Interpretation of complex wave number

[MaAl]

Dear forum members,

I'm wondering about the physical meaning of the imaginary part of a complex wave number (e.g., the context of fluid dynamics or acoustics). It is obvious that

$$w = \hat{w} \mathrm{e}^{i k_z z}$$

describes an undamped wave if $$k_z = \Re(k_z)$$ and an evanescent wave if $$k_z = \Im(k_z)$$.

If $$k_z = \Re(k_z)$$ is proportional to the energy of the wave, can I interpret
$$k_z = \Im(k_z)$$ as a kind of dissipation/reduction of energy per length z?

Thanks!

 

[Delta2]

$\Re(K_z)$ is proportional to the wavelength of wave and $\Im(K_z)$ as you say , relates to the energy reduction per length z.

 

[boneh3ad]

$\Re(K_z)$ is proportional to the wavelength of wave and $\Im(K_z)$ as you say , relates to the energy reduction per length z.

Or energy increase, in the case of an unstable wave. $\Im(k_z)$ needn't be positive.