Waves in the atmosphere : atmospheric infrasound and gravity waves : their generation and propagation
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...The importance of critical levels in the dynamics of the atmosphere has long been recognized [e.g., Bretherton, 1966; Booker and Bretherton, 1967; Hines, 1968; Breeding, 1971; Gossard and Hooke, 1975; Huang et al., 1998; Gardner and Taylor, 1998]....
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...[12] When Ri becomes less than 0.25 but greater than zero, Kelvin-Helmholtz billows form from the dynamical instability [e.g., Hauritz, 1964; Lloyd et al., 1973; Gossard and Hooke, 1975; Chandrasekhar, 1981]....
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...While the basic nature of KH billows is well known [Gossard and Hooke, 1975], the wave-caused convective instability has only recently been well characterized [Fritts et al., 1997] using three-dimensional modeling....
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...It was even questioned as to whether such an instability would form since it was felt that the dynamical instability might preempt the convective instability because the latter occurred first [see, e.g., Gossard and Hooke, 1975]....
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...[6] The stability of atmospheric regions is most easily quantified by the Richardson number [Richardson, 1920; Beer, 1974;Gossard and Hooke, 1975], Ri, which is given by Ri ¼ w 2 B dU=dzð Þ2 ð1aÞ Ri ¼ g=Tð Þ dT=dzþ g=Cp dU=dzð Þ2 ; ð1bÞ where wB is the Brunt-Vaisala frequency and dU/dz is the…...
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