The Diurnal and the Semidiurnal Atmospheric Solar Tide

Abstract

World-wide oscillations generated by the sun are examined by applying the hydrodynamical equations to a rotating spherical model atmosphere. The oscillations are described as small perturbations on a static state in which the atmosphere is at rest relative to the earth's surface. Let q denote the heat supplied per unit mass and unit time. Let p and α denote perturbations in pressure and specific volume of a particle of air and let the displacement of the particle from its equilibrium position be given by θ, θ, φ z, i.e. the variations of its colatitude, longitude and height, respectively. Consider the simplest oscillation of 24-hour period rotating with the sun:

q = C_q sin (Ψ + n_q), x = C_x sin (Ψ + n_x),

where φ denotes local time reduced to angle and x denotes any one of the variables p, α, z, φ, θ. The amplitudes and phase angles are variable with latitude and height. q, p, α, z, φ are symmetric with respect to the equator.

It is shown that, if Ca, ηq are given as analytic functions of latitude and height, then the quantities Cx, ηx are determined by the equations of motion, the equation of continuity and the first law of thermodynamics.

Considering in like manner the simplest oscillation of 12-hr. period rotating with the sun:

q = C_q sin (₂Ψ + n_q), x = C_x sin (₂Ψ + n_x),

we find that, when Cq, ηq are given, the Cx, ηx satisfying the above mentioned equations contain an arbitrary function of height, f(Z).

The absence in the first case of an arbitrary function which might be adapted to boundary conditions, may partly explain the weak development of the 24-hr. wave as a global phenomenon in spite of the marked diurnal period in the heat supply q.

A special case of non-linear equations is considered in order to study certain relations between the 24-hr. and the 12-hr. wave. A heat supply of 24-hr. period of the form q = Cq sin (φ + ηq) can generate a wave of 12-hr. period.