{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Turbulence lecture 24

# Turbulence lecture 24 - Turbulence Lecture 24 ^ ^ ui k)u j...

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

Turbulence Lecture 24 () () * ˆˆ ij k uk t ± ±± The contribution from the non-linear terms () ( ) ( ) ( ) { } ( ) ( ) () ( ) ( {} ** * , , ˆ ˆ ˆˆ ˆ ˆ ˆ ss i j j i k i j i j k ik u k u u kk u k i k u uk k u kuku −− =− A ± ± A ± ± AA A A ± ± ± ± ) ˆ = A From continuity ˆ 0 ku k Ai A So ku k u k −= iA A i Note that for real. ax Then () ( ) * ak a k ( ) ( ) ( ) ( ) ( ) { } , ˆ 0! i j i j k k u u A = ± ± / / Because integrating over all and k . A ( ) ( ) jj = A ± ± uu k Total energy – nonlinear term – no effect. * 2 0 ˆ 0 k i k ukuk t t = ± ± ± Inertial terms transfer energy from one part of spectral domain to another, without changing total energy, even without changing total energy in any component ( u, v, w ). What can we say about the direction of the transfer to different wave numbers? In general – can’t say anything, it depends on flow conditions type of flow, etc. 1

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

View Full Document
e.g. in most 3D flows, the net energy transfer is from large scales to small scales, but in
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Turbulence lecture 24 - Turbulence Lecture 24 ^ ^ ui k)u j...

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

View Full Document
Ask a homework question - tutors are online