Particle dispersion and mixing induced by breaking internal gravity waves

The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave — the primary wave — either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D’Asaro, E.A., 1995. J. Fluid Mech. 289, 115–128; Winters, K.B., D’Asaro, E.A., 1996. J. Fluid Mech. 317, 179–193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265–301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41–63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999].A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow.The eddy diffusion coefficient, K, is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number, equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared.We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small scale in the ocean.Comparisons between the analysis of the two-dimensional and high resolution (256³) three-dimensional direct numerical simulations of the primary wave were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results from the fact that, for a statically stable wave, the dynamics of the initially two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking.     

The observed generation and breaking of atmospheric internal gravity waves over the ocean

Observations are presented for internal gravity waves and their breaking at a height of 23.5 m over the ocean in surface-based inversions which are formed because of the advection of warm air over cold water. The spectral and cospectral analyses of velocity and temperature fluctuations were made to establish the characteristic features of the waves. Flow visualization photographs of smoke released during the breaking of a wave are also presented. Comparison between the turbulent energies present during and after breaking of a wave indicates enormous mixing and dispersion occurring during breaking.This research was performed under Contract No. EY-76-C-02-0016 with the United States Energy Research and Development Administration.     

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.

     

A STUDY OF THE EFFECT OF GRAVITY WAVE BREAKING ON MIDDLE ATMOSPHERIC CIRCULATION*

McFarline's gravity drag theory is simply reviewed,and it is indicated that the fault of McFarline's theory is that the effect of dissipation induced by gravity wave breaking on mean flow is not fully considered.Based on McFarline's theory,in this paper,the effect mentioned above is well considered.A new dissipation coefficient D is calculated,and a relatively complete parameterized scheme of the influence of gravity wave breaking on meanflow is put forward here.This is a better parameterized scheme than McFarline's if it is used in GCM.     

Marginal mixing theories

Abstract

Mixing near the sloping boundaries of oceans or lakes may be a significant mechanism of diapycnal transport. The basic physics of this is reviewed, with emphasis on the reduction of the effectiveness of the process due to both reduced stratification and the restratifying secondary circulation driven by buoyancy forces. This re stratification is shown to reduce the effectiveness of intermittent mixing events as well as steady mixing. It is argued that for boundary mixing to be effective in the abyssal ocean it must extend sufficiently far from the boundary that the stratification can be maintained; this may be true for breaking bottom‐reflected internal waves. The alongslope flow implied by steady‐state boundary mixing theories is downwelling‐favourable and has a magnitude related to the thickness and other properties of the boundary layer. Mixing near a boundary may thus tend to drive a downwelling‐favourable mean circulation in the interior. If the interior circulation is imposed by other forces, the bottom boundary layer may evolve to a steady state if the interior flow is downwelling‐favourable, but if it is upwelling‐favourable initially a steady state seems unlikely and the downwelling‐favourable alongslope flow induced by the boundary mixing will tend to diffuse slowly into the interior. The nature of the solution in all these cases is sensitive to the Burger number, N² sin² θ/f², where θ is the bottom slope, and to the eddy Prandtl number.     

基于新型往返式探空观测的下平流层重力波特征分析

利用2018年6月9日—7月10日安庆、长沙、赣州、南昌、宜昌、武汉6个探空站的往返式探空观测试验数据,研究分析了重力波参数(能量密度、固有频率、波长及传播方向),统计了试验地区6—7月的重力波特征,比较了各站之间以及上升与下降段之间重力波的差异.主要结果如下:(1)该区域重力波动能分布在0.2—1.2 J/m3,平均...     

A STUDY OF THE EFFECT OF GRAVITY WAVE BREAKING ON MIDDLE ATMOSPHERIC CIRCULATION

McFarline's gravity drag theory is simply reviewed,and it is indicated that the fault ofMcFarline's theory is that the effect of dissipation induced by gravity wave breaking on mean flowis not fully considered.Based on McFarline's theory,in this paper,the effect mentioned above iswell considered.A new dissipation coefficient D is calculated,and a relatively completeparameterized scheme of the influence of gravity wave breaking on meanflow is put forward here.This is a better parameterized scheme than McFarline's if it is used in GCM.     

The role of molecular diffusion in the deepening of the mixed layer

Turbulent mixing across heat-stratified density interfaces was studied in the laboratory using oscillating-grid generated turbulence. The aim was to study the transition between the entrainment regimes dominated by interfacial wave-breaking and molecular diffusion, and to study the characteristics of the latter. It was observed that, above a critical Richardson number Ri_c, which depends on the Peclet number Pe, the mixing due to wave breaking disappears and that Ri_c Pe⁻ⁿ, where the mean value of the exponent n is approximately . Above Ri_c, the entrainment is molecular-diffusion dominated and takes place through a sequence of events: the buoyancy gradient of the initially sharp density interface is weakened by molecular diffusion until the mixed-layer eddies can engulf a portion of the interfacial layer wherefore the interface sharpens again. Thus, the entrainment events are recurrent with a rate-controlling diffusion stage between them. An entrainment law of the form E Ri⁻²Pe⁻², where E is the entrainment coefficient and Ri is the Richardson number, is suggested for the diffusion-dominated entrainment regime.     

Shear instability and gravity wave saturation in an asymmetrically stratified jet

Motivated by the mean current and stratification structure associated with the equatorial undercurrent (EUC), we examine the stability and wave propagation characteristics of a highly idealized model flow: the asymmetrically stratified jet. This is a parallel shear flow in which the depth-varying current has the sech² form of a Bickley jet. The stratification has a step function structure: the buoyancy frequency takes uniform values above and below the center of the jet, with the larger value occurring below. The spectrum contains three classes of unstable normal modes. Two are extensions of the sinuous and varicose modes of the unstratified Bickley jet; the third has not been described previously. The asymmetric stratification structure allows instabilities to radiate gravity wave energy from the upper flank of the jet to the lower flank, where it encounters a critical layer. From here, wave energy may be reflected, absorbed or transmitted. Absorption results in wave saturation and momentum transfer to the mean flow, in close analogy with the breaking of orographic gravity waves in the middle atmosphere. Transmission beyond the lower flank may partly account for wave signals observed in the deep equatorial oceans. All of these processes exert zonal forces on the jet that alter its speed and shape. The wave structures and associated fluxes developed by the idealized model are compared with observations of the EUC.     

The propagation of inertia-gravity waves and their influence on zonal mean flow part two: Wave breaking and critical levels

The gravity wave breaking is crucial to the large-scale circulation of middle atmosphere. In this paper, we follow Lindzen (1981) to draw out the parameterization of two-dimensional gravity wave breaking including inertial effect. Also we present some properties of critical levels and inertial critical levels.     

Numerical prediction of an intense convective system associated with the July 1987 montreal flood. part I: Gravity waves and the squall line

Abstract

In this study, a 24‐h high‐resolution numerical prediction of a prefrontal squall line associated with the 14 July 1987 Montreal flood is employed to investigate the origin and role of mesoscale gravity waves in the development of the squall system. The 24‐h integration using an improved mesoscale version of the Canadian regional finite‐element model is first validated against available observations; then non‐observable features are diagnosed to reveal the relationship between deep convection and gravity wave events. It is shown that the model reproduces well many aspects of the squall line, such as the propagation and organization of the convective system, as well as its associated precipitation. It is found that gravity waves are first excited near Lake Erie, following the initiation of early convective activity. Then, these waves propagate eastward and northeastward at speeds of 20 and 35 m s^‐1, respectively. As the waves propagate downstream, deep convection radiates rapidly behind the wave trough axis, forming a long line of squall convection. Because the squall line moves with the gravity waves in a “phase‐locked” manner, deep convection has a significant influence on the structure and amplitude of the gravity waves. The sensitivity of the wave‐squall prediction to various parameters in convective parameterization is also examined.     

Further evidences of deep convective vertical transport of water vapor through the tropopause

A few years ago, we identified a deep convective transport mechanism, of water vapor through the tropopause, namely, storm top gravity wave breaking, such that tropospheric water substance can be injected into the lower stratosphere via this pathway. The main evidence presented previously was taken from the lower resolution AVHRR images of the storm anvil top cirrus plumes obtained by polar orbiting satellites. Recent observations have provided further supporting evidence for this important cross-tropopause transport mechanism. There are now many higher resolution satellite images, mainly from MODIS instrument, that show more definitely the existence of these plumes, many of which would probably be unseen by lower resolution images.Furthermore, a thunderstorm movie taken in Denver (USA) area during STEPS2000 field campaign and another thunderstorm movie taken by a building top webcam in Zurich also demonstrate that the jumping cirrus phenomenon, first identified by T. Fujita in 1980s, may be quite common in active thunderstorm cells, quite contrary to previous belief that it is rare. We have used a cloud model to demonstrate that the jumping cirrus is exactly the gravity wave breaking phenomenon that transports water vapor through the tropopause.These additional evidences provide increasing support that deep convection contributes substantially to the troposphere-to-stratosphere transport of water substance. This corroborates well with recent studies of the stratospheric HDO/H₂O ratio which is much highly than it would be if the transport is via slow ascent. The only explanation that can be used to interpret this observation at present is that water substance is transported through the tropopause via rapid vertical motion, i.e., deep convection.     

Generation mechanisms of convectively induced internal gravity waves in a three-dimensional framework

The generation mechanisms of convective gravity waves in the stratosphere are investigated in a three-dimensional framework by conducting numerical simulations of four ideal storms under different environmental conditions: one un-sheared and three constant low-level sheared basic-state winds with the depth of the shear layer of 6 km and the surface wind speeds (U_s) of 8, 18, and 28 m s^?1, using the Advanced Regional Prediction System (ARPS) model. The storms simulated under the un-sheared (U_s = 0 m s^?1), weakly sheared (U_s = 8 and 18ms^?1), and strongly sheared (U_s = 28ms^?1) basicstate winds are classified into single-cell, multicell, and supercell storms, respectively. For each storm, the wave perturbations in a control simulation, including nonlinearity and microphysical processes, are compared with those in quasi-linear dry simulations forced by diabatic forcing and nonlinear forcing that are obtained from the control simulation. The gravity waves generated by the two forcing terms in the quasi-linear dry simulations are out of phase with each other for all of the storms. The gravity waves in the control simulation are represented by a linear sum of the wave perturbations generated by the nonlinear forcing and diabatic forcing. This result is consistent with the results of previous studies in a two-dimensional framework. This implies that both forcing mechanisms are important for generating the convective gravity waves in the three-dimensional framework as well. The characteristics of the three-dimensional gravity waves in the stratosphere were determined by the spectral combination of the forcing terms and the wave-filtering and resonance factor that is determined from the basic-state wind and stability as well as the vertical structure of the forcing.     

On the Dependence of the Equilibrium Range of Sea Wave Spectra with Wave Age

Donelan and Pierson have proposed a semiphysical model of the equilibrium sea wave spectrum, based upon a parameterization of wave growth and dissipation terms. Their model is applicable for fully developed seas only. In the framework of Donelan and Pierson's approach, this paper explores the dependence of the equilibrium spectrum upon wave age. To this end, we examine how the dissipation through wave breaking is expected to vary with wave age, according to the approach proposed by Longuet-Higgins in 1969. The constraint imposed by Longuet-Higgins' theory requires an increase of the equilibrium spectrum F(k,0) in the wind direction with increasing inverse wave age U/C_p. This is in accordance with Banner's empirically deduced statement that F(k,0) is proportional to (U/C_p)^0.5 in the equilibrium range. Our inferred F(k,0) tends to increase more or less linearly with U/C_p (we find F(k,0) proportional to 1 + 0.25(U/C_p - 0.83), rather than through a power law. If a power law is fitted we obtain F(k,0) approximately proportional to (U/C_p)^0.35 for the range 0.83 < U/C_p > 5. Finally, the roughness length of the air-sea interface is inferred from our modelled spectrum through integration of the form drag over wave number under rough conditions. This shows a wave age dependence that is compatible with measurements of wind stress performed in the field at various wave ages.     

A NOTE ON THE APPLICATION OF LINEAR WAVE THEORY AT A CRITICAL LEVEL

The purpose of this note is to estimate the accuracy and practical limitations of applying linear theory at a critical level over a realistic range of atmospheric stabilities for an idealized surface terrain. These estimates are made by comparing the results of a linear model with a nonlinear numerical model at a critical level. Essentially similar results are obtained from each model for wave stress, wave breaking height and wave dissipation through the critical level. Because gravity waves can be either evanescent or internal depending on the relative sizes of the Scorer parameter and the wavenumber of the ground surface disturbance, the somewhat paradoxical result develops that wave breaking and non-linearity increase with increasing bulk Richardson number. It is recommended that steady linear wave theory be used in gravity wave drag parameterizations provided near real time profiles of background velocity and temperature are available.     

The Impact Of Air-Flow Separation On The Drag Of The Sea Surface

An approach that allows assessment ofthe impact of air-flow separation (AFS) fromwave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumedthat the dynamics of the AFS from wave breaking crests is similar to thatfrom the backward facing step. The form drag supported by an individualbreaker is described by the action of the pressure drop distributed alongthe forward face of the breaking front. The total stress due to the AFS isobtained as a sum of contributions from breaking fronts of different scales.Outside the breaking fronts the drag of the sea surface is supported by theviscous surface stress and the wave-induced stress. To calculate the stressdue to the AFS and the wave-induced stress a physical model of the wind-wavespectrum is used. Together with the model of the air flow described in termsof surface stresses it forms a self-consistent dynamical system for the seasurface-atmosphere where the air flow and wind waves are strongly coupled.Model calculations of the drag coefficient agree with measurements. It is shownthat the dimensionless Charnock parameter (roughness length normalized onthe square of the friction velocity and the acceleration of gravity)increases with the increase of the wind speed in agreement with fieldmeasurements. The stress due to the AFS normalized on the square of thefriction velocity is proportional to the cube of wind speed. At low windsthe viscous surface stress dominates the drag. The role of the form drag,which is the sum of the stress due to the AFS and the wave-induced stress, isnegligible. At moderate and high winds the form drag dominates. At windspeeds higher than 10 m s^-1 the stress supported by the AFS becomescomparable to the wave-induced stress and supports up to 50% of the totalstress.     

A simple gravity wave drag parametrization for use in medium‐range weather forecast models

Abstract

A simple gravity wave drag parametriiation over mountainous terrain is tested for its ability to reduce the systematic errors of medium‐range weather forecasts. Following Boer et al. (1984), this parametrization is a function of the low‐level wind speed and stability, the local Froude number, and the variance of the subgrid‐scale orographie features.

A comparison study of ten 7‐day forecasts obtained with envelope orography, wave drag or standard orography, shows that wave drag is as effective as envelope orography in reducing the systematic errors. A further comparison where the combined effects of the wave drag and that of a complementary enhanced orography (that is one that includes only the subgrid‐scale elements not treated separately by wave drag) are taken into account shows this latter approach to be the most promising in reducing orographically‐related systematic errors.     

深对流系统中初始误差增长和传播的热动力机制

利用WRF模式模拟一个典型的超级单体风暴,揭示了深对流系统中初始误差增长和传播的热动力机制,讨论了系统的高度非线性作用和可预报性等问题。结果表明：影响深对流系统发展强度的不稳定能量和潜热释放是影响误差增长和空间分布的主要因素;误差增长主要集中在对流区,对流区域外的初始扰动有向对流区域传播的趋势,并可在对流区域内迅速增长。随着对流系统的强烈发展,量级为O(10^-2)的初始扰动在210 min时即可达到量级O(10⁰),反映了系统高度的非线性作用和单一确定性预报显著的局限性。另外还发现,初始扰动对的相关性迅速增加,这将导致集合离散度偏低,给集合预报捕获极端天气的能力设置了障碍。误差的传播主要以声波和重力波两种波动形式传播。声波主要表现在积分初期,能量较小。重力波则能够在对流系统以外的区域激发新的对流中心(目前这种误差是不可预报的),进而限制了系统的可预报性。     

A Study of Shallow Cumulus Cloud Droplet Dispersion by Large Eddy Simulations

Cloud droplet dispersion is an important parameter in estimating aerosol indirect effect on climate in general circulation models (GCMs). This study investigates droplet dispersion in shallow cumulus clouds under different aerosol conditions using three-dimensional large eddy simulations (LES). It is found that cloud droplet mean radius, standard deviation, and relative dispersion generally decrease as aerosol mixing ratio increases from 25 mg⁻¹ (clean case) to 100 mg⁻¹ (moderate case), and to 2000 mg⁻¹ (polluted case). Under all the three simulated aerosol conditions, cloud droplet mean radius and standard deviation increase with height. However, droplet relative dispersion increases with height only in the polluted case, and does not vary with height in the clean and moderate cases.     

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。