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_Ir) at ω_F and ω_F±2π/χ ("sum" and "difference") and has a "continuum" of frequencies for ω_Ir<ω_F+2π/χ. The momentum flux spectrum peaks at ω_Ir∼ω_F and decreases rapidly as ω_Ir 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 = 2π/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 perturbations T′ have large ω_Ir and arrive at t ∼ 90 - 130 min. If |α|=ω_F+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 ω_F. For a packet with λ_H = 190 km, τ_F = 14 min, χ = 30 min, and height h₀=1.3 m, the maximum T′ at z = 250 km is ∼9, 22, and 40 K for σ_z = 1, 2, and 4 m, respectively.