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If κ is the wavenumber and ε is the rate of dissipation of turbulent energy, which of these is proportional to the spectral energy of the inertial sub-range of turbulence?

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If κ is the wavenumber and ε is the rate of dissipation of turbulent energy, which of these is proportional to the spectral energy of the inertial sub-range of turbulence?

(a) κ^-5/3ε^-2/3

(b) κ^5/3ε^-2/3

(c) κ^5/3ε^2/3

(d) κ^-5/3ε^2/3

The question was posed to me in my homework.

The query is from Turbulence Modelling topic in chapter Turbulence Modelling of Computational Fluid Dynamics

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Right choice is (d) κ^-5/3ε^2/3

To explain: The spectral energy in terms of the wavenumber and the rate of dissipation of turbulent energy is given by E(κ) ∝ κ^-5/3 ε^2/3. Where the proportionality constant is 1.5 (obtained experimentally)

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