Deep Water Tsunami Physics And Approx Run Up Heights

[enki2000]

I would like to see quality feedback on a small physics "problem". Mathematical modeling of Tsunamis is non-exisent. Waves themselves are loosely modeled under shallow water wave differential equations. It is my understanding that this moedling system does not apply to Tsunami mathmateical models.

For instance shallow water wave differental equations basically state (to my understanding) that the run up height of a Tsunami can not be over 100 ft regardless of initial energy imparted to the model... yet the Lituya Bay Tsunami has a run-up height of over 1500 feet and evidence of Tsunamis that have hit the tip of Madagascar in Ancient history had a run-up height of at least 900 feet.

So the "problem" I would like to discuss is thus. I recently watched a discovery special which talked about "mega tsunamis". They showed an example which I assume had some mathematical validlity to it. In this example Mauna Loa had an eruption in which one whole side of the volcane collapased into the sea. The raw displacement was 360 cubic miles of rocked sliding down on an at least 45 degree slope directly into the pacific ocean. In their model the wave would reach Oahu in 30 minutes and have a run-up height of over 1,000 feet and a land speed of 50mph or more and charging inland approx 22 - 25 miles.

Assuming their is some validity to mathematical modeling... I would like to enlarge the scenario and get feedback from qualified physicists. Assume the mass is Antartica and the ice pack is some 10 times the size it is today. Assume ocean levels are 200 - 300 feet more shallow than today. Assume that a mass of ice approx 5000 cubic miles in volume slid down a similar 45 degree slope into the Antartic ocean.

In this equation the persian gulf would not exist as it is extremely shallow (270 feet at its deepest) and the sea levels in the scenario are 200 - 300 feet lower. Assume then that the persian gulf is a River Valley with rivers dumping into the Indian Ocean (just as the Tigris and Euphrates dump into the Persian Gulf today).

In this scenario, with the displacement of 5000 cubic miles of ice into the AntArtic Ocean, is there sufficient energy in the system to produce of run up height of approx 3,000 to 4,000 feet in the River Valley which would sit where the Persian gulf sits today ? Although this is thousands of miles from Antartica the Tsunami would lose little energy across the deep Antartic and Indian Oceans.

 

[stewartcs]

I would like to see quality feedback on a small physics "problem". Mathematical modeling of Tsunamis is non-exisent. Waves themselves are loosely modeled under shallow water wave differential equations. It is my understanding that this moedling system does not apply to Tsunami mathmateical models.

For instance shallow water wave differental equations basically state (to my understanding) that the run up height of a Tsunami can not be over 100 ft regardless of initial energy imparted to the model... yet the Lituya Bay Tsunami has a run-up height of over 1500 feet and evidence of Tsunamis that have hit the tip of Madagascar in Ancient history had a run-up height of at least 900 feet.

So the "problem" I would like to discuss is thus. I recently watched a discovery special which talked about "mega tsunamis". They showed an example which I assume had some mathematical validlity to it. In this example Mauna Loa had an eruption in which one whole side of the volcane collapased into the sea. The raw displacement was 360 cubic miles of rocked sliding down on an at least 45 degree slope directly into the pacific ocean. In their model the wave would reach Oahu in 30 minutes and have a run-up height of over 1,000 feet and a land speed of 50mph or more and charging inland approx 22 - 25 miles.

Assuming their is some validity to mathematical modeling... I would like to enlarge the scenario and get feedback from qualified physicists. Assume the mass is Antartica and the ice pack is some 10 times the size it is today. Assume ocean levels are 200 - 300 feet more shallow than today. Assume that a mass of ice approx 5000 cubic miles in volume slid down a similar 45 degree slope into the Antartic ocean.

In this equation the persian gulf would not exist as it is extremely shallow (270 feet at its deepest) and the sea levels in the scenario are 200 - 300 feet lower. Assume then that the persian gulf is a River Valley with rivers dumping into the Indian Ocean (just as the Tigris and Euphrates dump into the Persian Gulf today).

In this scenario, with the displacement of 5000 cubic miles of ice into the AntArtic Ocean, is there sufficient energy in the system to produce of run up height of approx 3,000 to 4,000 feet in the River Valley which would sit where the Persian gulf sits today ? Although this is thousands of miles from Antartica the Tsunami would lose little energy across the deep Antartic and Indian Oceans.

NOAA has some deep water models. Also try searching some Ocean Engineering Journals.

http://nctr.pmel.noaa.gov/model.html

CS

 

[LURCH]

Flood theory?

It is important to remember that the models used for a regular tsunami will not apply to a megatsunami. Modeling has shown that the extremely high run-up of megatsunamies is a result of water being displaced not only by the volume of debris involved in a landslide, but also by a pocket of air many times that same value.

 

[arildno]

I would like to see quality feedback on a small physics "problem". Mathematical modeling of Tsunamis is non-exisent. Waves themselves are loosely modeled under shallow water wave differential equations. It is my understanding that this moedling system does not apply to Tsunami mathmateical models.

For instance shallow water wave differental equations basically state (to my understanding) that the run up height of a Tsunami can not be over 100 ft regardless of initial energy imparted to the model...

Complete nonsense.
Shallow water equations is, essentially, a perturbative technique that can be taken to arbitrary order of accuracy with respect to a wave number parameter.

That linearized, first-order shallow water equations might not get all physical results correct is only to be expected.

The great advantage with shallow water equations by specifying, say, the vertical velocity distribution in a perturbative manner (for example with the use of polynomials in "z") is that the calculational burden is reduced by at least one order of magnitude.

 

[enki2000]

Flood theory?

I would rather not taint it as such, and keep it strictly mathematical.

 

[enki2000]

Complete nonsense.
Shallow water equations is, essentially, a perturbative technique that can be taken to arbitrary order of accuracy with respect to a wave number parameter.

That linearized, first-order shallow water equations might not get all physical results correct is only to be expected.

The great advantage with shallow water equations by specifying, say, the vertical velocity distribution in a perturbative manner (for example with the use of polynomials in "z") is that the calculational burden is reduced by at least one order of magnitude.

Would you be willing to help us with some of the mathematical analysis ? it is for a show in development and you will receive credit.

 

[RTW69]

Oregon State University has one of the largest research programs in the world on tsunamis including a Tsunami wave basin. Google Tsunami research Oregon State University.