# Difference between revisions of "CMS-Flow Coordinate System"

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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 <math>x_i = \overrightarrow{x} = (x,y,z) </math>, 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<sub>b</sub>)'' is measured from the vertical datum (i.e., negative downwards). | 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 <math>x_i = \overrightarrow{x} = (x,y,z) </math>, 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<sub>b</sub>)'' is measured from the vertical datum (i.e., negative downwards). | ||

− | + | [[Image:fig_2_1.bmp|thumb|center|400px| Vertical conventions used for the bed and mean water surface elevation.]] | |

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## Latest revision as of 19:41, 9 March 2020

## 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 , 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).