Sea to lake flow.

Assume that for the period of calculation the flow is from sea to lake only then from equation (55)...

Where is the salt concentration of sea water () and M is a constant of integration.

Then evaluating the integral gives us...

Now at time t=0 we have..

Substituting in for the value of and solving for M we have...

Thus finally...

Salt load for sea to lake flow.

 

Notes...

1. Except in the transient, the salt load depends only weakly on the estuary constant.
2. Unlike the volume equation where the effect of the initial volume fades exponentially, there is no effect beyond the diffusive effect of the water flow in and out of the system to decrease the impact of the initial salt load.

The steady state concentration for sea to lake flow. In the long term, beyond the effect of the transients, the concentration is...

Note that the numerator consists of three physically separate terms.

1. the initial salt load.
2. the salt movement due to the difference in initial level and the asymptotic level .
3. the salt load due to inflow of sea water to compensate for the evaporation of lake water.

Remember that this is for the case of negative inflow. Ie Evaporative losses exceeding river and rain inflow. In the long term in the volume equation, the estuary flow rate merely determines the head difference between the sea and the lake (I/k). This head difference is usually small compared to the depth of the lake, (maximum 0.40m versus 1m). Even if we were to open the estuary to the maximum, ie k tending to infinity, little significant difference would be made. The primary source of increase in the salinity is transport of salt into the system. Thus the long term concentration is effectively independent, in this model, of the estuary flow rates. In this respect then we can say ``Potter's channel'' has no effect on the salinity of lake St. Lucia.