# Wave equation derivation for ocean waves

• swedishfishh
In summary, the conversation is about a mechanical engineering student who is interested in physical oceanography and is looking for sources to understand the wave equation and its application in studying ocean waves. Some recommended resources include the book "Introduction to Physical Oceanography" by John A. Knauss and the website of the National Oceanic and Atmospheric Administration.
swedishfishh
Hi there,

I'm a mechanical engineering student who's extremely interested in going into physical oceanography after finishing undergrad.

I'm trying to find a good source for the wave equation as it relates to physical oceanography, as well as orbital paths of particles, and have yet to find one. Mechanical vibrations and differential equations have taught me about the wave equation as it relates to engineering, and specifically material mechanics, but I'm having a hard time relating it to fluids and ocean waves.

Does anybody have any good explanations or sources for the derivation?

Thanks!

swedishfishh, Welcome to Physics Forums!

"More recently, significant wave-height is calculated from measured wave displacement. If the sea contains a narrow range of wave frequencies, H1/3 is related to the standard deviation of sea-surface displacement (NAS, 1963: 22; Hoffman and Karst, 1975) (equation)(16.13)
where (equation) is the standard deviation of surface displacement. This relationship is much more useful, and it is now the accepted way to calculate wave-height from wave measurements.

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_01.htm

and:

http://www.bom.gov.au/marine/waves.shtml

Hi there,

I am also interested in physical oceanography and have come across some helpful resources for understanding the wave equation in relation to ocean waves. One source that I have found particularly useful is the book "Introduction to Physical Oceanography" by John A. Knauss. It has a thorough explanation of the wave equation and its application in physical oceanography.

Another helpful resource is the website of the National Oceanic and Atmospheric Administration (NOAA), specifically their section on ocean waves. They have a lot of information on the different types of waves and their characteristics, as well as the mathematical equations used to study them.

I hope this helps and good luck with your studies!

## What is the wave equation for ocean waves?

The wave equation for ocean waves is a mathematical formula that describes the behavior of waves in the ocean. It is a partial differential equation that relates the spatial and temporal variations of a wave's amplitude and wavelength.

## How is the wave equation derived?

The wave equation is derived using the principles of fluid dynamics, specifically the Navier-Stokes equations. It takes into account the effects of gravity, surface tension, and viscosity on the ocean waves.

## What are the assumptions made in the derivation of the wave equation for ocean waves?

The derivation of the wave equation assumes that the ocean is an ideal fluid with a uniform depth, and that the waves are small and non-breaking. It also neglects the effects of wind and other external forces.

## What are the applications of the wave equation for ocean waves?

The wave equation for ocean waves is used in various fields such as oceanography, coastal engineering, and marine renewable energy. It helps in predicting the behavior of ocean waves and designing structures that can withstand their forces.

## Are there any limitations to the wave equation for ocean waves?

The wave equation has limitations in accurately predicting the behavior of large and complex ocean waves, such as storm waves and tsunamis. It also does not consider the effects of wave breaking and wave interactions, which can affect the accuracy of its predictions.

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