Radial ripple from top to bottom of a sphere

[Leila Choudhry]

What is the term used for a radial that starts at a single point at the north most pole of a sphere and continues to equally expand and move to the alternate pole of the sphere until it contracts to a single point again please ?

[Genady]

Spherical spiral? 

Project.pdf (redwoods.edu)

[Leila Choudhry]

Sorry, the link does not work.

A spiral is close, but it more like a ripple with all edges moving at a constant speed.

[Genady]

Like consecutive circles of latitude?

(btw, the link works for me, strange...)

[Leila Choudhry]

Yes.

Is there a term known for a single pass ?

[iNow]

Geodesic

[Genady]

4 minutes ago, iNow said:

Geodesic

I doubt. Geodesic on a sphere is a great circle.

[exchemist]

Could it be a Rayleigh wave? : https://en.wikipedia.org/wiki/Rayleigh_wave

 

[Leila Choudhry]

Maybe this pop-culture reference will explain it better: 

 

 

For my purposes a single pass of equal distance over the entire circumference of the sphere, from pole to pole.

[TheVat]

Just called a spherical wave isn't it?  Or maybe one could elaborate and say spherical wave originating at the pole of a sphere.  If we were on Waterworld, Kevin Costner could drop a big rock in the ocean at one pole and the wave would travel in the manner described in the OP (in real world, obv, it would be disrupted by other currents and Coriolis).

[Genady]

1 minute ago, TheVat said:

Just called a spherical wave isn't it?

I don't think so. Spherical wave radiates from a center out.

Rather, a circular wave on a spherical surface.

[John Cuthber]

Reminds me of this.

 

[Leila Choudhry]

Very good reference Cuthber, I think perhaps I could say north to south sweeping meridians ?

 

[Genady]

7 minutes ago, Leila Choudhry said:

Very good reference Cuthber, I think perhaps I could say north to south sweeping meridians ?

 

Do you mean "sweeping parallels"? Meridians are lines which connect the poles,

[Leila Choudhry]

Outside of a mathematical context sweeping parallels doesn’t necessarily make the connection.

What about southward sweeping meridian line ?

[Genady]

41 minutes ago, Leila Choudhry said:

Outside of a mathematical context sweeping parallels doesn’t necessarily make the connection.

What about southward sweeping meridian line ?

The blue line here

is a meridian. It connects the North Pole with the South Pole. What do you mean for it to be sweeping southward?

[Leila Choudhry]

Point taken.

I can't believe there is no commonly used term for this.

[Genady]

1 hour ago, Leila Choudhry said:

I can't believe there is no commonly used term for this.

Maybe because it is not a commonly referred to thing? Where would you apply this term?

[TheVat]

Maybe some esoteric type of event in geoscience or astrophysics?  Asteroid impact or something impacting a point on a planet or sun?  

[Leila Choudhry]

It's a very common visual effect used.

[Genady]

3 minutes ago, Leila Choudhry said:

It's a very common visual effect used.

Then computer graphics and animation people could know.

[exchemist]

3 hours ago, TheVat said:

Maybe some esoteric type of event in geoscience or astrophysics?  Asteroid impact or something impacting a point on a planet or sun?  

It looks to me as if Rayleigh waves, as observed in earthquakes, seem to be of this type: https://en.wikipedia.org/wiki/Rayleigh_wave 

[studiot]

Since there is some interest in this subject I will post the outline mathematics.

 

I am sorry I can no longer do the LaTex since SF will not let me post from WinXP.
So if anyone can help with that I can expand.

Basically we start with Laplace's equation in 3 dimensions, in polar format, and apply a potential , V.  This can be colour value /intensity, or other quantity to produce the 'ripple' across the object.

Successive radial (r) values of V are calculated for various values of two sectional angles theta and phi., where it intersect the object from geometrical model

This is my first equation.

The general subject is called spherical harmonics, which is concerned with solutions to this equation.

A homogeneous algebraic equation separating r and the angles in the form of my second expression, rⁿf(theta, phi) gives values of V satisfying the first equation, in polar coordinates.
These are known as solid spherical harmonics of the nth degree.
The function f(theta phi) is known as a surface spherical harmonic of the nth degree.

 

The equation can be simplified by symmetry when V is independent of phi.

 

This lead to my second equation whcih upon the transformation indicated becomes

Legendre's equation

The solutions are known as Surface Zonal Harmonics, as indicated by John Cuthber.

These may result in 'patterning'.

 

This is not only used in CGI but also in computer tomography (CT scanning) via a finite element mesh.

The equations are normally solved numerically by substituting suitable simple function such as' hat' functions on the mesh, with the computer doing lots of calculations.

 

 

[Genady]

Perhaps I misunderstood the process described in OP. I thought that it is about a function,

t -> {x,y,z | z=t, x²+y²+z²=1}

for a sphere of radius 1 and t in [-1,+1].

[sethoflagos]

16 hours ago, exchemist said:

It looks to me as if Rayleigh waves, as observed in earthquakes, seem to be of this type: https://en.wikipedia.org/wiki/Rayleigh_wave 

+1

Lamb or Love waves are variations on this theme. Orbital waves seem synonymous.

A more general term might be spherical surface wave (as opposed to spherical wave which is something quite different).