Schroedinger's Wave Equation

[saintbert]

I recently watched a Discovery Channel special that tried to research and provide theories for: rogue waves at sea, their places of prominence around the worlds oceans, and their frequency. Near the end of the show, it had been deemed that Shroedingers Wave Equation was the best possible explanation for these.

Basically in the deep ocean, waves it would seem, travel with consistency and with order; with each wave sharing similar trough/crest size, have similar wavelengths, and more importantly travel in the same direction. But in this seemingly organized series of huge waves, something happens...or so this thoery says. Something not organized. In fact any random wave at any random time can "steal", if you will, energy from its surrounding waves to create these giagantic formations. They not only steal energy, but can create chaos by travelling in a different direction or sometimes even perependicular to the set of waves that it was created from. What is even stranger, is that this theft of energy is only temporary. For after a few seconds or minutes the extra energy is then "given" back to the same surrounding waves. The rogue wave sinks back down into normalcy and randomness can occur again, at any given place at any time.

I am just wondering if this theory might apply to things other waves where energy is "stolen".

 

[paadness]

Well.. Its not what u call "stolen". Energy is taken by one molecule, it becomes unstable and has to lose that energy to regain stability.

You have not mentioned anything complex here, just simple physics. There is more in water waves than just energy.

First of all, i know u are very interested in this topic and discovery channel has put some sort of effect on you. Previously im sure u have never heard of waves stealing energy.

If u simply replace the word steal by "gains" then yes this happens in many other circumstances.

 

[saintbert]

Originally posted by: paadness
First of all, i know u are very interested in this topic and discovery channel has put some sort of effect on you.


...And my questions have put some sort of effect on you. You taking time out of your day to reply to me will have some effect on your life. Maybe you should have gone to the store 5 minutes ago, or maybe now your wife is mad at you for not spending enough time with her and punching keys all day.

 

[paadness]

Discovery channel is for kids, i dunno why they still have discovery kids.

 

[saintbert]

Originally posted by: paadness
Discovery channel is for kids, i dunno why they still have discovery kids.

Probably because Discovery channel is not targeted towards children. If you want, I can send you a MENSA application. Or maybe that is for kids too. Make sure to say I referred you. I get a referral reward- even when you fail.

 

[f95toli]

Originally posted by: saintbert
I recently watched a Discovery Channel special that tried to research and provide theories for: rogue waves at sea, their places of prominence around the worlds oceans, and their frequency. Near the end of the show, it had been deemed that Shroedingers Wave Equation was the best possible explanation for these.

Basically in the deep ocean, waves it would seem, travel with consistency and with order; with each wave sharing similar trough/crest size, have similar wavelengths, and more importantly travel in the same direction. But in this seemingly organized series of huge waves, something happens...or so this thoery says. Something not organized. In fact any random wave at any random time can "steal", if you will, energy from its surrounding waves to create these giagantic formations. They not only steal energy, but can create chaos by travelling in a different direction or sometimes even perependicular to the set of waves that it was created from. What is even stranger, is that this theft of energy is only temporary. For after a few seconds or minutes the extra energy is then "given" back to the same surrounding waves. The rogue wave sinks back down into normalcy and randomness can occur again, at any given place at any time.

I am just wondering if this theory might apply to things other waves where energy is "stolen".

I remember seeing that documentary and wondering what the heck tthe orignaly researchers were doing.

It is not exactly correct to say that a Schroedinger equation (SE) is the best explanation because SE is an equation that describes dynamics in quantum physics; SE is just one of many examples of equations where you get non-linear wave phenomena and everyone who uses SE and similar equations are aware of the possibility of phenomena similar to the "rouge waves".
An obvious example is non-linear optics and photonics where this type of phenomena are studied an used all the time.
So there was no "new" physics in this, all of was already well known but apparantly no one had thought of trying to use the proper equations to model water waves.

If I remember correctly they were orignally trying to model these waves using a linearized model which in my opinion was just bad science, there is nothing wrong with using simplified models but you have to be very carefull when you interpret the results and they should simply have known better.

 

[eLiu]

I was under the impression that the Navier-Stokes equations are still the most accurate descriptors of water waves.

In fact we often model deep ocean waves w/the same eqns as shallow water waves (not surprisingly, most applications used the linearized version). It's kind of a rough derivation (but not too bad), but shallow water wave eqn is derived from the NS eqns. It's only when deep water waves approach the coast that the behavior becomes highly nonlinear.

 

[f95toli]

Originally posted by: eLiu
I was under the impression that the Navier-Stokes equations are still the most accurate descriptors of water waves.

In fact we often model deep ocean waves w/the same eqns as shallow water waves (not surprisingly, most applications used the linearized version). It's kind of a rough derivation (but not too bad), but shallow water wave eqn is derived from the NS eqns. It's only when deep water waves approach the coast that the behavior becomes highly nonlinear.

It is, and AFAIK N-S can be used to describe rogue waves very accurately. But it is a very complex equation so as you say simplfied versions are usually used; the problem in this case was that the linerized version they were originally using was too simplified and therefore highly non-linear phenomena like rouge waves could not be modelled.

My point was that they should have known this, I don't understand why they were trying to model somthing that is so obviously non-linear phenomena with a linerized model.
Bad science.

The version of the equation they ended up using was apparantly similar to a SE and included enough "non-linearity" to capture the essential features of this phenomena.

 

[CycloWizard]

Originally posted by: f95toli
If I remember correctly they were orignally trying to model these waves using a linearized model which in my opinion was just bad science, there is nothing wrong with using simplified models but you have to be very carefull when you interpret the results and they should simply have known better.

:thumbsup: Linear fluid dynamics cannot describe the flow instabilities that create rogue waves. The nonlinearity of the system allows such instabilities to exist, so linear models could never predict them.

Journal articles in the fields of fluid dynamics have, fairly recently, been able to describe the occurrence of rogue waves as flow instabilities. These instabilities are very similar to those found in magma flows that often result in volcanic eruption. Essentially, pressure waves may coincide synergistically to produce a local pressure singularity. As we know well, flow proceeds from points of high pressure to points of low pressure. Thus, when many pressure waves coincide at a given point, the point pressure is extremely high. Fluid will attempt to equalize the pressure by flowing away from this point as quickly as its kinematic viscosity allows. The mathematics describing these phenomena are fairly complex, but I can link to a couple journal articles with the development if anyone is interested.

Originally posted by: f95toli
It is, and AFAIK N-S can be used to describe rogue waves very accurately. But it is a very complex equation so as you say simplfied versions are usually used; the problem in this case was that the linerized version they were originally using was too simplified and therefore highly non-linear phenomena like rouge waves could not be modelled.

My point was that they should have known this, I don't understand why they were trying to model somthing that is so obviously non-linear phenomena with a linerized model.
Bad science.

The version of the equation they ended up using was apparantly similar to a SE and included enough "non-linearity" to capture the essential features of this phenomena.

Again I agree. The Navier-Stokes equation is actually exact for any type of fluid flow. In its essence, it is simply a momentum conservation equation. Since momentum must be conserved, the equation is exactly true for every flow system. It is often simplified using linear constitutive relations (i.e. Newton's 'law' of viscosity) to allow analytical solutions, but this is only a limitation of the user of the equation, not the equation itself. Indeed, I believe these flow instabilities can actually be described using Newton's law of viscosity, despite its linearity, as nonlinearities arise elsewhere in the Navier-Stokes equation when one must consider both diffusive and convective momentum transfer.

 

[Merovingian]

Originally posted by: paadness
Well.. Its not what u call "stolen". Energy is taken by one molecule, it becomes unstable and has to lose that energy to regain stability.

You have not mentioned anything complex here, just simple physics. There is more in water waves than just energy.

First of all, i know u are very interested in this topic and discovery channel has put some sort of effect on you. Previously im sure u have never heard of waves stealing energy.

If u simply replace the word steal by "gains" then yes this happens in many other circumstances.

Borrow would be a more accurate term here.

 

[PowerEngineer]

I'm afraid that the Discovery Channel often promotes "junk science" like this notion that quantum mechanics and the small-scale uncertainity between energy and position have any application to a large system like an ocean and its waves. Another example was their investigation of the Bermuda Triangle.

Better to watch Discovery Channel for the choppers!

 

[f95toli]

As far as I remember this had nothing to do with the Heisenberg principle.
The only reason SE was mentioned was because the physicist that helped them solve the problem usually worked on problems in quantum mechanics; he was simply familiar with non-linear PDEs like SE and knew that you can not linearize equations of that type and expect so correctly model complex phenomena like deep-sea waves.

 

[Merovingian]

I agree, the idea on a macro scale seems a retarded, linear eq's would certainly be used in such a solution. But I love discovery HD for the animal aspects, you have never seen a lion eat a zebra at full speed like you see it on HD unless your there, amazing. I saw some Heisenberg uncertainty episode and it was pretty damn flawed at times. If you want to understand this stuff on a basic level, books under titles by hawking are good for the average person but I like greene best. IMO.