25 votes

Why does Coriolis determine the rotation direction of a cyclone but not my drain?

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 ...
17 votes

Why does Coriolis determine the rotation direction of a cyclone but not my drain?

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 ...
  • 14k
16 votes
Accepted

Why is aerodynamic resistance defined inversely?

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 ...
  • 3,302
13 votes

Why does Coriolis determine the rotation direction of a cyclone but not my drain?

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). ...
10 votes

Why is aerodynamic resistance defined inversely?

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 ...
  • 4,933
10 votes

coriolis force in atmospheric/ocean modeling

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 ...
  • 20.7k
9 votes
Accepted

Similarities and differences between lava flows and fluvial geomorphology (rivers)

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 ...
  • 4,225
7 votes

coriolis force in atmospheric/ocean modeling

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....
  • 14.8k
6 votes

coriolis force in atmospheric/ocean modeling

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 ...
5 votes

Hydrology- flow accumulation

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 ...
  • 751
5 votes

What is the difference between an inertial instability and a symmetric instability?

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 ...
  • 14k
4 votes
Accepted

Deriving shallow water equations: why is the vertical velocity equal to the material derivative of the surface level?

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 ...
4 votes
Accepted

What is the simplest meteorological model to operate?

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 ...
4 votes

Similarities and differences between lava flows and fluvial geomorphology (rivers)

In terms of rheology, there is a key difference between water and lava: water is a Newtonian fluid, lava isn't. In early volcanology days, there has been attempts to model lava as a Newtonian fluid (...
4 votes

A problem of the 2-Layer hydrostatic model

Let's say our goal is to find $\eta$ which is the displacement of the fluid relative to its resting position at $z = H_2$. We find \begin{equation} \begin{split} p_2 - p_1 &= \require{cancel} \...
3 votes
Accepted

At what point are water droplets too small to make a rainbow?

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 ...
  • 2,137
2 votes
Accepted

What affects the surface characteristics of cumulus clouds?

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 ...
  • 1,043
2 votes

comparing use of Laplace equation with diffusion equation to simulate flow of fluid/water through porous media?

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. ...
2 votes

Unrealistic solution for advection-diffusion-reaction PDE with heterogeneous porous media

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,...
2 votes
Accepted

Why would geostrophic theory be invoked in the tropics with regards to the MJO?

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 ...
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2 votes
Accepted

What is the relationship between air pressure and temperature?

Or if the math of the other answers is a bit complex, in a broad sense, the balancing relationship is: $$\frac{\mathrm{density} \cdot \mathrm{temperature}}{\mathrm{pressure}} = \mathrm{constant}$$ For ...
2 votes
Accepted

What is "small layer thickness" defined as in terms of bulk Richardson number approaching gradient Richardson number?

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}\...
2 votes
Accepted

Can air be slowed down by Fricton?

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 ...
2 votes

Is it meaningful to assume static pressure to be constant along a streamline?

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 ...
2 votes

Deriving shallow water equations: why is the vertical velocity equal to the material derivative of the surface level?

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}{\...
2 votes
Accepted

Is COMSOL Multiphysics good for subduction CFD modelling? Are there alternatives?

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 ...
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1 vote

Vertical air speed

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{\...
1 vote

If the top layer of a large river freezes, is the remainder's rate of flow affected?

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 ...

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