CMS-Flow:Salinity Calculation: Difference between revisions
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The depth-averaged 2-D salinity transport equation is given by | The depth-averaged 2-D salinity transport equation is given by | ||
<math> \frac{\partial ( h C_{sa} ) }{\partial t} + \frac{\partial (U_j h C_{sa})}{\partial x_j} = \frac{\partial }{\partial x_j} \biggl[ | <math> \frac{\partial ( h C_{sa} ) }{\partial t} + \frac{\partial (U_j h C_{sa})}{\partial x_j} = \frac{\partial }{\partial x_j} \biggl[ K_{sa} h \frac{\partial C_{sa} }{\partial x_j} \biggr] </math> | ||
where <math> t </math> is time, <math> U_j </math> is the current velocity in the jth direction, <math> h </math> is the total water depth, <math> C_{sa} </math> is the salinity concentration, and <math> | where <math> t </math> is time, <math> U_j </math> is the current velocity in the jth direction, <math> h </math> is the total water depth, <math> C_{sa} </math> is the salinity concentration, and <math> K_{sa} </math> is the salinity mixing coefficient. | ||
== Initial and Boundary Conditions == | == Initial and Boundary Conditions == | ||
Revision as of 21:16, 6 October 2009
CMS-Flow: Salinity Calculation (V3.75) - UNDER CONSTRUCTION
Introduction
In some estuaries the spatial variation of salinity can be an important driving force in the circulation, since salinity gradients produce density gradients. Salinity is also a key water quality variable since it affects the chemical and biological processes in estuaries. Salinity is simulated in the Coastal Modeling System (CMS) in a depth-averaged sense. This means that the estuary or body of water is assumed to be well mixed vertically and the salinity is constant over the water column.
Governing Equation
The depth-averaged 2-D salinity transport equation is given by
![{\displaystyle {\frac {\partial (hC_{sa})}{\partial t}}+{\frac {\partial (U_{j}hC_{sa})}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}{\biggl [}K_{sa}h{\frac {\partial C_{sa}}{\partial x_{j}}}{\biggr ]}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/b8f039f3e553cdb739382fdbe14a64618b2a893f)
where is time, is the current velocity in the jth direction, is the total water depth, is the salinity concentration, and is the salinity mixing coefficient.
Initial and Boundary Conditions
The initial salinity is specified as a constant in the whole domain. The value of the constant is specified in the SMS 10.1 interface. Inflow salinity concentrations are applied at specified salinity boundary cell strings. Salinity cell strings are specified in the same manner as the hydrodynamic boundary cells strings.
Numerical Methods
The salinity transport equation is solved with an explicit, finite volume method. The advection term is discretized with upwind scheme, and the diffusion term is discretized with the standard central difference scheme.