Multiphase Hele-Shaw Flows: from Beaches to Dredgers - School of ...
Multiphase Hele-Shaw Flows: from Beaches to Dredgers - School of ...
Multiphase Hele-Shaw Flows: from Beaches to Dredgers - School of ...
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Asymp<strong>to</strong>tic Analysis: depth averaging<br />
<strong>Hele</strong>-<strong>Shaw</strong><br />
<strong>Flows</strong><br />
Onno<br />
Bokhove<br />
Introduction<br />
Design<br />
Wave<br />
Breaking<br />
Beach<br />
Morphology<br />
Challenges<br />
Conclusions<br />
3. Kinematic conditions at bot<strong>to</strong>m & free surface:<br />
z = b(x, t) & z = b(x, t) + h(x, t); hydrostatic balance.<br />
Shallow water equations with damping:<br />
∂ t (hū) + ∂ x<br />
(<br />
hū 2 + gh 2 /2 )<br />
+ (γ − 1)hū∂ x ū = −gh∂ x b − 3νhū<br />
∂ t h + ∂ x (hū) = 0<br />
l 2<br />
(3a)<br />
(3b)<br />
and hū(x, t) = ∫ h+b<br />
b<br />
ū(x, z, t)dz.