Effects of mean winds and dissipation on the diurnal propagating tide: An analytic approach

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The effects of mean winds and dissipation on the vertical and horizontal structures of the diurnal propagating tide are investigated analytically using a set of “modified” (complex) Hough functions, velocity expansion functions, and equivalent depths. These are derived by introducing a doppler-shifted complex frequency σ ∗ into the “large ϵ” approximation of Longuet-Higgins (1968, Phil. Trans. R. Soc. (London) A262, 511) for his “Type 1” waves. An equivalent result can be obtained by utilizing an equatorial betaplane approximation. The imaginary part of σ ∗ represents effective Rayleigh friction and Newtonian cooling coefficients which parameterize diffusion of momentum (mechanical dissipation) and heat (thermal dissipation), respectively, and the real part of σ ∗ is doppler-shifted according to an average (latitude-dependent) zonal wind speed. Our results are utilized to interpret salient features of recent numerical simulations of the propagating diurnal tide, including formation of an amplitude peak near 90 km, coupling into evanescent modes above this altitude, amplitude and phase asymmetries about the equator, and amplitude broadening with latitude. We suggest that these functions can be utilized to interpret tidal observations in the 70–100 km region, and perhaps to serve as basis functions for fitting (decomposing) such data from a latitude chain of stations.