Comments on Modelling Short Atmospheric Frontal Waves

The idea of Gerstner's trochoidal waves is used to reconstruct a model of short, finite-amplitude progressive waves on frontal surfaces of the Margules Type. Stable waves associated with a negative (westward) group velocity occur in the model. A wave train can be maintained through the formation of new waves in the rear of the existing waves as a result of the westward energy transport.     

Transient eastward-propagating long-period waves observed over the South Pole

Observations of the horizontal wind field over the South Pole were made during 1995 using a meteor radar. These data have revealed the presence of a rich spectrum of waves over the South Pole with a distinct annual occurrence. Included in this spectrum are long-period waves, whose periods are greater than one solar day, which are propagating eastward. These waves exhibit a distinct seasonal occurrence where the envelope of wave periods decreases from a period of 10 days near the fall equinox to a minimum of 2 days near the winter solstice and then progresses towards a period near 10 days at the spring equinox. Computation of the meridional gradient of quasi-geostrophic potential vorticity has revealed a region in the high-latitude upper mesosphere which could support an instability and serve as a source for these waves. Estimation of the wave periods which would be generated from an instability in this region closely resembles the observed seasonal variation in wave periods over the South Pole. These results are consistent with the hypothesis that the observed eastward propagating long-period waves over the South Pole are generated by an instability in the polar upper mesosphere. However, given our limited data set we cannot rule out a stratospheric source. Embedded in this spectrum of eastward propagating waves during the austral winter are a number of distinct wave events. Eight such wave events have been identified and localized using a constant-Q filter bank. The periods of these wave events ranges from 1.7 to 9.8 days and all exist for at least 3 wave periods. Least squares analysis has revealed that a number of these events are inconsistent with a wave propagating zonally around the geographic pole and could be related to waves propagating around a dynamical pole which is offset from the geographic pole. Additionally, one event which was observed appears to be a standing oscillation.     

Seasonal variabilities of low-latitude mesospheric winds

Observations of mesospheric winds over a period of four years with the partial reflection radar at Tirunelveli (8.7°N, 77.8°E), India, are presented in this study. The emphasis is on describing seasonal variabilities in mean zonal and meridional winds in the altitude region 70–98 km. The meridional winds exhibit overall transequatorial flow associated with differential heating in the Northern and Southern Hemispheres. At lower altitudes (70–80 km) the mean zonal winds reveal easterly flow during summer and westerly flow during winter, as expected from a circulation driven by solar forcing. In the higher altitude regime (80–98 km) and at all altitudes during equinox periods, the mean zonal flow is subjected to the semi-annual oscillation (SAO). The interannual variability detected in the occurrence of SAO over Tirunelveli has also been observed in the data sets obtained from the recent UARS satellite mission. Harmonic analysis results over a period of two years indicate the presence of long-period oscillations in the mean zonal wind at specific harmonic periods near 240, 150 and 120 days. Results presented in this study are discussed in the context of current understanding of equatorial wave propagation.     

VHF radar observations of gravity waves at a low latitude

Wind observations made at Gadanki (13.5°N) by using Indian MST Radar for few days in September, October, December 1995 and January, 1996 have been analyzed to study gravity wave activity in the troposphere and lower stratosphere. Horizontal wind variances have been computed for gravity waves of period (2–6) h from the power spectral density (PSD) spectrum. Exponential curves of the form e^Z/H have been fitted by least squares technique to these variance values to obtain height variations of the irregular winds upto the height of about 15 km, where Z is the height in kilometers. The value of H, the scale height, as determined from curve fitting is found to be less than the theoretical value of scale height of neutral atmosphere in this region, implying that the waves are gaining energy during their passage in the troposphere. In other words, it indicates that the sources of gravity waves are present in the troposphere. The energy densities of gravity wave fluctuations have been computed. Polynomial fits to the observed values show that wave energy density increases in the troposphere, its source region, and then decreases in the lower stratosphere.     

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.     

Diurnal and semidiurnal tide in the upper middle atmosphere during the first year of simultaneous MF radar observations in northern and southern Japan (45°N and 31°N)

The climatology of mean wind, diurnal and semidiurnal tide during the first year (1996–1997) of simultaneous wind observations at Wakkanai (45.4°N, 141.7°E) and Yamagawa (31.2°N, 130.6°E) is presented. The locations of the radars allow us to describe the latitudinal dependence of the tides. Tidal amplitude and phase profiles are compared with those of the global scale wave model (GSWM). While the observed amplitude profiles of the diurnal tide agree well with the GSWM values, the observed phase profiles often indicate longer vertical wavelengths than the GSWM phase profiles. In contrast to the GSWM simulation, the observations show a strong bimodal structure of the diurnal tide, with the phase advancing about 6 hours from summer to winter.     

Vertical velocities associated with gravity waves measured in the mesosphere and lower thermosphere with the EISCAT VHF radar

The EISCAT VHF radar (69.4°N, 19.1°E) has been used to record vertical winds at mesopause heights on a total of 31 days between June 1990 and January 1993. The data reveal a motion field dominated by quasi-monochromatic gravity waves with representative apparent periods of 30–40 min, amplitudes of up to 2.5 m s^–1 and large vertical wavelength. In some instances waves appear to be ducted. Vertical profiles of the vertical-velocity variance display a variety of forms, with little indication of systematic wave growth with height. Daily mean variance profiles evaluated for consecutive days of recording show that the general shape of the variance profiles persists over several days. The mean variance evaluated over a 10 km height range has values from 1.2 m²s^–2 to 6.5 m²s^–2 and suggests a semi-annual seasonal cycle with equinoctial minima and solsticial maxima. The mean vertical wavenumber spectrum evaluated at heights up to 86 km has a slope (spectral index) of -1.36 ± 0.2, consistent with observations at lower heights but disagreeing with the predictions of a number of saturation theories advanced to explain gravity-wave spectra. The spectral slopes evaluated for individual days have a range of values, and steeper slopes are observed in summer than in winter. The spectra also appear to be generally steeper on days with lower mean vertical-velocity variance.     

The effect of Newtonian cooling on vertically propagating magneto-acoustic waves in a thermally conducting isothermal atmosphere (II)

In this article, we examine reflection, dissipation and attenuation of vertically propagating waves in an isothermal atmosphere under the combined effect of Newtonian cooling, thermal conduction and viscosity with a weak horizontal magnetic field. We consider the case in which the combined effect of viscosity and magnetic field is dominated by that of the thermal conduction and for small values of the Newtonian parameter. As a result, the atmosphere can be divided into three distinct regions that are connected by two transition regions. The lower and middle regions are connected by a semi-transparent barrier and the middle and upper regions are connected by an absorbing and reflecting barrier. In the connecting barriers the reflection and transmission of the waves takes place. The presence of Newtonian cooling effects on the adiabatic region, produces attenuation in the amplitudes of the waves and reduces the energy absorption in the transition regions. The reflection coefficient is determined in the lower and middle regions and the results are discussed in the context of the heating of the solar atmosphere.     

Intradiurnal wind variations observed in the lower thermosphere over the South Pole

The first meteor radar measurements of meridional winds in the lower thermosphere (about 95 ± 5 km), along four azimuth directions: 0°, 90°E, 180° and 90°W; approximately 2° from the geographic South Pole were made during two observational campaigns: January 19, 1995-January 26, 1996, and November 21, 1996-January 27, 1997. Herein we report analyses of the measurement results, obtained during the first campaign, which cover the whole one-year period, with particular emphasis on the transient nature and seasonal behavior of the main parameters of the intradiurnal wind oscillations. To analyze the data, two complementary methods are used: the well-known periodogram (FFT) technique and the S-transform technique. The most characteristic periods of the intradiurnal oscillations are found to be rather uniformly spread between about 7 h and 12 h. All of these oscillations are westward-propagating with zonal wave number s = 1 and their usual duration is confined to several periods. During the austral winter season the oscillations with periods less than 12 h are the most intensive, while during summer season the 12-h oscillations dominate. Lamb waves and internal-gravity wave propagation, non-linear interaction of the short-period tides, excitation in situ of the short period waves may be considered as possible processes which are responsible for intradiurnal wind oscillations in the lower thermosphere over South Pole.     

Analysis of gravity waves in the tropical middle atmosphere over La Reunion Island (21°S, 55°E) with lidar using wavelet techniques

The capabilities of the continuous wavelet transform (CWT) and the multiresolution analysis (MRA) are presented in this work to measure vertical gravity wave characteristics. Wave properties are extracted from the first data set of Rayleigh lidar obtained between heights of 30 km and 60 km over La Reunion Island (21°S, 55°E) during the Austral winter in 1994 under subtropical conditions. The altitude-wavelength representations deduced from these methods provide information on the time and spatial evolution of the wave parameters of the observed dominant modes in vertical profiles such as the vertical wavelengths, the vertical phase speeds, the amplitudes of temperature perturbations and the distribution of wave energy. The spectra derived from measurements show the presence of localized quasi-monochromatic structures with vertical wavelengths <10 km. Three methods based on the wavelet techniques show evidence of a downward phase progression. A first climatology of the dominant modes observed during the Austral winter period reveals a dominant night activity of 2 or 3 quasi-monochromatic structures with vertical wavelengths between 1/2 km from the stratopause, 3/4 km and 6/10 km observed between heights of 30 km and 60 km. In addition, it reveals a dominant activity of modes with a vertical phase speed of –0.3 m/s and observed periods peaking at 3/4 h and 9 h. The characteristics of averaged vertical wavelengths appear to be similar to those observed during winter in the southern equatorial region and in the Northern Hemisphere at mid-latitudes.     

Spectral characteristics of spring arctic mesosphere dynamics

The spring of 1997 has represented a stable period of operation for the joint University of Tromsø/University of Saskatchewan MF radar, being between refurbishment and upgrades. We examine the horizontal winds from the February to June inclusive and also include estimates of energy dissipation rates derived from signal fading times and presented as upper limits on the turbulent energy dissipation rate, . Here we address the periodicity in the dynamics of the upper mesosphere for time scales from hours to one month. Thus, we are able to examine the changes in the spectral signature of the mesospheric dynamics during the transition from winter to summer states.     

The 16-day planetary wave in the mesosphere and lower thermosphere

A meteor radar located at Sheffield in the UK has been used to measure wind oscillations with periods in the range 10–28 days in the mesosphere/lower-thermosphere region at 53.5°N, 3.9°W from January 1990 to August 1994. The data reveal a motion field in which wave activity occurs over a range of frequencies and in episodes generally lasting for less than two months. A seasonal cycle is apparent in which the largest observed amplitudes are as high as 14 ms⁻¹ and are observed from January to mid-April. A minimum in activity occurs in late June to early July. A second, smaller, maximum follows in late summer/autumn where amplitudes reach up to 7–10 ms⁻¹. Considerable interannual variability is apparent but wave activity is observed in the summers of all the years examined, albeit at very small amplitudes near mid summer. This behaviour suggests that the equatorial winds in the mesopause region do not completely prevent inter-hemispheric ducting of the wave from the winter hemisphere, or that it is generated in situ.     

Lunar tidal winds in the upper atmosphere over Collm

The lunar semidiurnal tide in winds measured at around 90 km altitude has been isolated with amplitudes observed up to 4 m s^–1. There is a marked amplitude maximum in October and also a considerable phase variation with season. The average variation of phase with height indicated a vertical wavelength of more than 80 km but this, and other results, needs to be viewed in the light of the considerable averaging required to obtain statistical significance. Large year-to-year variations in both amplitude and phase were also found. Some phase comparisons with the GSWM model gave reasonable agreement but the model amplitudes above a height of 100 km were much larger than those measured. An attempt to make a comparison with the lunar geomagnetic tide did not yield a statistically significant result.     

A comparative study of winds and tidal variability in the mesosphere/lower-thermosphere region over Bulgaria and the UK

Meteor radars located in Bulgaria and the UK have been used to simultaneously measure winds in the mesosphere/lower-thermosphere region near 42.5°N, 26.6°E and 54.5°N, 3.9°W, respectively, over the period January 1991 to June 1992. The data have been used to investigate planetary waves and diurnal and semidiurnal tidal variability over the two sites. The tidal amplitudes at each site exhibit fluctuations as large as 300% on time scales from a few days to the intra-seasonal, with most of the variability being at intra-seasonal scales. Spectral and cross-wavelet analysis reveals closely related tidal variability over the two sites, indicating that the variability occurs on spatial scales large compared to the spacing between the two radars. In some, but not all, cases, periodic variability of tidal amplitudes is associated with simultaneously present planetary waves of similar period, suggesting the variability is a consequence of non-linear interaction. Calculation of the zonal wave number of a number of large amplitude planetary waves suggests that during summer 1991 the 2-day wave had a zonal wave number of 3, but that during January/February 1991 it had a zonal wave number of 4.     

Can zonally symmetric inertial waves drive an oscillating zonal mean flow?

In the present paper zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation, a process currently discussed controversially.     

Scattered Surface Wave Energy in the Seismic Coda

One of the many important contributions that Aki has made to seismology pertains to the origin of coda waves (Aki, 1969; Aki and Chouet, 1975). In this paper, I revisit Aki's original idea of the role of scattered surface waves in the seismic coda. Based on the radiative transfer theory, I developed a new set of scattered wave energy equations by including scattered surface waves and body wave to surface wave scattering conversions. The work is an extended study of Zeng et al. (1991), Zeng (1993) and Sato (1994a) on multiple isotropic-scattering, and may shed new insight into the seismic coda wave interpretation. The scattering equations are solved numerically by first discretizing the model at regular grids and then solving the linear integral equations iteratively. The results show that scattered wave energy can be well approximated by body-wave to body wave scattering at earlier arrival times and short distances. At long distances from the source, scattered surface waves dominate scattered body waves at surface stations. Since surface waves are 2-D propagating waves, their scattered energies should in theory follow a common decay curve. The observed common decay trends on seismic coda of local earthquake recordings particular at long lapse times suggest that perhaps later seismic codas are dominated by scattered surface waves. When efficient body wave to surface wave conversion mechanisms are present in the shallow crustal layers, such as soft sediment layers, the scattered surface waves dominate the seismic coda at even early arrival times for shallow sources and at later arrival times for deeper events.     

A new technique for evaluating mesospheric momentum balance utilizing radars and satellite data

A new method for evaluating momentum balance in the mesosphere using radar and satellite data is presented. This method is applied to radar wind data from two medium frequency installations (near Adelaide, Australia and Christchurch, New Zealand) and satellite temperature data from the Improved Stratospheric and Mesospheric Sounder (ISAMS). Because of limitations in data availability and vertical extent, the technique can only be applied to evaluate the momentum balance at 80 km above the radar sites for May 1992. The technique allows the calculation of the residual terms in the momentum balance which are usually attributed to the effects of breaking gravity waves. Although the results are inconclusive above Adelaide, this method produces values of zonal and meridional residual accelerations above Christchurch which are consistent with expectation. In both locations it is apparent that geostrophic balance is a poor approximation of reality. (This result is not dependent on a mismatch between the radar and satellite derived winds, but rather is inherent in the satellite data alone.) Despite significant caveats about data quality the technique appears robust and could be of use with data from future instruments.     

Inertia-gravity waves in the troposphere and lower stratosphere associated with a jet stream exit region

Radar measurements at Aberystwyth (52.4°N, 4.1°W) of winds at tropospheric and lower stratospheric heights are shown for 12–13 March 1994 in a region of highly curved flow, downstream of the jet maximum. The perturbations of horizontal velocity have comparable amplitudes in the troposphere and lower stratosphere with downward and upward phase propagation, respectively, in these two height regions. The sense of rotation with increasing height in hodographs of horizontal perturbation velocity derived for hourly intervals show downwards propagation of energy in the troposphere and upward propagation in the lower stratosphere with vertical wavelengths of 1.7 to 2.3 km. The results indicate inertia-gravity waves propagating in a direction similar to that of the jet stream but at smaller velocities. Some of the features observed contrast with those of previous observations of inertia-gravity waves propagating transverse to the jet stream. The interpretation of the hodographs to derive wave parameters has taken account of the vertical shear of the background wind transverse to the direction of wave propagation.     

A reduced model for nonlinear dispersive waves in a rotating environment

Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.     

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.