Wave drag

Finally, we note that if the body is moving at speeds near and above the speed of sound (transonic and supersonic speeds), shock waves will occur that increase the pressure on the front portions of the body, contributing an additional source of pressure drag called wave drag. 

Snorkeling is rare, perhaps because swimming deep enough to keep wave drag low requires breathing against to much hydrostatic pressure. 

Fujino, M. and Kawamura, Y. (2003). Wave drag characteristics of an over-the-wing nacelle business-jet configuration. J. Aircraft, 40(6), 1177-1184. 

The infrared radiation scheme includes the effects of water vapor, carbon dioxide, ozone, and clouds. Gravity wave drag parametrization is based on a simplified linear theory for vertically propagating gravity waves generated in a statically stable flow over mesoscale orographic. GEM physics package version 4.2 was used in the current study. 

An accurate representation of wave drag is essential for chemical modeling because chemical species are advected by the mean meridional circulation and are also transported by the irreversible mixing which accompanies wave drag. Modeling studies (e.g., Schoeberl and Strobel, 1978 Holton and Wehrbein, 1980) sometimes use a Rayleigh coefficient to crudely parameterize the effects of wave dissipation. In this case, a deceleration is assumed to act linearly on u, and is substituted for the wave drag term Gu as follows ... 

Medvedev, A.S., and G.P. Klaassen, Vertical evolution of gravity wave spectra and the parameterization of associated wave drag. J Geophys Res 100, 25,841, 1995. 

At a high Reynolds number, the drag coefficient shows an increase with Mach number reaching a maximum value for light supersonic flow. This increase is due to the formation of shock waves on the particle and the attendant wave drag (essentially form drag). Mach number effects become significant for a Mach number of 0.6, which is the critical Mach number, that is, when sonic flow first occurs on the sphere. 

Miles, J.W. (1969). Wave and wave drag in stratified flows. Applied mechanics 50-76, M. Hetenyi, W.G. Vincenti, eds. Springer Berlin. 

Supersonic Wave Drag of Planar Singularity Distributions, AIAA Journal, May 1978... 

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