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- W2006193847 abstract "The goal of Weinstock (1976a, hereafter W76) was to treat analytically a spectrum of nonlinearly interacting atmospheric gravity waves. Specifically, W76 considered the strong-interaction case in which the fluid velocities exhibit a somewhat chaotic and practically unpredictable character; such motions have been referred to as nonlinear complexity (Lorenz 1969). The statistical renormalizations employed in W76 are one method that has been used to tackle strong nonlinearity. In his note, Hines (2002a, hereafter H02) has commented on the treatment of waves in that 1976 paper, and coincidentally, its subsequent use for the parameterization of gravity wave drag by Medvedev and Klaassen (1995, hereafter MK95). We are grateful for the attention given to those papers and for the opportunity to explain our views. In what follows, we show that H02’s claim of a “demonstrable mathematical error” in W76 rests on his misinterpretation of the behavior of the velocity and temperature coefficients of W76, vK and TK, respectively, and on a deficient conception of the role of the nonlinear advection terms in wave–wave interactions. We begin by outlining the asymptotic limits taken in W76 and present a new derivation that confirms the emergence of polarization relations in the presence of strong fluctuations. We shall address other key issues along the way, including H02’s time-lag arguments, Fig. 1 of MK95, the nature of diffusion in wave–wave interactions, as well as H02’s notion that W76 invoked “no instability whatever.” The arguments presented in H02 were motivated by the work of Allen and Joseph (1989, hereafter AJ89), Hines (2001, hereafter H01), and Hines (2002b, hereafter H02b). These authors maintain that the spectral “tail” found at large vertical wavenumbers in Eulerian measurements of atmospheric wave is present even when the wave system is nondissipative in the Lagrangian frame. In sections 9 and 10, we argue that the generation of turbulent eddies and dissipation represent fundamental aspects of nonlinear wave–wave interactions that cannot be neglected. We refer to recent measurements by Sica (1999) and Sica and Russell (1999) in support of our views." @default.
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- W2006193847 date "2007-03-01" @default.
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- W2006193847 title "Reply to “Comments on the Gravity Wave Theory of J. Weinstock Concerning Dissipation Induced by Nonlinear Effects”" @default.
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- W2006193847 doi "https://doi.org/10.1175/jas3865.1" @default.
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