Excitation of gravity waves by ocean surface wave packets: Upward propagation and reconstruction of the thermospheric gravity wave field

In this paper, we derive the atmospheric gravity waves (GWs) and acoustic waves excited by an ocean surface wave packet with frequency 𝜔F and duration 𝜒 in an f plane, isothermal, windless, and inviscid atmosphere. This packet is modeled as a localized vertical body force with Gaussian depth 𝜎z. The excited GW spectrum has discrete intrinsic frequencies ( 𝜔Ir) at 𝜔F and 𝜔F ±2𝜋∕𝜒 (“sum” and “difference”) and has a “continuum” of frequencies for 𝜔Ir <𝜔F + 2𝜋∕𝜒. The momentum flux spectrum peaks at 𝜔Ir ∼ 𝜔F and decreases rapidly as 𝜔Ir decreases. To simulate the effect these GWs have on the thermosphere, we present a new scheme whereby we sprinkle GW spectra in the ocean wave packet region, ray trace the GWs, and reconstruct the GW field. We model the GWs excited by ocean wave packets with horizontal wavelengths of 𝜆H = 190 km, periods of 𝜏F = 2𝜋∕𝜔F = 14 − 20 min and 𝜒 = 30 − 50 min. The excited GWs begin to arrive at z = 250 km at t ∼ 75 − 80 min. Those with the largest temperature perturbations T′ have large 𝜔Ir and arrive at t ∼ 90 − 130 min. If |𝛼| = 𝜔F + 2𝜋∕𝜒 is a solution of the GW dispersion relation and |𝛼| is less than the buoyancy frequency at z = 250 km, the sum and highest-frequency continuum GWs have much larger phase speeds and arrive 50–60 min earlier with larger T′ than the GWs with frequency 𝜔F.