Atmospheric tide

They can be excited by: The largest-amplitude atmospheric tides are mostly generated in the troposphere and stratosphere when the atmosphere is periodically heated, as water vapor and ozone absorb solar radiation during the day.

These tides propagate away from the source regions and ascend into the mesosphere and thermosphere.

Atmospheric tides can be measured as regular fluctuations in wind, temperature, density and pressure.

The reason for this dramatic growth in amplitude from tiny fluctuations near the ground to oscillations that dominate the motion of the mesosphere lies in the fact that the density of the atmosphere decreases with increasing height.

If the tide or wave is not dissipating, then its kinetic energy density must be conserved.

Since the density is decreasing, the amplitude of the tide or wave increases correspondingly so that energy is conserved.

This regular diurnal (daily) cycle in heating generates thermal tides that have periods related to the solar day.

However, observations reveal that large amplitude tides are generated with periods of 24 and 12 hours.

When this pattern is decomposed into separate frequency components using a Fourier transform, as well as the mean and daily (24-hour) variation, significant oscillations with periods of 12, 8 and 6 hours are produced.

Variations in the global distribution and density of these species result in changes in the amplitude of the solar tides.

[1] The migrating solar tides have been extensively studied both through observations and mechanistic models.

These non-migrating tides may be generated by differences in topography with longitude, land-sea contrast, and surface interactions.

An important source is latent heat release due to deep convection in the tropics.

The primary source for the 24-hr tide is in the lower atmosphere where surface effects are important.

This is reflected in a relatively large non-migrating component seen in longitudinal differences in tidal amplitudes.

Largest amplitudes have been observed over South America, Africa and Australia.

[4] Lunar (gravitational) tides are much weaker than solar thermal tides and are generated by the motion of the Earth's oceans (caused by the Moon) and to a lesser extent the effect of the Moon's gravitational attraction on the atmosphere.

The basic characteristics of the atmospheric tides are described by the classical tidal theory.

[5] By neglecting mechanical forcing and dissipation, the classical tidal theory assumes that atmospheric wave motions can be considered as linear perturbations of an initially motionless zonal mean state that is horizontally stratified and isothermal.

and doing some manipulations[7] yields expressions for the latitudinal and vertical structure of the tides.

Longuet-Higgins[8] has completely solved Laplace's equations and has discovered tidal modes with negative eigenvalues ε sn  (Figure 2).

The transition from internal to external waves appears at ε ≃ εc, or at the vertical wavenumber kz = 0, and λz ⇒ ∞, respectively.

The fundamental solar diurnal tidal mode which optimally matches the solar heat input configuration and thus is most strongly excited is the Hough mode (1, −2) (Figure 3).

Although its solar excitation is half of that of mode (1, −2), its amplitude on the ground is larger by a factor of two.

[9] For bounded solutions and at altitudes above the forcing region, the vertical structure equation in its canonical form is:

This is an important result for the interpretation of observations: downward phase progression in time means an upward propagation of energy and therefore a tidal forcing lower in the atmosphere.

Damping of the tides occurs primarily in the lower thermosphere region, and may be caused by turbulence from breaking gravity waves.

A similar phenomenon to ocean waves breaking on a beach, the energy dissipates into the background atmosphere.

[10][verification needed] At thermospheric heights, attenuation of atmospheric waves, mainly due to collisions between the neutral gas and the ionospheric plasma, becomes significant so that at above about 150 km altitude, all wave modes gradually become external waves, and the Hough functions degenerate to spherical functions; e.g., mode (1, −2) develops to the spherical function P 11 (θ), mode (2, 2) becomes P 22 (θ), with θ the co-latitude, etc.

[11] It is responsible for the electric Sq currents within the ionospheric dynamo region between about 100 and 200 km altitude.

Figure 1. Tidal temperature and wind perturbations at 100 km altitude for September 2005 as a function of universal time. The animation is based upon observations from the SABER and TIDI instruments on board the TIMED satellite. It shows the superposition of the most important diurnal and semidiurnal tidal components (migrating and nonmigrating).
Figure 2. Eigenvalue ε of wave modes of zonal wave number s = 1 vs. normalized frequency ν = ω /Ω where Ω = 7.27 × 10 −5 s −1 is the angular frequency of one solar day . Waves with positive (negative) frequencies propagate to the east (west). The horizontal dashed line is at ε c ≃ 11 and indicates the transition from internal to external waves. Meaning of the symbols: 'RH' Rossby-Haurwitz waves ( ε = 0 ); 'Y' Yanai waves; 'K' Kelvin waves; 'R' Rossby waves; 'DT' Diurnal tides ( ν = −1 ); 'NM' Normal modes ( ε ≃ ε c )
Figure 3. Pressure amplitudes vs. latitude of the Hough functions of the diurnal tide ( s = 1 ; ν = −1 ) (left) and of the semidiurnal tides ( s = 2 ; ν = −2 ) (right) on the northern hemisphere. Solid curves: symmetric waves; dashed curves: antisymmetric waves