Non-migrating tides can be thought of as global-scale waves with the same periods as the migrating tides. However, non-migrating tides do not follow the apparent motion of the Sun. Either they do not propagate horizontally, they propagate eastwards or they propagate westwards at a different speed to the Sun. 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.

Hence, atmospheric tides are eigenoscillations ( eigenmodes)of Earth's atmosphere with eigenfunctions Θ n {\displaystyle \Theta _{n}} , called Hough functions, and eigenvalues ε n {\displaystyle \varepsilon _{n}} . The latter define the equivalent depth h n {\displaystyle h_{n}} which couples the latitudinal structure of the tides with their vertical structure.n (Figure 2). There exist two kinds of waves: class 1 waves, (sometimes called gravity waves), labelled by positive n, and class 2 waves (sometimes called rotational waves), labelled by negative n. Class 2 waves owe their existence to the Coriolis force and can only exist for periods greater than 12 hours (or | ν| ≤ 2). Tidal waves can be either internal (travelling waves) with positive eigenvalues (or equivalent depth) which have finite vertical wavelengths and can transport wave energy upward, or external (evanescent waves) with negative eigenvalues and infinitely large vertical wavelengths meaning that their phases remain constant with altitude. These external wave modes cannot transport wave energy, and their amplitudes decrease exponentially with height outside their source regions. Even numbers of n correspond to waves symmetric with respect to the equator, and odd numbers corresponding to antisymmetric waves. The transition from internal to external waves appears at ε ≃ ε c, or at the vertical wavenumber k z = 0, and λ z ⇒ ∞, respectively. 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. Although atmospheric tides share much in common with ocean tides they have two key distinguishing features: Solar energy is absorbed throughout the atmosphere some of the most significant in this context are [ clarification needed] water vapor at about 0–15km in the troposphere, ozone at about 30–60km in the stratosphere and molecular oxygen and molecular nitrogen at about 120–170km) in the thermosphere. Variations in the global distribution and density of these species result in changes in the amplitude of the solar tides. The tides are also affected by the environment through which they travel.

Migrating solar tides [ edit ] 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).Its maximum pressure amplitude on the ground is about 60 Pa. [5] The largest solar semidiurnal wave is mode (2, 2) with maximum pressure amplitudes at the ground of 120 Pa. It is an internal class 1 wave. Its amplitude increases exponentially with altitude. Although its solar excitation is half of that of mode (1, −2), its amplitude on the ground is larger by a factor of two. This indicates the effect of suppression of external waves, in this case by a factor of four. [9] Vertical structure equation [ edit ] The migrating solar tides have been extensively studied both through observations and mechanistic models. [2] Non-migrating solar tides [ edit ] 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. As tides or waves propagate upwards, they move into regions of lower and lower density. 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. 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). It depends on local time and travels westward with the Sun. It is an external mode of class 2 and has the eigenvalue of ε 1

Atmospheric tides are also produced through the gravitational effects of the Moon. [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. s {\displaystyle s} and frequency σ {\displaystyle \sigma } . Zonal wavenumber s {\displaystyle s} is a positive Longuet-Higgins [8] has completely solved Laplace's equations and has discovered tidal modes with negative eigenvalues ε s At ground level, atmospheric tides can be detected as regular but small oscillations in surface pressure with periods of 24 and 12 hours. However, at greater heights, the amplitudes of the tides can become very large. In the mesosphere (heights of about 50–100km (30–60mi; 200,000–300,000ft)) atmospheric tides can reach amplitudes of more than 50m/s and are often the most significant part of the motion of the atmosphere.

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Atmospheric tides propagate in an atmosphere where density varies significantly with height. A consequence of this is that their amplitudes naturally increase exponentially as the tide ascends into progressively more rarefied regions of the atmosphere (for an explanation of this phenomenon, see below). In contrast, the density of the oceans varies only slightly with depth and so there the tides do not necessarily vary in amplitude with depth. 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. [3] Lunar atmospheric tides [ edit ]