7 The param eterization of wave stress

• Published in: International Geophysics Vol. 85; pp. 155 - 180
• Format: Book Chapter
• Language: English
• Published: Elsevier Science & Technology 2002
• ISBN: 0125140827; 9780125140829
• ISSN: 0074-6142
• DOI: 10.1016/S0074-6142(02)80275-3

For most numerical applications in regions of mountainous terrain or active cumulus convection, there are unresolved wave effects that need to be parameterized. This chapter examines the basics of these wave-stress parameterizations. The subject of wave saturation that describes the process of wave breaking in terms of wave amplitudes is introduced and several parameterization schemes to account for wave saturation in numerical models are described. Parameterizations of wave saturation are of two types, which can be referred to as either “analytical” or “analog.” Analytical parameterization schemes use mathematical expressions for wave stress and eddy diffusion directly in the model equations whereas analog schemes adjust the flow fields according to saturation theory. While the analytical parameterizations are both elegant and physically consistent, they do not lend themselves easily to operational forecast models. These types of models are limited by the number of grid cells and execution times. Many models of the general circulation solve the primitive equations of motion in terms of vorticity and divergence, which do not lend themselves to analytical expressions for eddy dissipation and wave drag. Thus, indirect techniques to account for wave saturation are required.