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The answer is the scale. The fluid movement of a sink has a much smaller curvature radius than the grand-scale movements of a hurricane. This curvature radius plays a big role on whether your movement due to a pressure gradient will be balanced by coriolis, or centrifugal forces, as thorougly discussed here. You can read this wikipage, but the essence is ...

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This question can be answered with a scaling argument. Let us start with the momentum equation (Navier-Stokes) in a non-intertial reference frame (e.g. on the rotating earth) and assuming inviscid flow (roughly true above the surface). $$\dfrac{\partial\mathbf u}{\partial t} = - \mathbf u \cdot \nabla \mathbf u -\dfrac{1}{\rho}\nabla p-2 \mathbf \Omega \... 16 It's partly historical, partly point-of-view, but it's not a mistake. The friction coefficient emphasises the effect of the surface on a property of the boundary layer, i.e., greater surface friction slows the near-surface wind more. Aerodynamic resistance emphasises the effect of the boundary layer on surface-atmosphere exchange, i.e., greater mixing ... 13 You can think about it like this: It takes one day for the earth to perform a full rotation (about 86k seconds), on the other hand, it takes a few seconds for your sink to drain (lets say 10 seconds). So it takes 8600 times longer for the earth to do a full rotation than it takes the water to drain down the sink. It is not too hard to imagine that the earth'... 10 This is a good question, and the answer is, aerodynamic resistance is not defined inversely. It is rather, defined in a context that is often misinterpreted. In your question, you state that aerodynamic resistance is basically how much the roughness of the surface slows air movement down. This statement is not correct, and it seems to stem from the ... 10 Here are your choices with regard to modeling the atmosphere. There aren't many, and only one of them makes sense. Model the atmosphere from the perspective of an inertial frame of reference. Good luck with that! As an advisor told me decades ago, "Name one!" It's certainly not an Earth-centered frame; the Earth is orbiting the Sun. It's certainly not Sun-... 8 The similarities pretty much end at the fact that both water and lava flow downhill seeking the lowest possible level. As even the most fluid lavas flow somewhat slower than water because of their higher density and viscosity, their lower speed and in particular their viscosity makes them far less erosive of the terrain they flow over/through. In fact lava ... 7 The Coriolis acceleration is only present in a rotating reference frame as is the case with Earth. The Coriolis effect is caused by Earth's rotation and the inertia of the mass experiencing the effect. If you are in an inertial frame of reference, thus non-accelerating, there will be no Coriolis effect. Let's assume that you are capable of modeling the ... 6 If your question is: I have an equation with force term F(x,t), and suppose that F(x,t) is caused by effect A, then will the solution of the equation be the same as if the force F(x,t) had been caused by effect B, then the answer is of course "yes". Same force (i.e., same magnitude, same direction) will always cause the same reaction of the system, ... 5 The flow accumulation algorithm essentially determines the upstream contributing area of every grid cell; in other words, what area or how many other cells will drain into a given cell. The flow accumulation algorithm is independent of rainfall as it simply determines which areas drain where, which will later be used to determine how much water actually ... 5 Inertial instability is similar to the centrifugal instability in that we are looking at the stability of parcels to horizontal perturbations. In the inertial case, however, the initial state is geostrophic balance rather than cyclostrophic balance. Symmetric instability is the case where a parcel is inertially stable to horizontal perturbations and ... 4 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 ... 4 I think you are asking a question with a variety of different constraints. I'll tackle a couple of them. What is the simplest atmospheric model to operate? That would be the Zero-dimensional energy balance model. It has almost zero resolution and no temporal capacity. What is an atmospheric model that can be easily installed and run? The Weather ... 3 Some time ago I posted this answer about how rainbows are formed, and the Wikipedia link Trond Hansen posted mentions droplet size relative to the wavelength of light. For a rainbow to form, the droplet size has to be large enough, relative to the color with the longest wavelength of visible light, for it to be refracted before reflecting off the backside ... 2 No, clouds don't really have a 'surface' that could have tension like a body of water. The different looks in these two examples (left Cumulonimbus Calvus and right Cumulus Humilis) are greatly dependent on how they have formed and how are they evolving now. The large Cumulonimbus is still growing in a relatively rapid speed. The cloud is reaching higher ... 2 The Laplace equation, (d^2 Ψ)/(dx^2 )+(d^2 Ψ)/(dy^2 )+(d^2 Ψ)/(dz^2 )=0, is just a steady state 3D flow equation. It's a black box conservation of hydraulic potential. Diffusion doesn't come into it. The Diffusion equation (assuming homogeneous isotropic conditions) is (∂^2 Ψ)/(∂x^2)+(∂^2Ψ)/(∂y^2)+(∂^2 Ψ)/(∂z^2)= S_s/K ∂h/∂t. This discretizes the time ... 2 It's not clear exactly what is being modelled here, but it seems to me that there are two ways in which the concentration can 'go negative'. Firstly, the rate of change of concentration can be massive, in which case see what happens when modelling with much smaller time steps. Or, the diffusion term substantially exceeds the advection term, which is ... 2 Recent literature points to an attempt to understand the theoretical dynamics behind the MJO as seen in these two publications - Dynamics moisture mode vs. moisture mode in MJO dynamics and A general theoretical framework for understanding essential dynamics of Madden–Julian oscillation As concluded in the original paper by Madden and Julien oscillation the ... 2 Strictly speaking, \lim_{\Delta z \to 0} Ri=Ri_b. This is because the gradient Richardson number:$$Ri=\frac{\frac{g}{T_v}\frac{\partial \theta_v}{\partial z}}{\left(\frac{\partial U}{\partial z}\right)^2++\left(\frac{\partial V}{\partial z}\right)^2}$$can be approximated as$$Ri \approx\frac{\frac{g}{T_v}\frac{\Delta \theta_e}{\Delta z}}{\left(\frac{\...

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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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If you assume both hydrostatic and pure geostrophic balance, that is a valid assumption. In Einstein notation, $$u_i=-\frac{1}{f \rho}\frac{\partial P}{\partial x_j}\epsilon_{ij3}$$ If we look at the equation for the streamline:$$u_i=-\frac{\partial \psi}{\partial x_j}\epsilon_{ij3}$$, then we can see that $$-\frac{\partial \psi}{\partial x_j}\epsilon_{... 2 As a refresher, let's refer back to the definition of the material derivative:$$\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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No, the rate of flow would usually be unaffected. The same volume of water has to get to the sea, so unless the ice was so thick and so well anchored to the riverbank as to exert pressure on the flow of water beneath, which is very unlikely, the rate of flow would remain the same. If, in the unlikely event that the ice exerted pressure on the water, the rate ...

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This equation is a form of the Shallow-water equations, which are derived from Navier-Stokes in the incompressible limit and the vertical direction is integrated out. One then takes the equation for the vorticity (which has only one component then) from the Shallow-water equations. The vorticity is split into planetary vorticity, as is the Coriolis term ...

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If the pumping well is partially penetrating in the aquifer or the source above the aquifer (e.g., unconfined aquifer, leaky aquifer, under the stream), the vertical flow should be accounted. The groundwater equation like Thies' solution is not considering the vertical flow. Incorporating the vertical flow would change the governing equation (P.D.E.) form ...

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