9.1 History of friction in MOM

A brief history of discretizing friction in MOM is the following:

• Bryan (1969): Scalar Laplacian plus metric term for constant viscosity.
• Cox (1984): Omitted metric terms for constant viscosity.
• Rosati and Miyakoda (1988): Smagorinsky scheme in which friction, with a non-constant viscosity, was determined from derivatives of the stress tensor components.
• MOM1: Reintroduced metric terms for constant viscosity.
• MOM2/MOM3: Scalar Laplacian plus constant viscosity metric terms of Bryan (1969) and non-constant viscosity terms of Wajsowicz (1993).
• MOM3/MOM4 (after Summer 1999): Functional formalism in which discretization of the derivatives of the stress tensor are provided. Approach valid for constant and non-constant viscosity and generalizes easily to arbitrary orthogonal horizontal curvilinear coordinates.

In the remainder of this chapter as well as Appendix D, the details of these approaches will be described.