[Falu]

Hey People,

Im a little bit confused with the terms "Length Scale" and "Wavenumber".

In the idea of richardsons energy cascade, it is called that the energy flows from the big eddies to small eddies. The smallest eddies have the kolmogorov length scale l_k. The different areas of the energy cascade are distinguished on the basis of the length scale.

Is this term of "length scale" equivalent to the term of the wavenumber? I think it is, but why are some scientific articles or simulation programms refering to the wavenumber, others to the length scale?

[FMDenaro]

Originally Posted by Falu

Hey People,

Im a little bit confused with the terms "Length Scale" and "Wavenumber".

In the idea of richardsons energy cascade, it is called that the energy flows from the big eddies to small eddies. The smallest eddies have the kolmogorov length scale l_k. The different areas of the energy cascade are distinguished on the basis of the length scale.

Is this term of "length scale" equivalent to the term of the wavenumber? I think it is, but why are some scientific articles or simulation programms refering to the wavenumber, others to the length scale?

No, a wavelenght is dimensionally a lenght, the wavenumber is an integer.
To understand better, consider a periodic function over a lenght L. This way, L is the maximum wavelenght in the domain. It corresponds to the wavenumber 1.

Mathematically you can see that from the Fourier basis exp(i*k*x) where



k=n*2*pi/L



being n the wavenumber and k the spatial frequency (dimension L^-1). That means the L=2*pi/k is the wavelenght at the wavenumber =1.

[Falu]

Allright, Thanks for the reply.

But now i wonder, is the length scale the same as 1/(spatial frequency)? Or is there no correlation?

[FMDenaro]

Originally Posted by Falu

Allright, Thanks for the reply.

But now i wonder, is the length scale the same as 1/(spatial frequency)? Or is there no correlation?

yes, you can read a spatial frequency, for example in an anergy spectrum, as associated to a certain lenght scale.