Salinity Transport

Salinity Transport

Overview

The characteristics of salinity are important in the coastal environment because salinity can impact marine plants and animals and influence the dynamic behavior of cohesive sediments. Because modifications of coastal inlets, such as channel deepening and widening and rehabilitation or extension of coastal structures, may alter the salinity distribution within estuaries or bays, it is often useful and convenient to simulate the salinity within the scope of an engineering project to determine if a more detailed water quality modeling study is necessary. It is important to emphasize that the CMS is not intended to be used as a water quality model. The CMS solves the depth-averaged (2DH) salinity transport equation and should be used only for cases where the water column is well mixed. If there is flow stratification, a 3D model should be utilized. It is also noted that the salinity is not used to update the water density which is assumed to be constant. Thus any horizontal water density gradients due to varying salinity on the hydrodynamics are assumed to be negligible.

Transport Equation

CMS calculates the salinity transport based on the following 2DH salinity conservation equation (Li et al. 2012):

${\frac {\partial (hC_{sal})}{\partial t}}+{\frac {\partial (hV_{j}C_{sal})}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\left(v_{sal}h{\frac {\partial C_{sal}}{\partial x_{j}}}\right)+S_{sal}$

(1)

where:

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 C_{sal}} = depth-averaged salinity [usually in ppt or psu]

h = water depth [m]

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 V_j} = total flux velocity [m/s]

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_{sal}} = horizontal mixing coefficient 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_{sal} = \nu_t / \sigma_{sal}\ [m^2 /s]}

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 = } total eddy viscosity [m²/s]

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 \sigma_{sal} = } Schmidt number for salinity (approximately equal to 1.0) [-]

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 S_{sal} = } source/sink term [ppt m/s].

The above equation represents the horizontal fluxes of salt in water bodies and is balanced by exchanges of salt via diffusive fluxes. Major processes that influence the salinity are as follows: seawater exchange at ocean boundaries, freshwater inflows from rivers, precipitation and evaporation at the water surface, and groundwater fluxes (not included here).

Initial Condition

The initial condition for salinity transport may be specified as a constant, a spatially variable dataset usually calculated from a previous simulation or by solving a 2DH Laplace equation:

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 \bigtriangledown^2 C_{sal} = 0 }

(2)

where 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 \bigtriangledown^2} is the Laplace operator. The equation is solved given any number of user-specified initial salinity values at locations within the model domain, using the initial salinity values at open boundaries and applying a zero-gradient boundary condition at all closed boundaries.

Boundary Conditions

At cell faces between wet and dry cells, a zero-flux boundary condition is applied. A salinity time series must be specified at all open boundaries and is applied when the flow is directed inward of the modeling domain. If the flow is directed outward of the modeling domain, then a zero-gradient boundary condition is applied.