Question

Which of these is the spectral cut-off filter function?

(a) \(\prod_{i=1}^3\frac{sin[(x_i-x_i^{‘})/\Delta]}{(x_i-x_i^{‘})}\)

(b) \(\prod_{i=1}^3 sin[(x_i-x_i^{‘})/\Delta] \)

(c) \(\prod_{i=1}^3\frac{sin[(x_i-x_i^{‘})]}{(x_i-x_i^{‘})}\)

(d) \(\prod_{i=1}^3 sin[(x_i-x_i^{‘})/\Delta]\)

This question was posed to me in homework.

Enquiry is from Large Eddy Simulation for Turbulent Models topic in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Correct choice is (a) \(\prod_{i=1}^3\frac{sin[(x_i-x_i^{‘})/\Delta]}{(x_i-x_i^{‘})}\)

To explain I would say: The spectral cut-off filter is the product of \(\frac{sin[(x_i-x_i^{‘})]}{(x_i-x_i^{‘})}\) for all three directions of the x-vector. This gives a sharp cut-off in the energy spectrum at a wavelength of Δ/π.