Question

Which of these represent spatial averaging?

(a) \(\frac{1}{V}\sum\phi\)

(b) \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\)

(c) \(\frac{1}{T}\int_T \phi dT\)

(d) \(\frac{1}{N}\int_N \phi dN\)

This question was posed to me in my homework.

My question is taken from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Right option is (b) \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\)

The best explanation: Spatial averaging represents the mean based on a particular space interval or volume. So, equation \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\) represents spatial averaging.