Conversely, I suppose that melting of the ice in high-latitude Greenland and Antarctica will slow the Earth down? I hope so — I could use the extra time.
Newton’s First Law of Motion … the force I apply to the west to keep me on the longitude line is equal but opposite the force applied to the Earth to the east which causes the Earth to spin faster … the magnitudes of the accelerations are proportional to mass of the other …
But that’s not useful … moving the entire Japanese mainland 8 feet only shorten the day by 1.8 microseconds in 2011 {Cite} … so moving just one human up in latitude may only change the Earth’s rotational period by less than a pico-second … there’s other things that effect this period more … the better analogy is having a rabies virus moving from the figure skaters fingers to the brain … the spin won’t noticibly get any faster, and other things will change the spin more …
We’ve disagreed in the past about this … are you now concurring that a person must have a force applied to them pointed west in order to move up along a line of longitude … in spite this force being completely invisible from an “Aristotelian” rotational frame-of-reference? …
Yes, a person moving straight towards the nearest pole along a longitude line must have a (small) westward force applied to them (presumably, through their feet) in order to stay on that longitude line. I’m not sure what you’re calling an Aristotelian frame of reference: In a non-rotating frame, that force is serving to decrease the person’s angular momentum, and in a rotating frame, it’s counterbalancing the force from the Coriolis effect.
Those are the newfangled Risk tokens. The old-style ones were wooden like this.
Thank you … I’ll tell TubaDiva to check with you about this claim … it doesn’t matter how small the west force is, the cross-product is still counter-clockwise … right? …
Sorry, but a quick scan of the topics had me pause at misread Lingerie Geometric Questions.
Combined with a recent Jeopardy question / answer I watched, about four triangles adding up to almost nothing. " Bikini "
The cross product of what? And why would TubaDiva be involved?
Torque is defined as a cross-product … (distance vector) X (linear force vector) for a rigid body … in a fluid we’ll use the convective force to replace the distance vector … for north motion in the Northern Hemisphere, the Coriolis force is pointed east, the cross-product yields clockwise rotation, opposite of what is observed … in Post #23, you agreed there’s a force pointed to the west if we’re moving up along a line of longitude … the cross-product of the convective force with this west force yields our desired counter-clockwise rotation, consistent with cyclonic motion … and the pressure force serves our purpose most excellently …
There needs to be a Straight Dope on this, but Lil’ Ed required it to be less than 600 word to fit in the column space allowed in the various publications the SD appeared in … with the recent changes and TubaDiva now in charge … perhaps she’ll allow us to exceed this word limit … cross-products, Navier-Stokes, vortex mechanics … we’ll need more than 600 words to explain all this to the typical high school graduate … it might take 600 words just to explain why the convective force is pointed north or south …
But now I have the Offical™ SDMB Personification of Time agreeing 100% with me … maybe my efforts won’t get tossed in the garbage again … it’s an urban myth that the Coriolis force causes cyclones to spin, it’s not even pointed the right direction … and it doesn’t conserve energy … just amazing that intelligent people accept this answer generation after generation when it’s so utterly and obviously wrong …
I deeply appreciate you volunteering to help …
Staff reports have never been subject to a word-limit, since they’re online only. I’m not sure what you’re trying to say with your other points, other than to point out that cyclones are due to the Coriolis effect: Low-pressure systems rotate counterclockwise in the northern hemisphere and clockwise in the southern, just as Coriolis would predict.
The mantle is viscous, and as an example Antarctica is rising at more than 1.5" a year due to the ice melt. If it has any effect it will be tiny compared to effects like the tidal tractive forces that are slowing down the rotation.
My understanding may be outdated, and the Coriolis force and sinks myth is pervasive but.
Doesn’t the coriolis force give way to the larger pressure-gradient force, so while the coriolis force is clockwise in the northern hemisphere; the clockwise deflection of coriolis force results in a counter-clockwise spin as the air moves to the low pressure area? (only on major storm scales)
That tiny nudge to in the clockwise direction from the coriolis force, deflecting airflow away from the low and thus producing that larger counter-clockwise system as the air curves towards the low is the way I wrapped my head around it.
Yes. In other words, the counterclockwise rotation (in the northern hemisphere) is due to Coriolis. Jut like I said.
I think both of you are talking past each other, that said the very very tiny Coriolis force of someone walking would not be to the West, but slightly in the clockwise fashion no matter what the direction is in the North Hemesphere.
Maybe it is best to think of the counter force, which would be far closer to SSW than W, as the very tiny NNE change in CMG for someone headed due North. Or probably even more clear, a slight left turn, but not for someone walking due to friction.
If someone is walking due north in the northern hemisphere, then the Coriolis force on them is exactly due east, and thus there must be some force acting exactly due west to counteract it.
Thank you for joining us, rat avatar, your recent dissertation on tidal forces is what inspired me to bring this subject up … thus clearly demonstrating the corollary to the rule “don’t feed the trolls”, you shouldn’t feed the wolves either, notice how all the fluid mechanics flee in terror when I show up? …
You’ll need to define “Coriolis effect” here … that term has been removed from Wikipedia … they use “Coriolis force” throughout now-a-days …
First off, Coriolis force is a linear force, not a torque, so the Coriolis force is neither clockwise nor counter-clockwise … and if it was, then what you’re saying is positive clockwise torque is causing a positive counter-clockwise rotational acceleration (aka curl) … you see the problem with that idea? …
If we’re standing on one spot on Earth at 45º latitude, our velocity vector is pointed due east at 700 mph, just like the spot we’re standing on … we apply a force to ourselves pointed due north, now it doesn’t matter what changes to the north-south component of our velocity vector, the east-west component stays exactly the same, 700 mph due east … when we arrive at 60º latitude, we stop so that the north-south velocity is zero, but our east-west velocity is still 700 mph … the problem here is the ground is only moving 500 mph to the east … someone standing at 60º latitude (moving at 500 mph to the east) would claim we’re moving 200 mph over the surface of the Earth … note our momentum in the east-west direction hasn’t changed, so no force has been applied to us in this direction … the Coriolis force is a pseudo-force, there’s no exchange of energy … in the House of Meteorology, we don’t violate the Laws of Thermodynamics …
That’s in a vacuum … let’s add the atmosphere to this example … the air mass at 60º is also moving 500 mph to the east, we’re moving 700 mph … air pressure builds up in front of us, drops down behind us … and we experience a pressure force (from high to low) and this force is pointed west, this is an honest force, and is reducing our momentum, what aviators call “drag” … and most important is that the pressure force has been being applied to us the whole time we’ve been moving up in latitude …
Replace ourselves with an air parcel and our northward motion is almost along a single line of longitude … instead of a 200 mph wind speed at 60º, it’s closer to 10 mph … which is what we observe as the Westerlies in the temperate circulation cell …
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There are two steps to form a cyclone … I’m focused solely on the first step, take an atmosphere where there is NO rotation of any kind into an atmosphere where there IS rotation … the second step relies on the intrinsic property of rotation in a fluid that pressure is lowest along the axis of rotation, and the condensation (deposition) that occurs in saturated air when pressure is lowered … by definition, a cyclone is actively condensing (depositing) water vapor and releasing energy into the system … some of which is applied as torque in the direction the original vortex was spinning …
It is the first step that establishes the direction of rotation … and in this step we must create torque where there was no torque before … torque is defined as a cross-product, thus my questions about cross-products …
Alas … Wikipedia starts their discussion with an existing low pressure when their task was to explain where the low pressure comes from in the first place … consensus at it’s worst …
Suppose you had a ten dimensional space.
So you have an equality with 10 variables , thats a surface in that 10 D space,well surface meaning it has as many dimensions as the space.
If you add another 10 variable equality, you can remove one variable, and thus have a 9 dimensional feature.
Add another 10 variable equality, you then have an 8 dimensional feature defined.
So two 3d surfaces intersect at a line, which is 2d, and add a third surface, you get 1d… which is a point.
As long as all of the relations are independent.
This is either incorrect or stated in a confusing way.
Consider a space of n dimensions; say n=3. Now consider a surface defined by a single equation, e.g., x² + y² - 1 = 0. One would expect the dimension of the surface to be n-1, in particular strictly less than the dimension of the ambient space, not n.
x² + y² - 1 = 0 (in a space with three dimensions, x, y, and z)) is a two-dimensional surface (an infinite cylinder). You can find any point on the surface by the point’s angle from a particular reference point, and the height, z.
This is confusing - but it’s the mathematical convention: the surface of a globe is a “2-sphere,” a circle is a “1-sphere” etc. (n-sphere - Wikipedia).
That’s what I meant: start with 3-dimensional space, impose a single polynomial equation, and end up with a 2-dimensional subspace. (Over the real numbers it’s more complicated because of possibilities like x² + y² = 0, but we can stick with linear equations for the sake of this discussion.) Impose a second independent constraint and the dimension goes down to 1, etc. I just found Isilder’s phrasing ambiguous so offered a concrete example (sphere, cylinder and plane work equally well to make this point).