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This is a statement of the kinematic free surface boundary condition: there can be no normal flow through the boundary, only tangential flow along it. Equivalently, the normal velocity (relative to the interface) of the free surface position is the same as the velocity of the fluid. Defining the position of the free surface as $$ z = \eta(x,y,t) $$ then ...


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Air is affected by friction. A brief search of AMS journals shows over 14,000 times friction is mentioned. How it is manifested in the equations that describe the atmosphere is complicated. Let's think of wind as 'air moving' or perhaps space moving which air occupies. At some point, called the roughness length, the wind is 0 m/s (or knots or mph). If such a ...


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As a refresher, let's refer back to the definition of the material derivative: $$\frac{D}{Dt}=\frac{\partial}{\partial t}+u\frac{\partial}{\partial x}+v\frac{\partial}{\partial y}+w\frac{\partial}{\partial z}$$ If we apply it to $\eta$, then we get: $$\frac{D \eta}{Dt}=\frac{\partial \eta}{\partial t}+u\frac{\partial\eta}{\partial x}+v\frac{\partial\eta}{\...


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numerical modelling is a vast field and the tool to address your problem depends strongly on ... your problem and your approach! Are you a master student? a PhD student with very short time to wrap up your thesis? A plumber with an intelectual interest in plate tectonics? In short: Comsol may be an adequate tool. However, with large displacements (larger ...


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That's... a pretty specific question. Well, we start with making assumptions. Let's write the continuity equation with the Boussinesq approximation: $$\frac{\partial \omega}{\partial P}=-\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}=D\tag{1}$$. If we assume a priori that the divergence varies linearly with pressure, then we can write divergence ...


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