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Cyclone and Storm Surge - Iczmpwb.org

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4.20<br />

formulation. However, the retention in (9) of terms such as<br />

( u<br />

2<br />

, u<br />

2<br />

)<br />

leads to a fundamental difficulty<br />

as they can not be evaluated within the framework of a vertically integrated model. In many well -<br />

documented applications of non-linear vertically integrated equations (8) to (10), it is usual to make<br />

assumptions typified by:<br />

2 2<br />

( u − u<br />

) = 0 ,<br />

2 2<br />

( v − v<br />

) =<br />

0 ,<br />

(14)<br />

( uv − uv ) =<br />

0<br />

u<br />

<strong>and</strong><br />

v<br />

This is equivalent to saying that the currents do not vary significantly in the vertical <strong>and</strong> the flow<br />

is dominated by the midstream flow. The validity of the assumption (14) has been demonstrated by<br />

Nihoul (1975) <strong>and</strong> Johns (1981). In the latter work it has been found that<br />

2 2<br />

(<br />

u / u )

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