If you can imagine looking down at the Earth from the North Pole, the image of the hemisphere you see appears as a disc. An initial West vector of a location not on the equator will appear as the beginning of a great-circle route that, if continued in a straight line, intersects the equator. As the Earth turns, the intended equatorial destination moves to the left of the vector; viewing from the destination spot it appears that the travelled path is curving to the right.
An E-W displacement corresponds to a movement on a circle with constant radius around the spin axis of the planet. There is no change in angular moment so the movement will not be deflected by Coriolis force. If you want to see an effect of the Coriolis force, the object needs to change latitude.
The distances around the Earth that are closer to the poles are less, and the orbital velocity is less. The distances around the Earth that are closer to the equator
are greater and the speed is greater.
The force of gravity is toward the center of the Earth, but the centrifugal force
is perpendicular to the spin axis, and is greater the farther from the spin axis
that you are ( closer to the equator ).
With out getting mathematical, it is all the forces and directions of the forces and the
magnitude of the forces that determine the spin of fluids.
As you probably realise, the Coriolis force cannot affect motion in an East-West direction. What causes the deflections seen in cyclones, anti-cyclones and oceanic eddies are actually caused by changes in vorticity as the air or water moves vertically. The vorticity is a horizontal component , which increases to 100% at the poles, of the Earth's rotation. Angular momentum increases with radius of the rotation, thus if air ascends as in a cyclone the angular momentum increases causing the air to rotate in one direction. Conversely, in an anticyclone the air descends and its angular momentum decreases causing it to rotate in the opposite direction..
AFAIK, the fact that the Coriolis effect, which is due to the conservation of linear momentum, is not really responsible for those rotations is not generally recognised. In the following webpage, where the effects in the atmosphere are discussed, it is described as Coriolis vorticity.
Not to resurrect an old question but the answers here are... deeply wrong. I'd be having sharp words with undergrads who turned out these answers.
Point 1: Yes obviously there is a Coriolis force for E-W travel at all latitudes. Look at the equation $\Omega \cross v$. Eastward travel gets pushed up from the Earth's surface, Westward travel pushed down. These forces are invariably pathetic compared to gravity but they do exist.
Point 2: Without using equations, Coriolis is all about reference frames. For classic equator-to-pole travel, as you move away from the equator, the ground under your feet is moving West-to-East more slowly, so unless a force is applied to slow YOUR Westward velocity, you increasingly move west relative to the ground
For East-West travel, consider the Great circle corresponding to your latitude and your personal cartesian axes: North, East,Up. By heading "East" you move on a tangent to the great circle. The ground East of you has some component Downwards by your reference frame (and West ground moves "Upwards"). Thus, relative to the ground you seem to be accelerated Up as you go East and Down as you go West. Thus the Coriolis force we expect from the equation.
If you maintained an Eastward trajectory in your original cartesian frame, you start to have an Upward motion relative to the ground's reference frame and thus we get the third coriolis force direction, where you would appear to move East or West more slowly as your velocity vector is less and less aligned with the motion of the Earth's ground.
It is relatively simple. The earth is a sphere ( Ball spinning on an axial shaft). The closer to a pole you get, the slower the surface of the ball spins around the axis. The closer to the Equator you get, the faster the surface of the ball spins around axis. For ANY two locations on the surface of the Earth, one is closer to the pole, and one is closer to the equator, so there is a difference in how fast these two locations spin about the axis. This difference in speeds applies a Torque ( screwdriver, wrench ) to
all fluids that move vertically relative to the surface of the Earth.
( water down a drain, dust devils, Tornadoes). It does not matter whether the fluid moves up or down, air, or water, or both (water spout), a twisting motion is applied by the rotational movement of the Earth about it own spin axis. The faster the vertical movement, of the fluid, the faster the spin rate of the fluid.
If you go to the Moon, every fluid will spin slower. If you go to Jupiter, every fluid that moves vertically will spin faster.
If you go to exactly the equator, on any Planet, it does not want to
spin in either direction. In the Northern, and Southern Hemispheres, the spin is in opposite directions. Northern Hemisphere has Hurricanes. Southern Hemisphere has Typhooooooones. A great word.
You describe some accurate effects but you have the mechanics wrong. Coriolis is not caused by distance from the rotation axis, even though paths that change your distance from the rotation axis do experience coriolis force (so do the majority of paths that maintain this distance).
It's all about inertia and reference frames. I'd be very wary of talking about torque and motion being applied. When you move from one part of the earth to another the relative motion of the local frame changes and thus (unless a force is applied to you) you find yourself moving relative to the surface. Moving north from the equator is the easy example: The equator moves eastwards faster than does the land to the north, thus as you head north your own conservation of momentum leads you to move Eastward relative to the land underneath you.
Upwards or Eastward motions have similar effects, but are more complex to understand and have less obvious physical examples than hurricanes and Hadley cells.
(Also fluid spin is would involve varying gravities as well as coriolis effects.... not sure what you mean to draw attention to with the Moon and Jupiter examples)
As I recall the question was about "without equations", thus likely trying to paint a general, easy to grasp picture. I like part of Mr. Burley's answer: it really is about inertia and reference frames- if your local horizon/reference frame is doing a slow counterclockwise rotation which you cannot see because you're part of it, anything going straight across it will appear to you to deflect to the right of its motion (north of the equator), and that will be true for anything you send across the rotating local surface in any direction. It's similar to why the sun appears to move up and to the right and sets down and to the right north of the equator (up left/down left in southern hemisphere): our northern reference frame is slowly rotating to our left with us as the local "axis". Look down from above the north pole at a post-it note at your location on a globe, and the little yellow square makes one rotation to the left (counterclockwise) relative to its own center, in one earth rotation), so we see the sun move to our right at the edge of our local post-it note (or we see the local winds deflect to the right of motion). Watch for sunrise/sunset video clips to be wrong in the movies: they often are, as directors will run a sunset clip backwards to avoid getting the crew up early enough to film a sunrise. A rotating reference frame with something else either fixed or moving straight across it being deflected. And no equations! However, I must re-iterate from my previous post that this link gets you to an excellent description: https://www.ems.psu.edu/~fraser/Bad/BadFAQ/BadCoriolisFAQ.html
Thinking about the Moon versus Mars. The Moon does not really spin about its own Rotational Axis, so there may be no Coriolis effect on the Surface of the Moon. This would make for an interesting experiment to be sent to the Moon say at 45 degrees North or South of its equator, and allow water to drain down a pipe, and see if it spins, or not. The Same experiment on Mars would be instructive, though perhaps using a fluid that does not freeze, evaporate, and is not combustible might make more sense. I need to do a drawing and do all the Vector analysis for the Coriolis Effect.
Of course that will eliminate all the simple concepts Ideas.
If you are moving eastwards, the earth is also spinning towards the east, so you are taking longer to get to your destination. If towards the west, against Earth spin, so you get there sooner.
Thank you Jonathan M. A. Burley for these great (and unmathematical) explanations. I was just now having trouble understanding the forces on a foucault pendulum once it reaches E-W. Now it makes sense.