a reduced model for internal waves interacting with submarine ...
a reduced model for internal waves interacting with submarine ...
a reduced model for internal waves interacting with submarine ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Chapter 3<br />
A higher-order <strong>reduced</strong> <strong>model</strong><br />
Since we want to study wave interaction <strong>with</strong> highly variable topographies and<br />
<strong>submarine</strong> structures, we need to be able to account <strong>for</strong> higher order (vertical)<br />
coupling terms between the two layers. Namely we want to investigate if these<br />
higher order terms do indeed play a role in the dynamics. Hence in this chapter<br />
we improve the <strong>model</strong> from the previous chapter regarding the pressure term by<br />
allowing nonhydrostatic terms to come into play.<br />
3.1 Higher-order upper layer equations<br />
The purpose of this chapter is to improve the order of approximation of system<br />
(2.27) by using higher precision approximations <strong>for</strong> the pressure term <strong>with</strong><br />
respect to the dispersion parameterβ. Instead of orderβ, we seek order O(β 3/2 ).<br />
We start <strong>with</strong> the mean-layer equations (2.10) and (2.17) obtained in Section 2.1.<br />
36