Thermosphere - Dynamics

Dynamics

Within the thermosphere above about 150 km height, all atmospheric waves successively become external waves, and no signifiant vertical wave structure is visible. The atmospheric wave modes degenerate to the spherical functions P_nm with n a meridional wave number and m the zonal wave number (m = 0: zonal mean flow; m = 1: diurnal tides; m = 2: semidiunal tides; etc.). The thermophere becomes a damped oscillator system with low pass filter characteristics. This means that smaller scale waves (greater numbers of (n,m)) and higher frequencies are suppressed in favor of large scale waves and lower frequencies. If one considers very quiet magnetospheric disturbances and a constant mean exospheric temperature (averaged over the sphere), the observed temporal and spatial distribution of the exospheric temperature distribution can be described by a sum of spheric functions:

(3) T(φ,λ,t) = T_∞{1 + ΔT₂0 P₂0(φ) + ΔT₁0 P₁0(φ) cos + ΔT₁1 P₁1(φ) cos(τ - τ_d) + . . .}

Here, it is φ latitude, λ longitude, and t time, ω_a the angular frequency of one year, ω_d the angular frequency of one solar day, and τ = ω_dt + λ the local time. t_a = June, 21 is the time of northern summer solstice, and τ_d = 15:00 is the local time of maximum diurnal temperature.

The first term in (3) on the right is the global mean of the exospheric temperature (of the order of 1000 K). The second term represents the heat surplus at lower latitudes and a corresponding heat deficit at higher latitudes (Fig. 2a). A thermal wind system develops with winds toward the poles in the upper level and wind away from the poles in the lower level. The coefficient ΔT₂0 ≈ 0.004 is small because Joule heating in the aurora regions compensates that heat surplus even during quiet magnetospheric conditions. During disturbed conditions, however, that term becomes dominant changing sign so that now heat surplus is transported from the poles to the equator. The third term (with P₁0 = sin φ) represents heat surplus on the summer hemisphere and is responsible for the transport of excess heat from the summer into the winter hemisphere (Fig. 2b). Its relative amplitude is of the order ΔT₁0 ≃ 0.13. The fourth term (with P₁1(φ) = cos φ) is the dominant diurnal wave (the tidal mode (1,-2)). It is responsible for the transport of excess heat from the day time hemisphere into the night time hemisphere (Fig. 2d). Its relative amplitude is ΔT₁1≃ 0.15, thus of the order of 150 K. Additional terms (e.g., semiannual, semidiurnal terms and higher order terms) must be added to eq.(3). They are, however, of minor importance. Corresponding sums can be developed for density, pressure, and the various gas constituents.