lecture18 - Lecture 18- Marine Hydrodynamics Lecture 18 4.9...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 18- Marine Hydrodynamics Lecture 18 4.9 Turbulent Flow Reynolds Stress Assume a ow v with a time scale T . Let denote a time scale << T . We can then write for each component of the velocity u i = u i + u i (1) where by definition 1 u i = u i dt It immediately follows that u i u = u i u i = u i u i = 0 , also u i etc. = i x x Substitute Eq. (1) into continuity and average over , i.e., take ( ) + u i = 0 , = u i u i u i = 0 x i = x i x i x i u i u i u i , = u i = 0 x i but = 0 = + x i x i x i , just shown 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20 ( ) Substitute Eq. (1) into the momentum equations and take ( ) u i u i 1 ij 1 p 2 + u j = = + u i t x j x j x i 2 = 2 u i u i u i u i u i ; similarly + = t t t p = ( p + p ) = p x i x i etc....
View Full Document

This note was uploaded on 02/27/2012 for the course MECHANICAL 2.20 taught by Professor Dickk.p.yue during the Spring '05 term at MIT.

Page1 / 5

lecture18 - Lecture 18- Marine Hydrodynamics Lecture 18 4.9...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online