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Unfamiliar form of shallow water equations, help identifying?

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September 2, 2015, 22:12	Unfamiliar form of shallow water equations, help identifying?	#1
ScaledWheel New Member SW Join Date: Sep 2015 Posts: 1 Rep Power: 0	Hi all, I found an unfamiliar form of the SWE in some ocean dynamics literature, and it's unfamiliar to me. Mass is straightforward $\frac{\partial h}{\partial t} + \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} =0$ but I don't recognize the form of the momentum $h ( \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} - fv) = -gh \frac{\partial \eta}{\partial x} + \frac{\partial }{\partial x}( \nu h \frac{\partial u}{\partial x} ) + \frac{\partial }{\partial y} ( \nu h \frac{\partial u }{\partial y}) - b$ $h ( \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + fu) = -gh \frac{\partial \eta}{\partial y} + \frac{\partial }{\partial x}( \nu h \frac{\partial v}{\partial x} ) + \frac{\partial }{\partial y} ( \nu h \frac{\partial v}{\partial y}) - b$ where is a drag term. I'm more familiar with the conservative form of momentum used for finite volume approaches, but this looks to be something different. Anyone have any leads on the form of these momentum equations?

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