Two kinds of wave modes exist: class 1 waves (sometimes called gravity waves), and class 2 waves (rotational waves). Class 2 waves owe their existence to the Coriolis effect and can only exist for periods larger than 12 hours. 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. Each mode is characterized by four numbers: the zonal wave number n, positive for class 1 waves and negative for class 2 waves (their meridional structures becoming increasingly complex with increasing number n), a meridional wave number m, the eigenvalue, and the period, in our case one solar or lunar day, respectively. The modes are labeled as (m, n). Even numbers of n correspond to waves symmetric with respect to the equator, and odd numbers corresponding to antisymmetric waves.
