Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves

Abstract

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.     

Weakly non-linear analysis of small-amplitude internal gravity waves forced by isolated topography

Asymptotic methods and numerical simulations are used to examine the evolution of an internal gravity wave packet comprising a continuous spectrum of horizontal wavenumbers and propagating upwards in a continuously stratified shear flow. In the multiple-scale framework for a horizontally localized wave packet generated by stratified flow over a localized mountain range with multiple peaks, there are in general two horizontal scales: the “fast” scale which is defined by the oscillations within the packet, i.e. the number of peaks, and the “slow scale” which is defined by the horizontal extent of the packet, i.e. the width of the mountain range. The focus here is on the specific case of an isolated mountain where the spectrum of horizontal wavenumbers is centred at zero and the multiple-scaling procedure is thus simplified by the absence of the fast spatial scale. The background flow is vertically sheared and critical-level interactions occur. The time frame within which non-linear critical-level effects become significant is determined by the magnitude of the non-linear terms in the governing equations. With the isolated mountain forcing this time frame is significantly longer than in the case of a multiple-peak mountain range forcing and it depends on the horizontal scale of the forcing, as well as on the amplitude. At leading-order, the non-linear asymptotic solution approaches a steady state in the outer region at late time, but the zero-wavenumber component of the solution continues to evolve with time in the vicinity of the critical level.     

Cause of winter gravity wave spectrum saturation

Gravity waves play a significant role in establishing the large-scale circulation and structure of the middle atmosphere. Through gravity wave saturation proc-esses, such motions are believed to cause turbulence, resulting in divergence of momentum flux and the diffusion of heat and constituents in the meso-sphere[1,2]. The mechanisms that contribute signifi-cantly to the gravity wave saturation are thought to be the dynamical and convective instabilities[3]. However, it is difficult to distin…     

Nonlinear interactions between gravity waves and tides

In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.     

A numerical experiment on the general circulation of the middle atmosphere with a three-dimensional model explicitly representing internal gravity waves and their breaking

The general circulation of the middle atmosphere is simulated by means of a three-dimensional primitive equation model which covers from the south pole to the north pole but is limited to a ten-degree sector in the latitudinal direction; cyclic conditions are imposed at the east—west lateral boundaries. The model is capable of explicitly representing internal gravity waves of zonal wavelength greater than a few hundred kilometers with the use of a one-degree mesh, but planetary-scale waves were excluded. No parameterization is employed for subgrid-scale eddy viscosity (or diffusivity).With the assumption of a simple external-heating function corresponding to solstice conditions, a time integration was performed for about thirty days from the motionless state. During the whole period, random forcings were imposed on each grid of the lowest level in order to generate small-scale upwardly propagating internal gravity waves.The experiment has shown that small-scale waves were indeed excited, propagated upward, broke up near the mesopause, and greatly changed the thermally induced zonal mean motion and temperature fields in the upper mesosphere and lower thermosphere. As a result, important features of the general circulation at those levels, such as reversals of the zonal motion and the latitudinal gradient of zonal mean temperature were reproduced.     

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

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

The criterion of gravity wave instability induced by photochemistry in summer polar mesopause region

This paper studies the effect of photochemistry on the gravity wave instability in summer polar mesopause region. The calculation method of the effects of eddy viscosity, conductivity and eddy diffusion of chemical species on the gravity wave instability induced by photochemistry are studied. The critical wavelength of the instability is given in this paper. The influences of some parameters on it are discussed. The study shows that the gravity wave instability induced by photochemistry is sensitive to the temperature and atomic oxygen profiles.     

Reflection of an internal wave at an interface representing a rapid increase in viscosity

Abstract

Internal waves at high altitudes are greatly damped by the drastic increase in molecular viscosity and thermal diffusivity, resulting in important heating and other effects at those altitudes. Here we consider the case where this increase in viscosity is very rapid, idealized as an interface with inviscid flow in the lower layer and constant viscosity in the upper layer. The results show that waves are partially reflected by this interface, with a reflection coefficient that increases monotonically with an increase in the viscosity of the upper layer. This mechanism would have a significant impact on the vertical distribution of thermal energy at high altitudes.     

基于中国东港台站的OH气辉成像观测数据对重力波波源的事件分析

利用东港（40°N,124°E）台站于2013年9月15—16日的OH气辉成像观测数据报告了两个重力波事件（1和2）.同时,结合北京十三陵（40.3°N,116.2°E）台站的多普勒流星雷达风场数据和位于39.4°N,130.6°E位置处的SABER/TIMED卫星的温度参数分析发现,观测的两个重力波事件于2013年9月15—16日02:00—03:00 LT时间段,和70~110 km高度是自由传播的.利用反射线追踪方法分析表明,重力波事件1和事件2分别产生于（39.3°N,117.2°E）和（47.1°N,121.3°E）.且事件1的波源位置与对流活动和大气向上向下运动过程中产生的不稳定性吻合较好.然而,通过ECMWF再分析资料和MTSAT卫星观测数据分析表明,事件2可能由对流活动或大气向上运动过程中可能产生的不稳定性导致.利用MERRA自地面到约70 km高度的风场数据分析表明,观测的重力波事件1和事件2的水平相速度分别是83.5 m·s^-1（事件1）和80.1 m·s^-1（事件2）,均大于低层-中层大气风速-10~45 m·s^-1.因此,观测的两个重力波事件是可能从低层大气传播到中层-低热层大气的.

     

Constrains on gravity wave induced diffusion in the middle atmosphere

A review of the important constraints on gravity wave induced diffusion of chemical tracers, heat, and momentum is given. Ground-based microwave spectroscopy measurements of H₂O and CO and rocket-based mass spectrometer measurements of Ar constrain the eddy diffusion coefficient for constituent transport (K _zz ) to be (1–3)×10⁵ cm²s^–1 in the upper mesosphere. Atomic oxygen data also limitsK _zz to a comparable value at the mesopause. From the energy balance of the upper mesosphere the eddy diffusion coefficient for heat transport (D _H ) is, at most 6×10⁵ cm²s^–1 at the mesopause and decreasing substantially with decreasing altitude. The available evidence for mean wind deceleration and the corresponding eddy diffusion coefficient for momentum stresses (D _M ) suggests that it is at least 1×10⁶ cm²s^–1, in the upper mesosphere. Consequently the eddy Prandtl number for macroscopic scale lengths is >3.     

Seasonal variations in internal wave energy in a Scottish sea loch

Near-continuous observations of an internal wave field were made over a period of 13 months at a location in Inchmarnock Water at the northern end of the Clyde Sea. This paper sets out to determine the seasonal form of the energy density of the internal wave field at this location based on the hypothesis that it varies smoothly throughout the year, being greater in summer than in winter. The mooring was maintained between June 1999 and July 2000 in 150-m water with seven deployments. Estimates of kinetic and potential energy density were derived from Acoustic Doppler Current Profiler (ADCP) and vertical temperature profiles respectively. Both were shown to vary on time scales less than 1 month with median values of mean kinetic energy (KE) density0.5 J m^–3 and for mean potential energy (PE) density0.01 J m^–3. The energy of the internal wave field was found to be continuous and without a clear seasonal form. Further, it was also always non-zero with intermittent peaks of much higher energy. In the late autumn the system experienced complete vertical overturning driven by local convective processes destroying the thermocline and causing a reduction in the overall KE density.Responsible Editor: Jens KappeubergOrginally presented as a poster at PECS 2002, Hamburg Germany     

Seasonal variation of space–time parameters of internal gravity waves at Kharkiv (49°30′N, 36°51′E)

Internal gravity waves (IGWs) over Kharkiv (49°30′N, 36°51′E) have been studied by using an automatic goniometer of a meteor radar (AG MR), with its antenna directed to the East. The AG MR carries out Doppler measurements of the radial drift velocity and the position of the reflecting area of meteor trails. In order to obtain information about IGW parameters, an algorithm was used that processes the AG MR wind data by dividing the measured volume into several sub-volumes, and by carrying out wavelet analysis of wind variations in these areas. Results of 1 year (1987) of AG MR data show a good qualitative correspondence with literature results. There is an increase of IGW activity during the change of the zonal background wind in spring and autumn. It was found that the mean IGW horizontal phase velocity and predominating horizontal propagation direction change with season. However, the mean period (1.5 h), the dominant amplitude (30 m/s) and the vertical phase velocity do not strongly vary in the course of the year. The mean vertical and horizontal wavelengths were found to be 40 and 250 km, respectively.     

A review of gravity wave saturation processes,effects, and variability in the middle atmosphere

This paper provides a review of our current understanding of the processes responsible for gravity wave saturation as well as the principal effects and variability of saturation in the lower and middle atmosphere. We discuss the theoretical and observational evidence for linear and nonlinear saturation processes and examine the consequences of saturation for wave amplitude limits, momentum and energy fluxes, the diffusion of heat and constituents, and the establishment of a near-universal vertical wavenumber spectrum. Recent studies of gravity wave variability are reviewed and are seen to provide insights into the significant causes of wave variability throughout the atmosphere.     

A theory of enhanced saturation of the gravity wave spectrum due to increases in atmospheric stability

In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wavelength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical flux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar reflectivities appear to be consistent with the enhancements observed near the high-latitude summer mesopause. Estimates of the enhanced mean flow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-latitude summer mesopause in large-scale models of the atmosphere. Thus, this process may play a significant role in determining the global effects of gravity waves on the large-scale circulation.     

Statistics of gravity wave spectra in the troposphere and lower stratosphere over Beijing

We utilize the temperature profiles with a height resolution of 50-m obtained over the Beijing Observatory in the period between January of 2002 and December of 2002 to study vertical wavenumber spectra of normalized temperature fluctuations in the 1.67-8.02 km and 13.57-19.92 km altitude ranges and compare them with linear saturation model.Results indicate that individual vertical wavenumber spectra reveal a considerable variability in both slope and amplitude.The observed variability is not consistent wit...     

Earlier days of gravity waves revisited

The means whereby the author came to be involved in the study of atmospheric gravity waves, and then came to involve others in that study, are outlined. In particular, events leading up to, during and following the International Symposium on Fluid Mechanics in the Ionosphere, of July 1959, are described.     

Internal gravity wave selection in the upper troposphere and lower stratosphere observed by the MU radar: Preliminary results

Marked wavelike variations of the lower stratospheric wind observed on 7–10 May, 1985 by an MST radar in Japan (by the MU radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves. These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C _X ) slower than the mean westerly wind (). A statistical analysis of the zonal phase velocity shows thatC _X above andC _X below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet. A comparison between the MU radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed.     

Trapped internal waves over undular topography in a partially mixed estuary

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

利用瑞利激光雷达观测北京地区上平流层地形重力波活动

本文利用中国科学院空间科学与应用研究中心的瑞利激光雷达首次观测到了平流层地形重力波活动的现象,并结合美国国家环境预报中心(NCEP)的全球预报系统(GFS)的风场数据分析了该地形重力波的基本参数.与惯性重力波相比较,地形重力波的密度扰动没有下传的相位,在同一高度上,其扰动相位保持不变.北京空间科学与应用研究中心瑞利激光雷达自2012年开始观测实验以来,已经观测到多起地形重力波活动事件.本文以2013年11月11日的观测数据为例,研究北京上空的地形重力波活动,并结合GFS风场数据分析了北京上平流层地形重力波的波长、传播方向、传播速度等参量.通过分析得到在2013年11月11日北京上空存在一列传播方向为北偏西52.4°,水平波长为5.5 km,平均垂直波长约为6.0 km的地形重力波.     

The global distribution of gravity wave energy in the lower stratosphere derived from GPS data and gravity wave modelling: Attempt and challenges

Five years of global temperatures retrieved from radio occultations measured by Champ (Challenging Minisatellite Payload) and SAC-C (Satelite de Aplicaciones Cientificas-C) are analyzed for gravity waves (GWs). In order to separate GWs from other atmospheric variations, a high-pass filter was applied on the vertical profile. Resulting temperature fluctuations correspond to vertical wavelengths between 400 m (instrumental resolution) and 10 km (limit of the high-pass filter). The temperature fluctuations can be converted into GW potential energy, but for comparison with parameterization schemes GW momentum flux is required. We therefore used representative values for the vertical and horizontal wavelength to infer GW momentum flux from the GPS measurements. The vertical wavelength value is determined by high-pass filtering, the horizontal wavelength is adopted from a latitude-dependent climatology. The obtained momentum flux distributions agree well, both in global distribution and in absolute values, with simulations using the Warner and McIntyre parameterization (WM) scheme. However, discrepancies are found in the annual cycle. Online simulations, implementing the WM scheme in the mechanistic COMMA-LIM (Cologne Model of the Middle Atmosphere—Leipzig Institute for Meteorology) general circulation model (GCM), do not converge, demonstrating that a good representation of GWs in a GCM requires both a realistic launch distribution and an adequate representation of GW breaking and momentum transfer.