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 ω F 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 σ z . The excited GW spectrum has discrete intrinsic frequencies ( ω I r ) at ω F and ω F ±2 π / χ (“sum” and “difference”) and has a “continuum” of frequencies for ω I r < ω F +2 π / χ . The momentum flux spectrum peaks at ω I r ∼ ω F and decreases rapidly as ω I r decreases. To simulate the effect these GWs have on the thermosphere, we present a new scheme whereby we sprinkle N 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 λ H = 190 km, periods of τ F = 2 π / ω F = 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 perturbationsT ′have large ω I r and arrive at t ∼ 90 − 130 min. If | α |= ω F +2 π / 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 largerT ′than the GWs with frequency ω F . For a packet with λ H = 190 km, τ F = 14 min, χ = 30 min, and height h 0 =1.3 m, the maximumT ′at z = 250 km is ∼9, 22, and 40 K for σ z = 1, 2, and 4 m, respectively.