CMS-Flow:Hydro Eqs

Governing Equation

The depth-averaged 2-D continuity and momentum equations are given by

        Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle  \frac{\partial h  }{\partial t} + \frac{\partial (h u_j )}{\partial x_j} = S }

for $j=1,2$

        ${\frac {\partial (hu_{i})}{\partial t}}+{\frac {\partial (hu_{i}u_{j})}{\partial x_{j}}}-\epsilon _{ij3}f_{c}u_{j}h=-gh{\frac {\partial \eta }{\partial x_{j}}}-{\frac {h}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}+{\frac {\partial }{\partial x_{j}}}{\biggl (}\nu _{t}h{\frac {\partial u_{i}}{\partial x_{j}}}{\biggr )}+{\frac {\tau _{i}}{\rho }}$  

for $i=1,2$ and $j=1,2$

Symbol	Description	Units
$t$	Time	sec
$h$	Total water depth $h=\zeta +\eta$	m
$\zeta$	Still water depth	m
$\eta$	Water surface elevation with respect to the still water elevation	m
$u_{j}$	Current velocity in the jth direction	m/sec
$u_{j}$	Current velocity in the jth direction	m/sec
$S$	Sum of Precipitation and evaporation per unit area	m/sec
$g$	Gravitational constant	m/sec2
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho }	Water density	kg/m3
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle p_a }	Atmospheric pressure	Pa
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_t }	Turbulent eddy viscosity	m2/sec

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