Abstract
We study the modulation of atmospheric nonisothermality and wind shears on the propagation of seismic tsunami-excited gravity waves by virtue of the vertical wavenumber, m (with its imaginary and real parts, m i and m r , respectively), within a correlated characteristic range of tsunami wave periods in tens of minutes. A generalized dispersion relation of inertio-acoustic-gravity (IAG) waves is obtained by relaxing constraints on Hines’ idealized locally-isothermal, shear-free and rotation-free model to accommodate a realistic atmosphere featured by altitude-dependent nonisothermality (up to 100 K/km) and wind shears (up to 100 m/s per km). The obtained solutions recover all of the known wave modes below the 200-km altitude where dissipative terms are assumed negligible. Results include: (1) nonisothermality and wind shears divide the atmosphere into a sandwich-like structure of five layers within the 200-km altitude in view of the wave growth in amplitudes: Layer I (0–18) km, Layer II (18–87) km, Layer III (87–125) km, Layer IV (125–175) km and Layer V (175–200) km; (2) in Layers I, III and V, the magnitude of m i is smaller than Hines’ imaginary vertical wavenumber ( m i H ), referring to an attenuated growth in the amplitudes of upward propagating waves; on the contrary, in Layers II and IV, the magnitude of m i is larger than that of m i H , providing a pumped growth from Hines’ model; (3) nonisothermality and wind shears enhance m r substantially at an ∼100-km altitude for a tsunami wave period T t s longer than 30 min. While Hines’ model provides that the maximal value of m r 2 is ∼0.05 (1/km 2 ), this magnitude is doubled by the nonisothermal effect and quadrupled by the joint nonisothermal and wind shear effect. The modulations are weaker at altitudes outside 80–140-km heights; (4) nonisothermality and wind shears expand the definition of the observation-defined “damping factor”, β: relative to Hines’ classical wave growth with β = 0 , waves are “damped” from Hines’ result if β > 0 and “pumped” if β < 0 . The polarization of β is determined by the angle θ between the wind velocity and wave vector.
Highlights
For more than 10 years, LiDAR has recorded both atmospheric nonisothermality and large wind shears (e.g., 100 m/s per km) between ∼85- and 95-km altitudes [1,2,3,4,5]
Serious concerns were naturally attracted towards such fundamental questions, like to what extent the nonisothermality and wind shears influence the propagation of acoustic-gravity waves and what the mechanism is for amplitude A to be modulated in wave damping or growing versus altitude
Summary and Discussion We generalized Hines’ ideal locally-isothermal, shear-free and rotation-free model of gravity waves to accommodate a realistic atmosphere featured with altitude-dependent nonisothermality and wind shears
Summary
For more than 10 years, LiDAR has recorded both atmospheric nonisothermality (featured with temperature gradients up to 100 ◦K per km) and large wind shears (e.g., 100 m/s per km) between ∼85- and 95-km altitudes [1,2,3,4,5]. In theoretical studies on acoustic-gravity waves, the earliest work focused on an idealized atmosphere featured with an isothermal temperature, homogeneous horizontal wind speeds, rotation free and dissipation free. Based on a “multi-layer” approximation, Hines and Reddy [19] calculated the coefficients of the energy transmission through a stratified atmosphere They argued that nonideal conditions, like vertically-changing temperature and wind speeds, do not severely attenuate incident waves propagating upward through the mesosphere; stronger attenuation can be expected low in the thermosphere. Serious concerns were naturally attracted towards such fundamental questions, like to what extent the nonisothermality and wind shears influence the propagation of acoustic-gravity waves and what the mechanism is for amplitude A to be modulated in wave damping or growing versus altitude. How do atmospheric nonisothermality and wind shears influence the damping and growth of seismic tsunami-excited acoustic-gravity waves?
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