Turbulent Pipe Flow 

1. Re_tau=180

   • Mean of velocity and pressure  

   • Variances of velocity and pressure components 

   • Variances of vorticity components and pressure  

   • Reynolds stress transport equation 

     • uzuz

     • urur

     • utut

     • uruz

     • k

   • 1D energy spectra

2. Re_tau=550

   • Mean of velocity and pressure  

   • Variances of velocity and pressure components 

   • Variances of vorticity components and pressure  

   • Reynolds stress transport equation 

     • uzuz

     • urur

     • utut

     • uruz

     • k

   • 1D energy spectra

3. Re_tau=1000

   • Mean of velocity and pressure  

   • Variances of velocity and pressure components 

   • Variances of vorticity components and pressure  

   • Terms in Reynolds stress transport equation 

   • 1D energy spectra

4. Re_tau=2000

   • Mean of velocity and pressure  

   • Variances of velocity and pressure components 

   • Variances of vorticity components and pressure  

   • Terms in Reynolds stress transport equation 

   • 1D energy spectra