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:

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

h = water depth [m]

$V_{j}$ = total flux velocity [m/s]

$\nu _{sal}$ = horizontal mixing coefficient $\nu _{sal}=\nu _{t}/\sigma _{sal}\ [m^{2}/s]$

$\nu _{t}=$ total eddy viscosity [m²/s]

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

$S_{sal}=$ 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:

$\bigtriangledown ^{2}C_{sal}=0$

(2)