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## Abstract

Substantial variations in density, temperature and winds in the high-latitude thermosphere during geomagnetic substorms have been recorded using a wide variety of observational techniques. The disturbed state of the thermosphere may be brought about by a sudden addition of heat or momentum. The heating may be due either to Joule heating or energetic particle precipitation, and the momentum source is due to the drag that neutrals feel when colliding with ions. We have studied dynamical adjustment of the disturbed high-latitude thermosphere toward geostrophic equilibrium using an idealized high-resolution time-dependent scale model that includes the effects of the earth's rotation. The model describes the response of a compressible stratified atmosphere to horizontally and vertically extended sources. Our results show that the effect of rotation depends strongly upon the type and vertical scale of the forcing. In the ion-drag case, the pressure gradients that are required to maintain steady balanced motion develop slowly if the forcing is in a shallow layer, and much of the energy of the initial flow goes into inertial-gravity waves; but if the forcing is in a deep layer, pressure gradients develop quickly and most of the initial energy comes into geostrophic balance in a time much less than the inertial time scale. In the heating case there is little residual motion in the source region unless the forcing is quite shallow. For deep forcing the initial energy is transported away by inertial-gravity waves.

## Abstract

Substantial variations in density, temperature and winds in the high-latitude thermosphere during geomagnetic substorms have been recorded using a wide variety of observational techniques. The disturbed state of the thermosphere may be brought about by a sudden addition of heat or momentum. The heating may be due either to Joule heating or energetic particle precipitation, and the momentum source is due to the drag that neutrals feel when colliding with ions. We have studied dynamical adjustment of the disturbed high-latitude thermosphere toward geostrophic equilibrium using an idealized high-resolution time-dependent scale model that includes the effects of the earth's rotation. The model describes the response of a compressible stratified atmosphere to horizontally and vertically extended sources. Our results show that the effect of rotation depends strongly upon the type and vertical scale of the forcing. In the ion-drag case, the pressure gradients that are required to maintain steady balanced motion develop slowly if the forcing is in a shallow layer, and much of the energy of the initial flow goes into inertial-gravity waves; but if the forcing is in a deep layer, pressure gradients develop quickly and most of the initial energy comes into geostrophic balance in a time much less than the inertial time scale. In the heating case there is little residual motion in the source region unless the forcing is quite shallow. For deep forcing the initial energy is transported away by inertial-gravity waves.

## Abstract

Calculations of the semidiurnal atmospheric tide at the equinoxes using improved heating rates and realistic mean winds and temperatures are presented. The heating rates for equinox are quite similar to those reported by Forbes and Garrett (1978) and significantly different from those of Lindzen and Hong (1974).

The basic conclusions of this study based on present heating rates are as follows: 1) Although effects of mean-wind-related (nonclassical) generation are clearly discernible, the improved agreement with observations of the present study over earlier classical studies with respect to wavelengths in the region 80â€“115 km is due primarily to the present heating rates rather than nonclassical effects; 2) with present heating rates there is no phase shift below 30 km as predicted by the earlier classical model; 3) without nonclassical effects the amplitude of the barometric tide is significantly underpredicted; 4) the solutions with nonclassical effects do not reproduce the rather large observed seasonal differences at the equinoxes; and 5) the sensitivity of resultant waves exhibiting substantial destructive interference to changes in the phases of the antisymmetric components may help to explain the large observed intermonthly and inter-annual variability in the meteor region.

## Abstract

Calculations of the semidiurnal atmospheric tide at the equinoxes using improved heating rates and realistic mean winds and temperatures are presented. The heating rates for equinox are quite similar to those reported by Forbes and Garrett (1978) and significantly different from those of Lindzen and Hong (1974).

The basic conclusions of this study based on present heating rates are as follows: 1) Although effects of mean-wind-related (nonclassical) generation are clearly discernible, the improved agreement with observations of the present study over earlier classical studies with respect to wavelengths in the region 80â€“115 km is due primarily to the present heating rates rather than nonclassical effects; 2) with present heating rates there is no phase shift below 30 km as predicted by the earlier classical model; 3) without nonclassical effects the amplitude of the barometric tide is significantly underpredicted; 4) the solutions with nonclassical effects do not reproduce the rather large observed seasonal differences at the equinoxes; and 5) the sensitivity of resultant waves exhibiting substantial destructive interference to changes in the phases of the antisymmetric components may help to explain the large observed intermonthly and inter-annual variability in the meteor region.

## Abstract

A numerical simulation of the nonlinear evolution of an upward propagating gravity wave shows that over-turning (the turning over of isopotential temperature surfaces) is the mechanism responsible for limiting the growth of the wave. Wave saturation (the state in which wave amplitude is constant with height) in the mesosphere results in turbulence (random, subkilometer-scale motions), but turbulence is not responsible for limiting wave amplitude. Therefore, parameterizations of wave drag and wave-associated eddy diffusivity that derive from the turbulence model of wave saturation have no rigorous justification and could give erroneous results if employed in studies of middle atmosphere circulation and minor constituent mixing. The immediate consequence of wave overturning is small-scale convection (regular, cellular structures with length scales of several to tens of kilometers) in the moving unstable phases of the wave. Cellular convection grows at the expense of the wave and provides a stabilization of the gross stratification. Convection ultimately decays into turbulence. Strong residual gradients in stratification are removed by the turbulence. Turbulence is primarily an end product of the overturning process that limits wave amplitude. Strong overturning is possible before the onset of convection, and, as a result, the transport of heat and constituents is up, rather than down, the mean gradient over the unstable phase of the wave. Net heat and constituent transports over the entire phase of the wave are reduced by the counter-mean gradient contributions to the transports. Overturning is confined to only a limited region of the wave (the unstable phase); it leads to localization of intense convection and turbulence. Extremely large values of mixing would be required to halt wave growth without a significant degree of overturning. The effects of localization on eddy diffusivity parameterizations may be incorporated through multiplication of the Lindzen eddy diffusivity by the factor [1 âˆ’ (Î´/2Ï€) sin(2&pi/*Î´*)]^{âˆ’1} where 1/*Î´* is the fraction of the wave involved in turbulence. Wave kinetic energy rapidly reaches a level of slow growth during the nonlinear growth of the wave and then rapidly decreases after the onset of convection. In contrast, wave available potential energy increases monotonically until convection begins, at which time it exceeds wave kinetic energy by a large amount. Self-acceleration of the wave retards self-destruction through critical level formation in the accelerated mean flow. The Doppler-shifted phase speed is relatively constant with height as a consequence of self-acceleration and the tendency for the prevalence of faster waves, excited by the finite duration of forcing, to increase with altitude. Wave transience is responsible for generating a substantial mean wind which persists in the region of wave breakdown. The normal growth with height of transient nonlinear gravity waves is substantially less than the inverse square root of density growth because breakdown occurs before a steady state can be established through a deep layer, and because wave energy flux is diminished to supply the conversion of wave kinetic energy to wave available potential energy. As a consequence, wave momentum fluxes vary with height approximately as if the wave had reached constant amplitude, even prior to breakdown by overturning. Therefore, observations of limited wave growth with height may reflect the natural and gradual nonlinear evolution of upward propagating gravity waves rather than their breakdown and saturation.

## Abstract

A numerical simulation of the nonlinear evolution of an upward propagating gravity wave shows that over-turning (the turning over of isopotential temperature surfaces) is the mechanism responsible for limiting the growth of the wave. Wave saturation (the state in which wave amplitude is constant with height) in the mesosphere results in turbulence (random, subkilometer-scale motions), but turbulence is not responsible for limiting wave amplitude. Therefore, parameterizations of wave drag and wave-associated eddy diffusivity that derive from the turbulence model of wave saturation have no rigorous justification and could give erroneous results if employed in studies of middle atmosphere circulation and minor constituent mixing. The immediate consequence of wave overturning is small-scale convection (regular, cellular structures with length scales of several to tens of kilometers) in the moving unstable phases of the wave. Cellular convection grows at the expense of the wave and provides a stabilization of the gross stratification. Convection ultimately decays into turbulence. Strong residual gradients in stratification are removed by the turbulence. Turbulence is primarily an end product of the overturning process that limits wave amplitude. Strong overturning is possible before the onset of convection, and, as a result, the transport of heat and constituents is up, rather than down, the mean gradient over the unstable phase of the wave. Net heat and constituent transports over the entire phase of the wave are reduced by the counter-mean gradient contributions to the transports. Overturning is confined to only a limited region of the wave (the unstable phase); it leads to localization of intense convection and turbulence. Extremely large values of mixing would be required to halt wave growth without a significant degree of overturning. The effects of localization on eddy diffusivity parameterizations may be incorporated through multiplication of the Lindzen eddy diffusivity by the factor [1 âˆ’ (Î´/2Ï€) sin(2&pi/*Î´*)]^{âˆ’1} where 1/*Î´* is the fraction of the wave involved in turbulence. Wave kinetic energy rapidly reaches a level of slow growth during the nonlinear growth of the wave and then rapidly decreases after the onset of convection. In contrast, wave available potential energy increases monotonically until convection begins, at which time it exceeds wave kinetic energy by a large amount. Self-acceleration of the wave retards self-destruction through critical level formation in the accelerated mean flow. The Doppler-shifted phase speed is relatively constant with height as a consequence of self-acceleration and the tendency for the prevalence of faster waves, excited by the finite duration of forcing, to increase with altitude. Wave transience is responsible for generating a substantial mean wind which persists in the region of wave breakdown. The normal growth with height of transient nonlinear gravity waves is substantially less than the inverse square root of density growth because breakdown occurs before a steady state can be established through a deep layer, and because wave energy flux is diminished to supply the conversion of wave kinetic energy to wave available potential energy. As a consequence, wave momentum fluxes vary with height approximately as if the wave had reached constant amplitude, even prior to breakdown by overturning. Therefore, observations of limited wave growth with height may reflect the natural and gradual nonlinear evolution of upward propagating gravity waves rather than their breakdown and saturation.

## Abstract

Owing to the stochastic action of Stokes drift induced by a spectrum of noninteracting gravity waves, a parcel of air subject to a spectrum of randomly superposed waves will be displaced, on average, an increasing distance from an initial position as time goes on. The effect of this drift on an ensemble of parcels is to induce a diffusive-like growth in time of the mean-square separation between parcels. We refer to this process as Stokes diffusion. We have calculated trajectories for an ensemble of parcels moving under the influence of a spectrum of gravity waves and have found vertical diffusion coefficients inferred from the dispersion of parcels on the order of 10^{2} m s^{âˆ’2}, which is comparable to the values usually attributed to turbulence. If a constituent is distributed as a function of potential temperature, the dispersion due to conservative waves is not apt to accomplish a significant vertical transport. However, if the constituent has a significant gradient on wave-perturbed potential temperature surfaces, this dispersion might be an important cause of vertical transport in the mesosphere.

## Abstract

Owing to the stochastic action of Stokes drift induced by a spectrum of noninteracting gravity waves, a parcel of air subject to a spectrum of randomly superposed waves will be displaced, on average, an increasing distance from an initial position as time goes on. The effect of this drift on an ensemble of parcels is to induce a diffusive-like growth in time of the mean-square separation between parcels. We refer to this process as Stokes diffusion. We have calculated trajectories for an ensemble of parcels moving under the influence of a spectrum of gravity waves and have found vertical diffusion coefficients inferred from the dispersion of parcels on the order of 10^{2} m s^{âˆ’2}, which is comparable to the values usually attributed to turbulence. If a constituent is distributed as a function of potential temperature, the dispersion due to conservative waves is not apt to accomplish a significant vertical transport. However, if the constituent has a significant gradient on wave-perturbed potential temperature surfaces, this dispersion might be an important cause of vertical transport in the mesosphere.

## Abstract

A spectral theory is developed for the solar semidiurnal tides in an atmosphere with background zonal winds. According to this theory, the vertical structures of the spectral components of the tide are governed by a set of coupled second-order ordinary differential equations which have to be solved for appropriate lower and upper boundary conditions. The lower boundary condition, in particular, has to be properly formulated to take into account the latitudinal variation of the atmospheric basic-state parameters. While the solutions to the equations have to be obtained by numerical methods, several aspects of their behavior can be revealed by simpler mechanistic models and concepts which are introduced in this first part (Part I) of a two-part report. Discussion of the detailed numerical solutions and of the adequacy of their mechanistic interpretations is given in the companion paper (Part II).

## Abstract

A spectral theory is developed for the solar semidiurnal tides in an atmosphere with background zonal winds. According to this theory, the vertical structures of the spectral components of the tide are governed by a set of coupled second-order ordinary differential equations which have to be solved for appropriate lower and upper boundary conditions. The lower boundary condition, in particular, has to be properly formulated to take into account the latitudinal variation of the atmospheric basic-state parameters. While the solutions to the equations have to be obtained by numerical methods, several aspects of their behavior can be revealed by simpler mechanistic models and concepts which are introduced in this first part (Part I) of a two-part report. Discussion of the detailed numerical solutions and of the adequacy of their mechanistic interpretations is given in the companion paper (Part II).

## Abstract

Classical and nonclassical model calculations have been performed for the solar semidiurnal tidal oscillations in the earth's atmosphere, for prescribed basic-state parameters and heating functions appropriate for the solstitial seasons when the nonclassical effects associated with the mean zonal wind are expected to be maximum. It is found that the enrichment of the higher order spectral components characteristic of the nonclassical model is due to the cross-coupling rather than the self-coupling of the spectral components in the model. These cross-coupling effects are shown to be sufficiently well represented by a mode-coupling model described in Section 3 of Part I. As explained in Part I, the effect of cross-coupling may be considered as some kind of indirect forcing. Such indirect forcing, which can be applied either at the lower boundary or inside the medium, is obtained and compared for each spectral component with the direct thermal forcing.

It is demonstrated that the actual behavior of a particular spectral component (such as the *m*=4 component whose enrichment is an important aspect of the nonclassical model) in the progressive wave regime (where waves forced from below dominate) can be explained as the net result of forcings, both direct and indirect, at the lower boundary and from different altitude regions above. Results of our model calculations for wind, temperature and pressure oscillations are compared with available observations at various altitudes. While this comparison succeeds in exposing definite nonclassical influences in the observations, it also reveals significant inadequacies of our model.

## Abstract

Classical and nonclassical model calculations have been performed for the solar semidiurnal tidal oscillations in the earth's atmosphere, for prescribed basic-state parameters and heating functions appropriate for the solstitial seasons when the nonclassical effects associated with the mean zonal wind are expected to be maximum. It is found that the enrichment of the higher order spectral components characteristic of the nonclassical model is due to the cross-coupling rather than the self-coupling of the spectral components in the model. These cross-coupling effects are shown to be sufficiently well represented by a mode-coupling model described in Section 3 of Part I. As explained in Part I, the effect of cross-coupling may be considered as some kind of indirect forcing. Such indirect forcing, which can be applied either at the lower boundary or inside the medium, is obtained and compared for each spectral component with the direct thermal forcing.

It is demonstrated that the actual behavior of a particular spectral component (such as the *m*=4 component whose enrichment is an important aspect of the nonclassical model) in the progressive wave regime (where waves forced from below dominate) can be explained as the net result of forcings, both direct and indirect, at the lower boundary and from different altitude regions above. Results of our model calculations for wind, temperature and pressure oscillations are compared with available observations at various altitudes. While this comparison succeeds in exposing definite nonclassical influences in the observations, it also reveals significant inadequacies of our model.

## Abstract

Temperatures and pressures inferred from radio occultation data acquired by the *Pioneer Venus* orbiter between September 1982 and November 1983 are used to derive cyclostrophic zonal winds in the middle atmosphere of Venus (1350 to 2.1 mb, 10Â° to 70Â° latitude). The main feature of the wind field is a jet positioned just above the cloud tops at 70 km and â‰ˆ48Â° latitude. The maximum speed of the jet is about 130 m s^{âˆ’1}. A comparison with results of similar analyses on *Pioneer Venus* radio occultation data obtained between December 1978 and October 1981 suggests an equatorward shift of the jet and a decrease in jet speed during this five-year time interval. It is proposed that the poleward transport of westward zonal momentum by the upper branch of the cloud level Hadley cell supplies the excess momentum of the jet and maintains it against dissipation. The location of the jet thereby provides a minimum estimate of the latitudinal extent of the Hadley cell. Cyclostrophic zonal wind velocities decrease with height above about 70â€“75 km. It is suggested that this deceleration of the superrotation in equatorial latitudes is due to the dissipation of vertically propagating thermal tides forced primarily at altitudes around 65 km.

## Abstract

Temperatures and pressures inferred from radio occultation data acquired by the *Pioneer Venus* orbiter between September 1982 and November 1983 are used to derive cyclostrophic zonal winds in the middle atmosphere of Venus (1350 to 2.1 mb, 10Â° to 70Â° latitude). The main feature of the wind field is a jet positioned just above the cloud tops at 70 km and â‰ˆ48Â° latitude. The maximum speed of the jet is about 130 m s^{âˆ’1}. A comparison with results of similar analyses on *Pioneer Venus* radio occultation data obtained between December 1978 and October 1981 suggests an equatorward shift of the jet and a decrease in jet speed during this five-year time interval. It is proposed that the poleward transport of westward zonal momentum by the upper branch of the cloud level Hadley cell supplies the excess momentum of the jet and maintains it against dissipation. The location of the jet thereby provides a minimum estimate of the latitudinal extent of the Hadley cell. Cyclostrophic zonal wind velocities decrease with height above about 70â€“75 km. It is suggested that this deceleration of the superrotation in equatorial latitudes is due to the dissipation of vertically propagating thermal tides forced primarily at altitudes around 65 km.

## Abstract

Calculations of the semidiurnal atmospheric tide at solstice using improved heating rates are presented. The heating rates for solar absorption by water vapor are based on a global water vapor distribution (Jenne, 1969, 1975; Jenne *et al*., 1974), the data of McClatchey *et al*. (1972), and an absorptivity parameterization of Lacis and Hansen (1974); rates for solar absorption by ozone are based on the midlatitude ozone distribution of the U.S. Standard Atmosphere (COESA, 1976) and detailed radiative calculations using the solar fluxes and absorption cross sections of Ackerman (1971) with the Schumann-Runge band cross sections of Kockarts (1971). The heating rates for solstice are quite similar to those reported by Forbes and Garrett (1978) and significantly different from those of Lindzen and Hong (1974), which were used in the previous study of Walterscheid and Venkateswaran (1979b) investigating the influence of mean zonal motion and meridional temperature gradients on the solar semidiurnal tide.

The basic conclusions of this study based on the present heating rates are as follows: 1) Although effects of mean-wind related (nonclassical) generation are clearly discernible, the improved agreement with observations of the present results over those with the earlier rates with respect to wave-lengths of the semidiurnal tidal oscillations in the lower thermosphere (100â€“115 km) and with respect to both their wavelengths and amplitudes in the region (80â€“100 km) is primarily attributable to the improved heating rates; 2) without nonclassical generation the calculations exhibit a phase shift below 30 km in disagreement with observations; and 3) without mean-wind related effects the amplitude of the surface pressure oscillation is significantly underpredicted.

## Abstract

Calculations of the semidiurnal atmospheric tide at solstice using improved heating rates are presented. The heating rates for solar absorption by water vapor are based on a global water vapor distribution (Jenne, 1969, 1975; Jenne *et al*., 1974), the data of McClatchey *et al*. (1972), and an absorptivity parameterization of Lacis and Hansen (1974); rates for solar absorption by ozone are based on the midlatitude ozone distribution of the U.S. Standard Atmosphere (COESA, 1976) and detailed radiative calculations using the solar fluxes and absorption cross sections of Ackerman (1971) with the Schumann-Runge band cross sections of Kockarts (1971). The heating rates for solstice are quite similar to those reported by Forbes and Garrett (1978) and significantly different from those of Lindzen and Hong (1974), which were used in the previous study of Walterscheid and Venkateswaran (1979b) investigating the influence of mean zonal motion and meridional temperature gradients on the solar semidiurnal tide.

The basic conclusions of this study based on the present heating rates are as follows: 1) Although effects of mean-wind related (nonclassical) generation are clearly discernible, the improved agreement with observations of the present results over those with the earlier rates with respect to wave-lengths of the semidiurnal tidal oscillations in the lower thermosphere (100â€“115 km) and with respect to both their wavelengths and amplitudes in the region (80â€“100 km) is primarily attributable to the improved heating rates; 2) without nonclassical generation the calculations exhibit a phase shift below 30 km in disagreement with observations; and 3) without mean-wind related effects the amplitude of the surface pressure oscillation is significantly underpredicted.

## Abstract

Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the StratÃ©ole program reveal a peak with a frequency near 0.10 h^{âˆ’1}, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h^{âˆ’1} can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.

## Abstract

Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the StratÃ©ole program reveal a peak with a frequency near 0.10 h^{âˆ’1}, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h^{âˆ’1} can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.

## Abstract

A two-dimensional pole-to-pole numerical model with background solstitial winds has been used to study the global dynamical response of the thermosphere to high-latitude energy inputs associated with a model geomagnetic storm. This model storm has four distinct pulses of heat input over a 12-h period.

The thermospheric wave response to the sustained part of the storm heat input consists in the establishment of a global meridional circulation that is initiated in about 3 to 4 hours after storm commencement and never quite reaches steady state in the simulation.

The main purpose of this study is to investigate the interaction between the disturbances and the mean meridional flow associated with the storm. It is shown that this interaction can be represented in terms of an induced circulation. This induced circulation is forced by the transient nature of the eddy flux convergences (divergences) of heat and momentum. The equivalent temperature changes due to the induced circulation are one-third to one-fourth of the changes due to the mean meridional circulation at altitudes above 150 km in the equatorial region.

Spatial and temporal variations of the storm-time winds are responsible for the differences between Lagrangian and mean Eulerian trajectories of individual fluid elements. Such trajectory calculations show that the material transport of fluid does not occur all the way from the source regions to the equator. However, storm-generated waves, reaching the equator within 3 hours of storm onset, initiate fluid motions at low latitudes.

## Abstract

A two-dimensional pole-to-pole numerical model with background solstitial winds has been used to study the global dynamical response of the thermosphere to high-latitude energy inputs associated with a model geomagnetic storm. This model storm has four distinct pulses of heat input over a 12-h period.

The thermospheric wave response to the sustained part of the storm heat input consists in the establishment of a global meridional circulation that is initiated in about 3 to 4 hours after storm commencement and never quite reaches steady state in the simulation.

The main purpose of this study is to investigate the interaction between the disturbances and the mean meridional flow associated with the storm. It is shown that this interaction can be represented in terms of an induced circulation. This induced circulation is forced by the transient nature of the eddy flux convergences (divergences) of heat and momentum. The equivalent temperature changes due to the induced circulation are one-third to one-fourth of the changes due to the mean meridional circulation at altitudes above 150 km in the equatorial region.

Spatial and temporal variations of the storm-time winds are responsible for the differences between Lagrangian and mean Eulerian trajectories of individual fluid elements. Such trajectory calculations show that the material transport of fluid does not occur all the way from the source regions to the equator. However, storm-generated waves, reaching the equator within 3 hours of storm onset, initiate fluid motions at low latitudes.