CMS-Flow Coordinate System

Coordinate System

Before presenting the depth-integrated and wave-averaged governing equations, it is useful to define the coordinate system and basic variables. Variables are defined spatially in a Cartesian coordinate system $x_i=\overrightarrow{x}=(x,y,z)$, where x and y are the horizontal coordinates, and z is the vertical coordinate (positive is upwards). A schematic of several of the main variables in the vertical direction is provided in Figure 2-1. The vertical coordinate datum is usually the Still Water Level (SWL). The bed elevation (z_b) is measured from the vertical datum (i.e., negative downwards).

Vertical conventions used for the bed and mean water surface elevation.