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Interactions between diurnal tides and gravity waves in the lower thermosphere
Journal of Atmospheric and Terrestrial Physics. Vol. 56, No. 10, pp. 1365-1373, 1994 Copytight 0 1994 Elsevier Saence Ltd Printed in Great Britain. Allrightsreserved
Pergamon
0021-9169/94$7.00+0.00
Interactions between diurnal tides and gravity waves in the lower thermosphere S. MIYAHARA* and J. M.
FORBES?:
*Department of Earth and Planetary Sciences, Kyushu University, Fukuoka 8 12, Japan ; tHigh Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80303-3000. U.S.A. (Received in ,jinal,form Abstract-Recent upper mesosphere models.
15 June 1993 : accepted
I July 1993)
progress on interactions between breaking gravity waves and the diurnal and lower thermosphere
tide in the is reviewed, mainly based on the recent results of our numerical
1. INTRODUCTION
2. GRAVITY-WAVE/TIDEINTERACTION
The importance of stress due to dissipating internal gravity waves on larger scale motions in the upper mesosphere and lower thermosphere has been recognized since the pioneering works by LINDZEN (1981) and MATSUNO (1982). In their papers it is shown that the stress due to dissipating gravity waves acts to decelerate the zonal mean winds in the upper mesosphere and lower thermosphere. This effect of internal gravity waves on the mean winds is observationally confirmed by some radar observations (e.g. VINCENT and REID, 1983; FRITTS and VINCENT, 1987; TSUDA rt al., 1990). It is also observationally found that the mesospheric momentum flux due to gravity waves is modulated by the tidal frequency (FRITTS and VINCENT, 1987 ; WANG and FRITTS, 1991). FRITTS and VINCENT (1987) furthermore demonstrate that the modulated momentum flux divergence is sufficiently large to feed back and modify the tidal wind field. This hypothesis is supported by several numerical simulations (WALTERSCHEID,198 1; FORBESet al., 1991; MIYAHARA and FORBES, 1991). In the present paper the possible interactions between the diurnal tides and gravity waves are reviewed mainly based on the recent numerical results of our models. In Section 2, the idea of gravity-wave/ tide interaction proposed by FRITTS and VINCENT (1987) is briefly reviewed. In Section 3, some recent numerical results of our models are shown, and some unsolved problems are discussed.
Many aspects of gravity-wave/tide interactions are adequately reviewed by VIAL and FORBES (1989), so in the present paper only the basic idea of the breaking gravity-wave/tide interaction proposed by FRITTS and VINCENT (1987) is considered. In their model, parameterization of the momentum deposition by a monochromatic breaking gravity wave proposed by LINDZEN (1981) is applied to the gravity-wave/tide interaction. The momentum flux convergence due to a breaking gravity wave in the combined zonal mean and tidal winds is given by
:On leave from the Department of Aerospace and Mechanical Engineering and the Center for Space Physics, Boston University, Boston, MA 02215. U.S.A.
provided
that
where z is the altitude, zh the braking height, p the pressure, G the local zonal wind (zonal mean wind +zonal wind of the tide), tiZ the vertical shear of d, k the zonal wavenumber of the gravity wave, c the zonal phase velocity of the gravity wave, N the static stability and H the scale height. In this parameterization, the vertical propagation of the gravity wave is controlled by the locally combined zonal mean and tidal winds, so that the convergence has a tendency to decelerate the local wind speed. This effect will change the amplitude and phase of the tidal waves. It is observationally confirmed that the momentum flux due to short time scale gravity waves (periods are less than 1h) has the out-of-phase correlation with the back-
1365
S.
1366
MIYAHARA and J. M. FORBES
ground tidal winds, which supports the above parameterization, at least qualitatively (WANG and FRITTS, 1991). The original Lindzen’s parameterization assumes that the gravity waves break down after they achieve steady state. In the present situation, the steadiness is violated due to the existence of the time varying background wind field. However. the above parameterization is valid as a first approximation, if the vertical propagation of gravity waves is much faster than the tidally induced change in the background wind field. The WKB approximation is also used to derive the parameterization. In this approximation, the vertical wavelengths of the gravity waves are assumed to be much shorter than the typical vertical scale of the background wind field. There is a possibility of violation of this assumption in some cases due to the presence of the tide. These issues are closely related to the time scale and spatial scale separations between the gravity waves and tide. This will be mentioned in the next section. 3. SIMULATiONS OF GRAVITY-WAVELIKE INTERACTION 3.1. Results model
qfgravity
wuve breaking parameterization
It is shown by FORBESet al. (1991), using the abovementioned parameterization and the f-plane approximation of diurnal tide (FORBESand HAGAN, 1979) that breaking gravity waves with phase velocities of
0, 5 15, + 30 m s- ’ act to suppress the diurnal tide, and that the momentum flux convergence can induce tides having other frequencies (e.g. the semidiurnal tides). Figures I(a) and (b) show the time height sections of the local mean wind and the acceleration due to the breaking gravity waves by their model. The out-of-phase correlation between the local mean winds and the acceleration is evident. This out-ofmomentum flux convergence associated with the breaking gravity waves acts to suppress the tidal amplitude. It is also shown that the tidal modulation of the mean winds opens some channels of propagation of gravity waves into the lower thermosphere. The above approach has been extended into a twodimensional time-dependent numerical tidal model, in which gravity-wave/tide interactions are calculated at each spatial grid point and each time step to feedbackthemomentumfluxconvergencetothemomenturn equation of the tides (MIYAHARAand FORBES, 1991). Figures 2(a) and (b) show the meridional cross-sections of amplitude of the eastward wind of the diurnal tide obtained by the models with and without gravity wave interactions, respectively. The amplitude of the diurnal tide is suppressed by the momentum flux convergence of the breaking gravity waves. Moreover, the altitude of maximum is lowered, more consistent with observations (e.g. ASO and VINCENT.1981; VINCENTand BALL, 1977). As shown in MIYAHARAand FORBES(1991) this amplitude suppression is accompanied by a shift of about 2 h phase to earlier (later) local times equatorward (poleward)
ACCELEIUTION
100 P E ;a
80
80
Fig. I. (a) Total wind field at 6” latitude from f-plane calculation by FORBES et al. (1991). Contour intervals are 10m s- ‘. (b) Time-height section of acceleration (m se”’ day- ‘) due to breaking gravity waves from fplane calculation by FORBES~~ al, (1991). Contour intervals are 10m s-’ day- ‘. From FORBES~~al. (1991).
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LpiT I TUDE Fig. 2. Meridional cross-sections of amplitude (m s- ‘) of the eastward wind of the diurnal tide from the two-dimensional model of MIYAHARAand FORBES (1991). (a) with gravitywave/tide interaction ; (b) non-interaction case. Contour intervals are 10 rns- ‘_ of 40“ latitude. The longitudinal dist~butions of the momentum flux convergence are shown in Fig. 3 to show the out-of-phase correlations with the diurnal tidal winds at both the winter and summer hemispheres. It is notable that the longitudes where the momentum flux divergences have their peaks shift almost 180’ between both hemispheres. This is because in the winter (summer) hemisphere the westward (eastward) moving gravity wives are breaking at the longitudes where the zonal winds of the tide are in a westerly (easterly) phase. This situation is confirmed by the strong out-of-phase correlation between the zonal distributions of divergence and that of the zonal winds of tides at 5 km lower heights, approximately where the gravity waves are considered to be breaking.
1367
This figure shows the asymmetric distribution of tidal amplitude between the winter and summer hemispheres. The amplitude is stronger in the winter hemisphere than that in the summer hemisphere. This asymmetry is mainly due to the effect of mean background wind. In this model the gravity wave source is assumed to be symmetric between both hemispheres. In the real atmosphere, the gravity wave source may be different in each hemisphere, and this asymmetric distribution of gravity waves may cause asymmetric tidal amplitudes in the middle atmosphere. This effect must be taken into account in future studies of gravity-wave~tjde interactions. As shown in this figure, the longitudinal distribution of the convergence does not have a sinusoidal wave form, but consists of many zonai wavenumbers, and it generates the semidiurnal and terdiurnal tides of amplitudes of 5 m se ’ or less in the lower thermosphere. As mentioned in Section 2, spatial scale and time scale separations between the gravity waves and tides are assumed in applying the wave-mean flow parameterization of LENDZEN (1981). The time scale separation may be good enough if we can confine our discussion to the fast propagating gravity waves. However, the momentum flux due to the gravity waves with periods less than I h only accounts for 5&70% of the total fluxes (WANG and FRITTS, 1991). This suggests that the time scale separation in the actual atmosphere is not necessarily good enough to allow us to use the above-mentioned parameteri~tion. The spatial scale separation also may not be enough in the equatorial region, if the amplitude of the temperature oscillation of the diurnal tide is large. In this case, the local static stability N becomes small enough at some phases of the diurnal tide to make the vertical wavelength of the gravity waves long and make the WKB approximation invalid. In the above simulation the gravity-wave/tide interaction in the equatorial region is neglected to avoid this difficulty. Furthermore, in some large amplitude cases, the tidal fields may become convectively and/or dynamically unstable. The above parameterization is also not applicable for this case. A more comprehensive gravity wave breaking parameterization has to be developed to treat the interactions between tides and gravity waves under more general situations. 3.2. Resuh qfa general circulation model In order to see the gravity-wave/tide interaction more directly without using the gravity wave breaking parameterization, a preliminary analysis of diurnal tides in a middle atmosphere general circulation
S. MIYAHAKA and J. M.
1368
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model at Kyushu University has been conducted. The most energetic waves may be excited and present in the model, but the part of the spectrum responsible for most flux divergence is the waves having a horizontal wavelength about lOOkm, which is beyond the resolution of the model (and not part of the most energetic part of the spectrum). Gravity waves are generated in the model automatically by many physical processes included in the model, and their propa-
gation is explicitly calculated within the resolution of the model. The exponential growth of internal waves with height is suppressed locally by a convective adjustment process and by a local Richardson number dependent vertical eddy diffusion. The model description is found in MIYAHARA et al. (1992). The data used from the present analysis are obtained by a new version of the model, in which the molecular viscosity and conductivity are included in the lower thermo-
Diurnal tide and gravity wave interactions
1369
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Fig. 3. Lon~itudinaI distributions of the convergence of momentum flux due to breaking gravity waves (solid line), and the eastward wind component of the diurnal tide (dashed line) from MIYAHARAand FORBES(1991). (a) 20”N (winter hemisphere) ; (b)20”s (summer hemisphere).
that is used in the old version model to suppress the reflection by the top boundary. Figures 4(a) and (b) show the meridional crosssections of amplitude and phase of eastward winds of migrating diurnal tide, respectively. The amplitude has its peaks of the magnitude of 45 m s- ’ at 30” at about 100 km in both hemispheres. The phase distribution shows that the diurnal tide mainly consists sphere in place of the Rayleigh friction
of the St mode in the low latitude region, and consists of the negative mode in the high latitude region. The amplitude peaks are somewhat smaller than those of the self-breaking diurnal tide (about 60ms-‘) simulated by Wu et al. (1989) in which the amplitude of tide is limited by a convective adjustment scheme implemented in the model. This amplitude reduction may be due to the interactions between the tidal wave and gravity waves that are automatically excited in
S. MIYAHARA and J. M.
1370 AMPLITUDE OF MIGRATING
TIDE U (M/S)
FORHFS
(a)
PHASE OF MIGRATING TIDE U (LT)
40-
’
I
I
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-30
, 0
,, 30
60 LATlTUDE
LATITUDE
Ftp. 4. Meridional cross-sections of amplitude (a), and phase (b) of the migrating diurnal tide from Kyushu University GCM. Contour intervals are 5 m s- ’ for amplitude and 3 h for phase.
the model. Figures 5(a) and (b) show the 10 day mean of longitude-height distributions of vertical temperature gradient at 0200 and 1400 UTC at 2.8”N, respectively. A westward inclined wavenumber one structure is clearly seen in the lower thermosphere. This is associated with the migrating diurnal tide that propagates upward. The negative temperature gradient is greater than 10 K km s-- ‘. showing that the diurnal tidal field is convectively stable. However, this does not necessarily mean that the convective adjust-
DT/DZ AT02OOUTC
ment does not occur in the model. Figures 6(a) and (b) show the locations where the convective adjustment occurs at 0200 and 140OUTC in the IO days integration period, respectively. There is a tendency that the convective adjustment occurs in the region where the absolute value of the negative vertical temperature gradient is large. This means that the instantaneous temperature field is convcctively unstable in contrast to the fact that the IO day mean field is stable. Figure 7 shows an instantaneous vertical temperature gradi-
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Fig. 5. Longitude- height sections of the IO day mean vertical temperature gradient at 2.8 N from Kyushu University GCM. (a) 0200 UTC: 0-1)1400 UTC. Contour intervals arc 4 K km ‘.
90
Fig. 6. Longitude-hei#ht
0
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270
360
(a)
0
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1400UTC
LONGITUDE
180
DRY CONVECTION
fb)
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of the location where the convective adjustment occurs for the IO day period from Kyushu University GCM. (a) 0200 UTC; (b) 1400 UTC.
LONGITUDE
180
DRYCONVECTION0200UTC
Diurnal tide and gravity wave interactions DT/DZ AT OZOOUTC (INSTANTANEOUS)
0
90
180
270
1373
the superposed field of the diurnal tide and the gravity waves is unstable. Due to this superposition effect, the convective adjustment occurs at a smaller amplitude of diurnal tide than the case when only the diurnal tide exists. The convective adjustment limits the further growth of tidal amplitude with height by vertically mixing the temperature field. It is shown in the above analysis that the gravity waves act to suppress the diurnal tide through the convective instability. The momentum flux convergence associated with these breaking gravity waves may be acting to modify the tidal field in the model, if systematic gravity wave propagation and breaking occur in the model. A more thorough analysis of these preliminary results will be presented in a separate paper in the future.
360
LONGITUDE
Fig. 7. Longitude-height section of vertical temperature gradient at 2.8”N from Kyushu University GCM. Corresponding to instantaneous value at 020OUTC on the first simulation day. Contour intervals are 4 K km-.‘.
ent at 0200UTC of the first day. Comparing the 10 day mean value [Fig. 5(a)], the distribution has a smaller scale structure that can be attributable to the gravity waves in the model. These results suggest that the diurnal tidal field itself is convectively stable, but
AcknoM,ledgemenrs--J. M. Forbes acknowledges support from Grant ATM-9102200 from the National Science Foundation to Boston University. S. Miyahara acknowledges Y. Miyoshi, Y. Yoshida, T. Iwayama and E. M. P. Ekanayake for their GCM modeling and calculations. The National Center for Atmosphe~c Research is sponsored by the National Science Foundation. This study was supported by the ‘Studies of Global Environment Change with special reference to Asia and Pacific Regions-Integrated Development of Environmental Sciences of the World’, which is sponsored by the Japanese Ministry of Education, Science and Culture.
REFERENCES
Aso T. and VINCENTR. A. FORBES.J. M., Gu J. and M~YAHAKA S. FORBESJ. M. and HAGAN,M. E. FK~TTSD. C. and VINCENTR. A. LINXZENR. S. MATXJNOT. MIYAHARA S. and FORBF~J. M. MIYAHARA S., YOSHIDAY. and M~YOSHI Y. TSIJDAT., MURA~~~AM., YAMAMOTO M., KATOS. and FUKAOS. VIALF. and FORBESJ. M. VINCENTR. A. and BALLS. VINCENTR. A. and REIII 1. M. WALTERSCHEID R. L. WANG D.-Y. and FRITTSD. C. Wu D.-H., MIYAHAKA S, and MIYOSHIY.
1982
1991 1979 1987 1981 1982 1991 1992 1990 1989 1977
1983 1981 1991 1989
J.
atmos. terr. Phys. 44,267. Planet. Spuce Sci. 39, 1249. J. geophys. Res. 84, 803. J. atmos. Sci. 44, 605. J. geophys. Res. 86, 9707. J. met. Sot. Japan 60, 215. J. met. SM. Japan 69,523. J. atmos. terr. Phys. 55, 1039. Geophys. Rex. Lett. 17, 725. J. J. J. J. J. J.
atmos. terr. Phys. 51, 663. atmos. terr. Phys. 39, 956. atmos. Sci. 40, 1321. geophys. Res. 86, 9689. atmos. Sri. 48, 572. atmos. terr. Phys. 51, 1017.
Pergamon
0021-9169/94$7.00+0.00
Interactions between diurnal tides and gravity waves in the lower thermosphere S. MIYAHARA* and J. M.
FORBES?:
*Department of Earth and Planetary Sciences, Kyushu University, Fukuoka 8 12, Japan ; tHigh Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80303-3000. U.S.A. (Received in ,jinal,form Abstract-Recent upper mesosphere models.
15 June 1993 : accepted
I July 1993)
progress on interactions between breaking gravity waves and the diurnal and lower thermosphere
tide in the is reviewed, mainly based on the recent results of our numerical
1. INTRODUCTION
2. GRAVITY-WAVE/TIDEINTERACTION
The importance of stress due to dissipating internal gravity waves on larger scale motions in the upper mesosphere and lower thermosphere has been recognized since the pioneering works by LINDZEN (1981) and MATSUNO (1982). In their papers it is shown that the stress due to dissipating gravity waves acts to decelerate the zonal mean winds in the upper mesosphere and lower thermosphere. This effect of internal gravity waves on the mean winds is observationally confirmed by some radar observations (e.g. VINCENT and REID, 1983; FRITTS and VINCENT, 1987; TSUDA rt al., 1990). It is also observationally found that the mesospheric momentum flux due to gravity waves is modulated by the tidal frequency (FRITTS and VINCENT, 1987 ; WANG and FRITTS, 1991). FRITTS and VINCENT (1987) furthermore demonstrate that the modulated momentum flux divergence is sufficiently large to feed back and modify the tidal wind field. This hypothesis is supported by several numerical simulations (WALTERSCHEID,198 1; FORBESet al., 1991; MIYAHARA and FORBES, 1991). In the present paper the possible interactions between the diurnal tides and gravity waves are reviewed mainly based on the recent numerical results of our models. In Section 2, the idea of gravity-wave/ tide interaction proposed by FRITTS and VINCENT (1987) is briefly reviewed. In Section 3, some recent numerical results of our models are shown, and some unsolved problems are discussed.
Many aspects of gravity-wave/tide interactions are adequately reviewed by VIAL and FORBES (1989), so in the present paper only the basic idea of the breaking gravity-wave/tide interaction proposed by FRITTS and VINCENT (1987) is considered. In their model, parameterization of the momentum deposition by a monochromatic breaking gravity wave proposed by LINDZEN (1981) is applied to the gravity-wave/tide interaction. The momentum flux convergence due to a breaking gravity wave in the combined zonal mean and tidal winds is given by
:On leave from the Department of Aerospace and Mechanical Engineering and the Center for Space Physics, Boston University, Boston, MA 02215. U.S.A.
provided
that
where z is the altitude, zh the braking height, p the pressure, G the local zonal wind (zonal mean wind +zonal wind of the tide), tiZ the vertical shear of d, k the zonal wavenumber of the gravity wave, c the zonal phase velocity of the gravity wave, N the static stability and H the scale height. In this parameterization, the vertical propagation of the gravity wave is controlled by the locally combined zonal mean and tidal winds, so that the convergence has a tendency to decelerate the local wind speed. This effect will change the amplitude and phase of the tidal waves. It is observationally confirmed that the momentum flux due to short time scale gravity waves (periods are less than 1h) has the out-of-phase correlation with the back-
1365
S.
1366
MIYAHARA and J. M. FORBES
ground tidal winds, which supports the above parameterization, at least qualitatively (WANG and FRITTS, 1991). The original Lindzen’s parameterization assumes that the gravity waves break down after they achieve steady state. In the present situation, the steadiness is violated due to the existence of the time varying background wind field. However. the above parameterization is valid as a first approximation, if the vertical propagation of gravity waves is much faster than the tidally induced change in the background wind field. The WKB approximation is also used to derive the parameterization. In this approximation, the vertical wavelengths of the gravity waves are assumed to be much shorter than the typical vertical scale of the background wind field. There is a possibility of violation of this assumption in some cases due to the presence of the tide. These issues are closely related to the time scale and spatial scale separations between the gravity waves and tide. This will be mentioned in the next section. 3. SIMULATiONS OF GRAVITY-WAVELIKE INTERACTION 3.1. Results model
qfgravity
wuve breaking parameterization
It is shown by FORBESet al. (1991), using the abovementioned parameterization and the f-plane approximation of diurnal tide (FORBESand HAGAN, 1979) that breaking gravity waves with phase velocities of
0, 5 15, + 30 m s- ’ act to suppress the diurnal tide, and that the momentum flux convergence can induce tides having other frequencies (e.g. the semidiurnal tides). Figures I(a) and (b) show the time height sections of the local mean wind and the acceleration due to the breaking gravity waves by their model. The out-of-phase correlation between the local mean winds and the acceleration is evident. This out-ofmomentum flux convergence associated with the breaking gravity waves acts to suppress the tidal amplitude. It is also shown that the tidal modulation of the mean winds opens some channels of propagation of gravity waves into the lower thermosphere. The above approach has been extended into a twodimensional time-dependent numerical tidal model, in which gravity-wave/tide interactions are calculated at each spatial grid point and each time step to feedbackthemomentumfluxconvergencetothemomenturn equation of the tides (MIYAHARAand FORBES, 1991). Figures 2(a) and (b) show the meridional cross-sections of amplitude of the eastward wind of the diurnal tide obtained by the models with and without gravity wave interactions, respectively. The amplitude of the diurnal tide is suppressed by the momentum flux convergence of the breaking gravity waves. Moreover, the altitude of maximum is lowered, more consistent with observations (e.g. ASO and VINCENT.1981; VINCENTand BALL, 1977). As shown in MIYAHARAand FORBES(1991) this amplitude suppression is accompanied by a shift of about 2 h phase to earlier (later) local times equatorward (poleward)
ACCELEIUTION
100 P E ;a
80
80
Fig. I. (a) Total wind field at 6” latitude from f-plane calculation by FORBES et al. (1991). Contour intervals are 10m s- ‘. (b) Time-height section of acceleration (m se”’ day- ‘) due to breaking gravity waves from fplane calculation by FORBES~~ al, (1991). Contour intervals are 10m s-’ day- ‘. From FORBES~~al. (1991).
Diurnal tide and gravity wave interactions AWLINDE
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LpiT I TUDE Fig. 2. Meridional cross-sections of amplitude (m s- ‘) of the eastward wind of the diurnal tide from the two-dimensional model of MIYAHARAand FORBES (1991). (a) with gravitywave/tide interaction ; (b) non-interaction case. Contour intervals are 10 rns- ‘_ of 40“ latitude. The longitudinal dist~butions of the momentum flux convergence are shown in Fig. 3 to show the out-of-phase correlations with the diurnal tidal winds at both the winter and summer hemispheres. It is notable that the longitudes where the momentum flux divergences have their peaks shift almost 180’ between both hemispheres. This is because in the winter (summer) hemisphere the westward (eastward) moving gravity wives are breaking at the longitudes where the zonal winds of the tide are in a westerly (easterly) phase. This situation is confirmed by the strong out-of-phase correlation between the zonal distributions of divergence and that of the zonal winds of tides at 5 km lower heights, approximately where the gravity waves are considered to be breaking.
1367
This figure shows the asymmetric distribution of tidal amplitude between the winter and summer hemispheres. The amplitude is stronger in the winter hemisphere than that in the summer hemisphere. This asymmetry is mainly due to the effect of mean background wind. In this model the gravity wave source is assumed to be symmetric between both hemispheres. In the real atmosphere, the gravity wave source may be different in each hemisphere, and this asymmetric distribution of gravity waves may cause asymmetric tidal amplitudes in the middle atmosphere. This effect must be taken into account in future studies of gravity-wave~tjde interactions. As shown in this figure, the longitudinal distribution of the convergence does not have a sinusoidal wave form, but consists of many zonai wavenumbers, and it generates the semidiurnal and terdiurnal tides of amplitudes of 5 m se ’ or less in the lower thermosphere. As mentioned in Section 2, spatial scale and time scale separations between the gravity waves and tides are assumed in applying the wave-mean flow parameterization of LENDZEN (1981). The time scale separation may be good enough if we can confine our discussion to the fast propagating gravity waves. However, the momentum flux due to the gravity waves with periods less than I h only accounts for 5&70% of the total fluxes (WANG and FRITTS, 1991). This suggests that the time scale separation in the actual atmosphere is not necessarily good enough to allow us to use the above-mentioned parameteri~tion. The spatial scale separation also may not be enough in the equatorial region, if the amplitude of the temperature oscillation of the diurnal tide is large. In this case, the local static stability N becomes small enough at some phases of the diurnal tide to make the vertical wavelength of the gravity waves long and make the WKB approximation invalid. In the above simulation the gravity-wave/tide interaction in the equatorial region is neglected to avoid this difficulty. Furthermore, in some large amplitude cases, the tidal fields may become convectively and/or dynamically unstable. The above parameterization is also not applicable for this case. A more comprehensive gravity wave breaking parameterization has to be developed to treat the interactions between tides and gravity waves under more general situations. 3.2. Resuh qfa general circulation model In order to see the gravity-wave/tide interaction more directly without using the gravity wave breaking parameterization, a preliminary analysis of diurnal tides in a middle atmosphere general circulation
S. MIYAHAKA and J. M.
1368
FORBES
(a)
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model at Kyushu University has been conducted. The most energetic waves may be excited and present in the model, but the part of the spectrum responsible for most flux divergence is the waves having a horizontal wavelength about lOOkm, which is beyond the resolution of the model (and not part of the most energetic part of the spectrum). Gravity waves are generated in the model automatically by many physical processes included in the model, and their propa-
gation is explicitly calculated within the resolution of the model. The exponential growth of internal waves with height is suppressed locally by a convective adjustment process and by a local Richardson number dependent vertical eddy diffusion. The model description is found in MIYAHARA et al. (1992). The data used from the present analysis are obtained by a new version of the model, in which the molecular viscosity and conductivity are included in the lower thermo-
Diurnal tide and gravity wave interactions
1369
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0 -10
360
Fig. 3. Lon~itudinaI distributions of the convergence of momentum flux due to breaking gravity waves (solid line), and the eastward wind component of the diurnal tide (dashed line) from MIYAHARAand FORBES(1991). (a) 20”N (winter hemisphere) ; (b)20”s (summer hemisphere).
that is used in the old version model to suppress the reflection by the top boundary. Figures 4(a) and (b) show the meridional crosssections of amplitude and phase of eastward winds of migrating diurnal tide, respectively. The amplitude has its peaks of the magnitude of 45 m s- ’ at 30” at about 100 km in both hemispheres. The phase distribution shows that the diurnal tide mainly consists sphere in place of the Rayleigh friction
of the St mode in the low latitude region, and consists of the negative mode in the high latitude region. The amplitude peaks are somewhat smaller than those of the self-breaking diurnal tide (about 60ms-‘) simulated by Wu et al. (1989) in which the amplitude of tide is limited by a convective adjustment scheme implemented in the model. This amplitude reduction may be due to the interactions between the tidal wave and gravity waves that are automatically excited in
S. MIYAHARA and J. M.
1370 AMPLITUDE OF MIGRATING
TIDE U (M/S)
FORHFS
(a)
PHASE OF MIGRATING TIDE U (LT)
40-
’
I
I
-60
-30
, 0
,, 30
60 LATlTUDE
LATITUDE
Ftp. 4. Meridional cross-sections of amplitude (a), and phase (b) of the migrating diurnal tide from Kyushu University GCM. Contour intervals are 5 m s- ’ for amplitude and 3 h for phase.
the model. Figures 5(a) and (b) show the 10 day mean of longitude-height distributions of vertical temperature gradient at 0200 and 1400 UTC at 2.8”N, respectively. A westward inclined wavenumber one structure is clearly seen in the lower thermosphere. This is associated with the migrating diurnal tide that propagates upward. The negative temperature gradient is greater than 10 K km s-- ‘. showing that the diurnal tidal field is convectively stable. However, this does not necessarily mean that the convective adjust-
DT/DZ AT02OOUTC
ment does not occur in the model. Figures 6(a) and (b) show the locations where the convective adjustment occurs at 0200 and 140OUTC in the IO days integration period, respectively. There is a tendency that the convective adjustment occurs in the region where the absolute value of the negative vertical temperature gradient is large. This means that the instantaneous temperature field is convcctively unstable in contrast to the fact that the IO day mean field is stable. Figure 7 shows an instantaneous vertical temperature gradi-
DT/DZ AT 1400UTC
(aI
(bl
oc; \ \ . 90:
8C-
,\
Co
.-I
7c.',:I. ,41 0 90
I
,
, ,, 180
LONGITUDE
,
I
, ,,.::-, ,', 360 270
70: 0
-_\, I,,,
90
,;:4.,‘...I:
180
,:I
270
.,,,
'360
LONGITUDE
Fig. 5. Longitude- height sections of the IO day mean vertical temperature gradient at 2.8 N from Kyushu University GCM. (a) 0200 UTC: 0-1)1400 UTC. Contour intervals arc 4 K km ‘.
90
Fig. 6. Longitude-hei#ht
0
distributions
270
360
(a)
0
90
270
1400UTC
LONGITUDE
180
DRY CONVECTION
fb)
360
of the location where the convective adjustment occurs for the IO day period from Kyushu University GCM. (a) 0200 UTC; (b) 1400 UTC.
LONGITUDE
180
DRYCONVECTION0200UTC
Diurnal tide and gravity wave interactions DT/DZ AT OZOOUTC (INSTANTANEOUS)
0
90
180
270
1373
the superposed field of the diurnal tide and the gravity waves is unstable. Due to this superposition effect, the convective adjustment occurs at a smaller amplitude of diurnal tide than the case when only the diurnal tide exists. The convective adjustment limits the further growth of tidal amplitude with height by vertically mixing the temperature field. It is shown in the above analysis that the gravity waves act to suppress the diurnal tide through the convective instability. The momentum flux convergence associated with these breaking gravity waves may be acting to modify the tidal field in the model, if systematic gravity wave propagation and breaking occur in the model. A more thorough analysis of these preliminary results will be presented in a separate paper in the future.
360
LONGITUDE
Fig. 7. Longitude-height section of vertical temperature gradient at 2.8”N from Kyushu University GCM. Corresponding to instantaneous value at 020OUTC on the first simulation day. Contour intervals are 4 K km-.‘.
ent at 0200UTC of the first day. Comparing the 10 day mean value [Fig. 5(a)], the distribution has a smaller scale structure that can be attributable to the gravity waves in the model. These results suggest that the diurnal tidal field itself is convectively stable, but
AcknoM,ledgemenrs--J. M. Forbes acknowledges support from Grant ATM-9102200 from the National Science Foundation to Boston University. S. Miyahara acknowledges Y. Miyoshi, Y. Yoshida, T. Iwayama and E. M. P. Ekanayake for their GCM modeling and calculations. The National Center for Atmosphe~c Research is sponsored by the National Science Foundation. This study was supported by the ‘Studies of Global Environment Change with special reference to Asia and Pacific Regions-Integrated Development of Environmental Sciences of the World’, which is sponsored by the Japanese Ministry of Education, Science and Culture.
REFERENCES
Aso T. and VINCENTR. A. FORBES.J. M., Gu J. and M~YAHAKA S. FORBESJ. M. and HAGAN,M. E. FK~TTSD. C. and VINCENTR. A. LINXZENR. S. MATXJNOT. MIYAHARA S. and FORBF~J. M. MIYAHARA S., YOSHIDAY. and M~YOSHI Y. TSIJDAT., MURA~~~AM., YAMAMOTO M., KATOS. and FUKAOS. VIALF. and FORBESJ. M. VINCENTR. A. and BALLS. VINCENTR. A. and REIII 1. M. WALTERSCHEID R. L. WANG D.-Y. and FRITTSD. C. Wu D.-H., MIYAHAKA S, and MIYOSHIY.
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