The relation of gravity waves and turbulence in the mesosphere

Adv. Space Res. Vol. 7, No. 10, pp. (10)345—(10)348, 1987 Printed in Great Britain. All rights reserved.

0273—1177/87 $0.00 + .50 Copyright © 1987 COSPAR

THE RELATION OF GRAVITY WAVES AND TURBULENCE IN THE MESOSPHERE JUrgen Rottger EISCA T Scientific Association, Box 705, 5-981 27 Kiruna, Sweden (on leave from Max-Planck-Institut für Aeronomie, F. R. G.

ABSTRACT: VHF radar observations of the mesosphere generally reveal that the structure of turbulence is intermittent in space and time. Some examples of such turbulence layers and the concurrent gravity wave oscillations, observed in the low latitude mesosphere over the Arecibo Observatory/Puerto Rico are discussed. This turbulence structures which are intermittent on short time scales but persistently recur over periods of many hours at almost the same height are evidently not related to the simultaneously occurring short period gravity waves. These kinds of persistent turbulence structures are assumed to be related to very long period (inertia-) gravity waves, where instability takes place only by the wave induced shear in a narrow critical level. However, the short period gravity waves occasionally break into turbulence by overturning and convective instability. These interpretations offer a way to understand the generation mechanisms of the different kinds of turbulence structures, namely blobs, sheets and layers, which were reported in the early days of inesospheric VHF radar observations. INTRODUCTION Gravity wave saturation in the middle atmosphere is widely assumed to be due to the increase of wave amplitude with height or from the encountering of a critical level such that convective and/or shear instability limits the wave growth /1/.The growth of wave amplitude first results in a steepening of wave velocities, i.e. in the generation of harmonics before the wave eventually breaks into turbulence and gets saturated. As pointed out by Weinstock /2/, the saturation of the wave is accompanied by a near adiabatic lapse rate and turbulence. A wave-mean flow interaction results from the wave saturation by turbulence. FEATURES OF RADAR DETECTED TURBULENCE VHF MST radars with suitable sensitivity can detect turbulence in the mesosphere if the vertical gradient of electron densities sufficiently strong. It is unquestionable from many experiments that the radar-detected turbulence is intermittent in space and time. Figure 1 shows an example of layers or sheets of mesospheric echoes detected with the SOUSY-VHF-Radar at the Arecibo Observatory /3,4/. A clear feature in this figure is the splitting into several, periodically arranged sheets. Many authors have reported an apparent downward progression of such structures, which is not readily apparent in Fig. 1, however. These discrete sheets can be due to turbulence or due to very persistent steep electron density gradients. We cannot imagine that the latter can endure in the daylight ionosphere if they were not controlled by some kind of neutral atmosphere effect. It is often observed that longperiod atmospheric gravity waves or tides can give rise to turbulence layer generation /5/. The layers then should move downward which we do not observe. It is also reported that turbulence layers occur preferably in strong wind shear regions /6/. The simultaneously measured mean wind profiles indicate a downward moving shear in the zonal and meridional components which could be due to the diurnal tide. Since the shear move downward and occurs in the components but not in the amplitude, we have to exclude that the observed heightstationary turbulence sheets of Fig.1 have some relation to the tidal variation of velocity or temperature. I

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We cannot assume that the fairly thin and persistent sheets seen in Fig.1 are generated by short period gravity waves. A common explanation is that gravity wave breaking causes turbulence /7/ which we should be able to detect in our records. Fig. 2 shows time series of spectra-intensity plots for different altitudes. The intensity is printed in an absolute reflectivity scale, such that the height and time dependence of turbulence intensity (assuming no subtantial electron ~ensityprofile change), spectral width and mean radial velocity (almost vertical at 2.3 zenith angle) can be identified. We notice quite a substantial wave activity at many different periods from 4 minutes upwards. If wave breaking would occur, we should see an increase of intensity and spectrum-width at certain phases of these oscillations. Except occasionally in some upper heights, where some intensity bursts are apparent (e.g. at 78 km after 15 AST), we cannot clearly detect such phenomena. The intermittency in space and time of the turbulence echoes appears in the majority of times and heights not related to these short period gravity waves. When carefully viewing the velocity oscillations, we, however often find clear indications of a non-sinusoidal variation. This indicates a non-linear steepening effect /8,2/, which transfers energy from the fundamental into harmonics, - in our case mostely without leading to breaking into turbulence. Another peculiar effect is seen sometimes, when a high-frequency wave is superimposed on a low frequency wave (e.g. at 69.6 km after 13 AST). Klostermeyer /9/ has explained similar observations at thermospheric heights to be due to parametric instabilities.

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INTERPRETATION OF TURBULENCE FEATURES There is apparently no distinct amplitude growth with height of these wave oscillations (e.g., fairly clearly seen from 12-13 AST between 69.6 km and 76.8 km, as well as in Fig. 3 of Röttger /10/. We therefore have to imply a saturation process if we assume that these are vertically propagating waves, Since in our case study we seldom observe a clear indication for wave breaking into turbulence, we may invoke other dissipation effects which limit the wave growth, such as energy transfer into higher harmonics (non-linear steepening), parametric instabilities, radiative damping or dissipation due to kinematic viscosity and heat conduction. We also could assume that the observed short-period gravity waves are locally generated or guided in wave ducts, since most of the oscillations are confined to height ranges of a few kilometers onry.

The Relation of Gravity Waves and Turbulence

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Since we cannot prove that the mesospheric turbulence sheets (Fig. 1) are generated by the simultaneously existing short period 9ravity waves (Fig. 2), we have to assume other generation mechanisms than wave breaking. Possible mechanisms like lateral convection /11/, quasi-geostrophic flows at mesoscales /12/ or vortical modes of motion as seen in the ocean /13/ could be candidates. We are inclined to see a connection of these sheets or laminae /11/ with very long period internal waves because of the periodicity in their vertical structure and their long mean persistency (see Fig. 3, which shows their appearance at two time periods separated by 24 hours). Röttger /14/ had proposed that such structures seen by VHF radar in the stratosphere are due the modulation of the mean temperature and wind profiles by internal waves. The superposition of random or short-term wave-induced wind and temperature fluctuations with the background profile, modulated by very-long-period waves (quasi-inertia waves) then would yield the observed effects, namely could explain the vertical periodicity, the long—term mean persistency as well as some short-term variability of their intensity. Note, that this phenomenon does not need the short-term gravity waves to break into turbulence, rather than to add a small shear or temperature variation to the background profile modulated by linearly or non-linearly modified long-period waves, to lead to very thin laminae where the Richardson number is smaller than its critical value to initiate turbulence. The blobs and layers of turbulence /11/, however, have to be regarded as due to breaking of waves into turbulence by overturning and convective instability /7/. As discussed by Rfister and Klostermeyer /15/ and Röttger and lerkic /16/, the bursts or blobs of turbulence do move horizontally and vertically, and are indicative for KHI. I

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Height-time-intensity plots of mesospheric VHF-radar echoes detected at the same time on two different days.

Recently Mobbs /8/ has published a very detailed investigation of the propagation of nonlinear internal gravity waves at stratospheric and mesospheric heights. His conclusion is that wave-mean flow interactions result in the formation of a level of very low intrinsic frequency. Although the complete formation of a critical level is prevented by eddy viscosity, wave instability takes place near the wave induced critical level. Our observations of these sheets or laminae appears to be an indication of this kind of critical level effect, rather than an indication of wave breaking. CONCLUSION We could explain the turbulence structures detected by radars in the middle and lower atmosphere to result from a range of waves from very long down to the shortest periods near the Brunt-Väisälä period. Very long period waves undergo non-linear steepening or tilting when their phase velocity approaches the wind velocity. Through velocity shear, Kelvin-HelmholtzInstability (KHI) gets activated and quasi 2-dimensional turbulence (vertically thin and horizontally extended) is generated. Turbulence scatter or Fresnel reflection of VHF radar waves from the boundaries of the turbulence layers can occur. Also temperature inversions are caused by steepened long period waves. These can be seen as thin sheets or laminae by Fresnel reflection of VHF radar waves (particularly in the stratosphere). Short-period waves undulate these thin layers of turbulence or the laminae of temperature inversions. These waves can grow in amplitude by KHI (local generation) or due to energy conservation of upward propagating waves. Non-linear tilting, steepening and/or parametric instability can occur. The development of tilting and steepening can be observed by Fresnel reflection due to the concurrent distortion of isotherms during the development of KHI. Non-linear wave tilting will cause overturning and breaking through the Rayleigh—TaylorInstability (RTI). Since this happens at a certain phase of the wave, localized regions of turbulence occur. These are seen by VHF radars as blobs or bursts propagating with the phase speed of the waves, which is equal to the wind speed (condition for the originating KHI). Blobs can spread into wider spatial scales by multiple repetition of KHI/RTI, thus, causing thick layers of strong turbulence. Through the turbulence layers corrugated temperature gradients are generated /14/, and the layers can dissolve into multiple sheets or laminae /7,14/. Again waves, generated elsewhere, can undulate these turbulence layers and the sheets. We, thus, close the dynamical circle to explain the simultaneous observations of (often independent, individual) gravity waves and turbulence.

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The described interrelation of a variety of dynamical phenomena in the atmosphere can explain the earlier recognized characteristics of VHF radar echoes from the mesosphere /14,17,18/, namely the blobs, sheets and layers. REFERENCES: 1. Fritts, D.C. (1984), Gravity Wave Saturation in the Middle Atmosphere: A Review of Theory and Observations, Rev. Geoph. Space Phys., Vol. 22, p. 275-308. 2. Weinstock, J. (1985), Finite Amplitude Gravity Waves: Harmonics, Advective Steepening and Breaking, Manuscript, Aeronomy Laboratory, NOAA-Boulder, CO. 3. Röttger, J., P. Czechowsky and G.Schmidt (1981), First Low-Power VHF Radar Observations of Tropospheric, Stratospheric and Mesospheric Winds and Turbulence at the Arecibo Observatory, Journ. Atmos. Terr. Phys., Vol. 43, p. 789-800. 4. Czechowsky, P., G. Schmidt and R. RUster, (1984) The Mobile SOUSY nical Design and First Results, Radio Science, 19, p.441-450.

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5. Fritts, D.C., S.A. Smith, B.B. Balaley and C.R. Philbrick (1985), Evidence for Gravity Wave Saturation and Local Turbulence Production in the Summer Mesosphere and Lower Thermosphere During the STATE Experiment, Manuscript. 6. Rtister, R. (1984), Winds and Waves in the Middle Based Radars, Adv. Space Res., Vol. 4, p. 3-18. 7. Fritts, D.C. and P.K. Rastogi (1985), Gravity Wave Motions in the Lower and Science, Vol. 20., p. 1247—1277.

Atmosphere as

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Convective and Dynamical Instabilities Due to Middle Atmosphere: Theory and Observations, Radio

8. Mobbs, S.D. (1985), Propagation of internal gravity waves at stratospheric and mesospheric heights, Parts I-Ill, Annales Geophysicae, Vol. 3, p. 319—334, p.451-464, p.599— 608. 9. Klostermeyer, J. (1984), Observations Indicating Parametric Instabilities in Internal Gravity Waves at Thermospheric Heights, Geophys. Astrophys. Fluid Dynamics, Vol. 29, p. 117—138. 10. Röttger, J. (1986), The Use of the Experimentally Deduced Brunt-Väisälä—Frequency and Turbulent Velocity Fluctuations to Estimate the Eddy Diffusion Coefficient, 3. Workon Sci. and Techn. Aspects of MST Radar, Aguadilla, Puerto Rico, Oct. 1985, Handbook for MAP, to appear. 11. Röttger, J. (1980), Structure and Dynamics of the Stratosphere and by VHF Radar Investigations, Pageoph. Vol. 118, p. 494-527. 12. Lilly, O.K. (1983), Stratified Turbulence and the sphere, Jour. Atmos. Sci., Vol. 40, p. 749-761.

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13. MUller, P. and R. Pujalet, Editors (1984), Internal Gravity Waves and Small-scale Turbulence, Proc. Hawaiian Winter Workshop, University of Hawaii at Monoa, Jan. 1984. 14. Rbttger, J. (1980), The Dynamics of Stratospheric and Mesospheric Fine Structure Investigated with an MST VHF Radar, Handbook for MAP, Vol. 2, p. 341-350. 15. RUster, R. and J. Klostermeyer (1985), Instabilities and turbulence heights as observed by VHF radar, Handbook for MAP, 18, p. 216-219. 16. Röttger, J. and H.M. lerkic (1985), Poatset beam steering tions of VHF radars to study winds, waves and turbulence atmosphere, Radio Sci., 6, 1461—1480.

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and interferometer applicain the lower and middle

17. Röttger, J., P.K. Rastogi and R.F. Woodman (1979), High-resolution VHF radar observations of turbulence structures in the mesosphere, Geophys.Res.Lett., 6, 617-620. 18. Czechowsky, P., R. RUster and G. Schmidt (1979), Variations at different seasons, Geophys.Res.Lett., 6, 459-462.

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