I recall many years ago scientists in a lab built an airtight chamber. Inside was a sphere hanging and there was a port to access the interior. The chamber was a vacuum.
They performed an experiment that I'll never forget: while spinning the sphere they injected smoke and as it began to circulate, it began spinning in the same direction as the sphere, only faster. I don't mean faster because it's out farther and to keep up it would have to travel faster.
Yet, it gained ground and was making its rotation faster than the sphere.
The experiment can be explained using fluid mechanics a subject that was used recently to refute nonsense that windmills can permanently alter wind patterns.
To explain what is going on the sphere is reduced to a two dimensional case of fluid flow over a circle (actually a cylinder viewed side on for a two dimensional example) with the velocity of the fluid orientated with the rotation of the cylinder as shown.
Smoke is modelled as a fluid which is justifiable as it is composed of particulate matter suspended in air which has a viscosity and therefore internal friction.
When the smoke contacts the cylinder there is a ‘no slip’ condition where the velocity of the smoke particles is zero relative to the rotating cylinder and is therefore carried along by the rotating cylinder according to the equation:
vₒ = -2v sin θ + Г / 2πr
vₒ is the velocity of the smoke where the source “is a long distance” (theoretically an infinite distance from the cylinder) so it is not effected by the cylinder.
v is the tangential velocity of the smoke where it contacts the surface.
The - 2v sin θ term corresponds to a stationary cylinder, the Г / 2πr term is for a rotating cylinder.
This equation is for an incompressible inviscid (zero viscosity) fluid but since the smoke is moving at low velocities and has a very low viscosity it can be approximated as such.
A casual inspection of the equation reveals the tangential speed of the smoke which is the absolute value of velocity can exceed the velocity of the smoke before it reaches cylinder |v|> | vₒ|.
What would appear to be counterintuitive is the tangential velocity of the smoke will speed
up even if the cylinder was stationary.
The mass flow rate on either side of the cylinder is the same, this is known as the continuity equation and applies to incompressible fluids which the smoke is modelled on.
When the smoke flows over the curved surface of the cylinder it travels longer distances and in order for the mass flow rate to remain the same the tangential velocity of the smoke increases particularly at the angles θ = 90⁰ and θ = 270⁰.
Then it occurred to me that weather patterns do the same. You'd think if anything, the atmosphere would lag behind the earth's rotation.
Is this a well understood phenomenon to those members who enjoy such oddities in creation?
I am not well read nor do I process a great mind. I'm just curious.
When it comes to the atmosphere one would expect the atmosphere to have a larger tangential velocity than the surface based on the equation v = rdθ/dt for circular motion where r is the radius and dθ/dt is the angular velocity.
The further the distance from the surface the higher the tangential velocity.
In reality the atmosphere is much more complicated due to factors such as pressure gradients, temperature differences, and the Coriolis effect, which can radically alter the velocity characteristics of the atmosphere.
