Does Hyugen's principle apply in three dimensions?

[Tom79Tom]

Does Hyugens principle apply in three dimensions ?

If a surface wave (for simplicity an ocean wave) is propagating along the x-axis we know that this wave ray is a point source for wavelets on the y-axis but what about the z axis?

If this diagram was 3d would we see a spherical wave front expanding from each point

http://physics.ucdavis.edu/Classes/Physics9B_Animations/ReflRefr.html

 

[Charles Link]

The answer is yes it does, and a good example is the Bragg scattering in crystals. See also https://www.physicsforums.com/threads/davison-germer-experiment-bragg-condition.937293/#post-5924069 In introductory courses, the typical Huygens source is a narrow slit, but the theory holds in 3 dimensions for quite a variety of scenarios.

 

[Tom79Tom]

but the theory holds in 3 dimensions for quite a variety of scenarios.

Thanks Charles would this include mechanical waves ?
Intuitively this makes sense in fluids as they are unable to sustain shear any disturbance would be in all directions is this the logic ?

 

[Charles Link]

Thanks Charles would this include mechanical waves ?
Intuitively this makes sense in fluids as they are unable to sustain shear any disturbance would be in all directions is this the logic ?

I think it is likely that similar principles apply, but I don't have any expertise with the propagation of sound waves in fluids.

 

[haushofer]

Isn't Huygens principle merely a statement about linearity? I'd say if your partial differential equation is linear, then Huygens principle applies. The wave equation is linear in all three directions.

 

[Charles Link]

Huygens principle in many ways is more than that. Huygens principle says that you can pick any plane of a wavefront and consider the plane as consisting of infinitesimal sources that radiate in all directions, ( i.e. in all directions into the forward direction, but not in the reverse direction). $\\$ To the OP: Waves in liquids behave in many ways like other waves, and even in some ways like E&M waves, but again, I do not have expertise in this area of waves in liquids.

 

[sophiecentaur]

i.e. in all directions into the forward direction, but not in the reverse direction).

This is how the original Huygens principle was stated. On its own, that sounds too arbitrary to me and could do with some justification. I don't think there's an arm waving justification but an 'obliquely factor' was proposed, which suppresses the backward wave (in this link). A more formal source gives a reason for the backwards wave not existing.
The first stab at Huygens involves dealing with a flat (/plane) wavefront and this would involve all wavelets having the same amplitude. In a beam that's passed through some aperture, the amplitude will vary over the width, which makes things more complicated. The wavelets would have to be given appropriate amplitudes across the wave front.