Methodology

• The sample mean and variance of N independent observations from a random variable x are,

• Assumption: a normal distribution in x.

• Note that x and s² correspond to the phase-averaged velocity and normal Reynolds stress for the present study.

1. Statistical convergence of the mean value

• Confidence interval for mean value

where t_n is Student-t statistic and n = N-1. 

Or,

where,

• Statistical convergence error of mean value is defined as

2. Statistical convergence of the variance value

• Confidence interval for variance value is

where χ_n is chi-square statistic and n = N-1 is the degree of freedom.

Or,

where

• Statistical convergence error of variance is defined as