the one hand, the coupling of synoptic scale high- and low-level jets provides the environmental conditions for development of vortices and vertical circulations in the mesoscale vortex; On the other hand, the coupling of waves in mid-latitude westerlies and perturbations in low-latitude warm-moist flow under the influence of complex terrain makes the mesoscale vortex circulations strengthened. With the piecewise potential vorticity (PV) inversion method, PV anomalies in different regions are analyzed; also the vortex-vortex interactions and vortex-background flow interactions are diagnosed. Thus, the reasons why the mesoscale is quasi-stationary at first, while developing and deepening later are indicated. Under the condition of coupling effects, the vertical motions accompanied with the mesoscale vortex can be diagnosed with the PV-ω inversion system based on the analysis of quasi-balanced flow.     

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.     

3mm多普勒云雷达测量反演云内空气垂直速度的研究

垂直指向的W-波段大气云雷达(WACR)不仅测量云粒子的反射率因子Z, 而且测量多普勒速度谱。本文利用寿县气象站WACR在2008年11月1日一个时段的测量, 进行云内空气垂直速度反演试验。首先讨论个例中反射率、 Doppler平均速度及谱宽的分布特征及原因, 然后利用小粒子示踪法和改进的以小粒子示踪法为基础的粒子下降速度w0—反射率因子 (w0－Z) 关系法反演了云内空气垂直速度, 进而结合Doppler谱数据分析反演结果。结果显示: 小粒子示踪法在湍流较弱时能比较精确地反演空气垂直速度, 而湍流较强时, 湍流造成的误差不可忽略; 改进算法在湍流较强时能够减少湍流对反演结果的影响。