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Tsunami and math

jai6638

Golden Member
Hey.. i was wondering how math ( especially algebra ) could be used in gathering information about it that could help in its prevention? what are the formulae, if any, that can be used to find the distance/height, impact ,etc of the tsunami?

thanks
 
Originally posted by: jai6638
Hey.. i was wondering how math ( especially algebra ) could be used in gathering information about it that could help in its prevention? what are the formulae, if any, that can be used to find the distance/height, impact ,etc of the tsunami?

thanks

Im sure there are lot's, the physics of a tsunami is pretty well understood.
 
A tsunami is mathematically modeled by a particular form of a partial differential equation (PDE). Do a search for "soliton", "PDE", "mathematical", and/or "model" and I bet you'll find tons of web pages on the subject.

PDEs are often introduced to juniors/seniors in college who have had three semesters of calculus and one semester of ordinary differential equations. And even then, typically you aren't taught how to solve any but the most basic PDEs. Thus, to understand it, you need knowledge that is well beyond algebra. A true PDE class is typically first taught to masters students in math and engineering. There will be several other more advanced PDE courses for advanced masters and PhD students in math and engineering.

A typical PDE for a soliton may look like this (from a googled web page):

(du/dt) + 6 * u * (du/dx) + (d^3u/dx^3) = 0

where u is the height of the water, t is time, x is position. One particular solution to that equation looks like this:

u = sech[ a^0.5 * (x - 2 * t * a) / 2^0.5 ]^2 * a

where a is a constant (varies with the magnitude of the original disturbance). Of course, this is just a 2-D model of a soliton travelling in one direction (probably a decent simplification). The Earth is curved and that would really complicate matters beyond ability to get an algebraic solution. 😉 Or we can include other real world problems (such as uneven ocean floor height when the soliton approaches land). Something like that would really make algebraic solution impossible.
 
Originally posted by: dullard
A tsunami is mathematically modeled by a particular form of a partial differential equation (PDE). Do a search for "soliton", "PDE", "mathematical", and/or "model" and I bet you'll find tons of web pages on the subject.

PDEs are often introduced to juniors/seniors in college who have had three semesters of calculus and one semester of ordinary differential equations. And even then, typically you aren't taught how to solve any but the most basic PDEs. Thus, to understand it, you need knowledge that is well beyond algebra. A true PDE class is typically first taught to masters students in math and engineering. There will be several other more advanced PDE courses for advanced masters and PhD students in math and engineering.

A typical PDE for a soliton may look like this (from a googled web page):

(du/dt) + 6 * u * (du/dx) + (d^3u/dx^3) = 0

where u is the height of the water, t is time, x is position. One particular solution to that equation looks like this:

u = sech[ a^0.5 * (x - 2 * t * a) / 2^0.5 ]^2 * a

where a is a constant (varies with the magnitude of the original disturbance). Of course, this is just a 2-D model of a soliton travelling in one direction (probably a decent simplification). The Earth is curved and that would really complicate matters beyond ability to get an algebraic solution. 😉 Or we can include other real world problems (such as uneven ocean floor height (such as when the soliton approaches land). Something like that would really make algebraic solution impossible.

<head explodes, then the little pieces explode again>
 
If you want to prevent tsunami's with math, just figure out how to stop the tectonic plates from moving.
Otherwise all you can do is weaken the destructive strength.
 
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