Abstract
We study the atmospheric structure in response to the propagation of gravity waves under nonisothermal (nonzero vertical temperature gradient), wind-shear (nonzero vertical zonal/meridional wind speed gradients), and dissipative (nonzero molecular viscosity and thermal conduction) conditions. As an alternative to the “complex wave-frequency” model proposed by Vadas and Fritts, we employ the traditional “complex vertical wave-number” approach to solving an eighth-order complex polynomial dispersion equation. The empirical neutral atmospheric models of NRLMSISE-00 and HWM93 are employed to provide mean-field properties. In response to the propagation of gravity waves, the atmosphere is driven into three sandwich-like layers: the adiabatic layer (0–130 km), the dissipation layer (130–230 km) and the pseudo-adiabatic layer (above 230 km). In the lower layer, (extended-)Hines’ mode or ordinary dissipative wave modes exist, whereas viscous dissipation and thermal conduction fail to exert perceptible influences; in the middle layer, Hines’ mode ceases to exist, and both ordinary and extraordinary dissipative wave modes flourish; in the top layer, only extraordinary wave modes survive, and dissipations affect the real part of the vertical wavenumber ( m r ) substantially; however, they contribute little to the imaginary part, which is the vertical growth rate ( m i ). We also analyze the transition of Hines’ classical mode to ordinary dissipative wave modes, describe both the upward and downward modes of gravity waves and illustrate nonisothermal and wind-shear effects on the propagation of gravity waves of different modes.
Highlights
In the early 1970s, seismic tsunamis were demonstrated theoretically to be able to excite atmospheric acoustic-gravity waves, which propagate to the upper atmosphere where the conservation of wave energy causes the amplitudes of the wave disturbance enhanced appreciably due to the decrease of atmospheric density with increasing altitudes [1,2]
To show explicitly the effects contributed by nonisothermality, wind shear and viscosity, we show three modes in each panel: (1) Hines’ classical isothermal and motion-free mode given in Equation (2); (2) the extended Hines’ mode under nonisothermal and wind shear conditions given in Equation (13); and (3) the ordinary viscosity wave modes given in Equation (16)
Inspired by Vadas and Fritts’s pioneer work [62], we revisited a classical problem to understand the properties of upward-propagating atmospheric internal gravity waves under the influence of nonisothermality, wind shears and dissipations
Summary
In the early 1970s, seismic tsunamis were demonstrated theoretically to be able to excite atmospheric acoustic-gravity waves, which propagate to the upper atmosphere where the conservation of wave energy causes the amplitudes of the wave disturbance enhanced appreciably due to the decrease of atmospheric density with increasing altitudes [1,2]. The author concluded that the thermal conduction influences the gravity wave propagation only in cases with a small Prandtl number and negligible Newtonian cooling All of these contributions are based on Hines’ isothermal and shear-free atmospheric model with a 3D linear approximation, which assumes much smaller wave amplitudes than the background values. Vadas and Fritts’ series of work offered a landmark in the study of gravity waves It provides a necessary reference for generalizing Hines’ classical theory analytically and semi-numerically under dissipative conditions, and for exploring the damping/pumping effect of the dissipative terms on the propagation of gravity waves in a more realistic atmosphere.
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