| 79 | | The evaluation of turbulent fluxes should be consistent to the decretization in the prognostic equations, else some unphysical effects will occur. For example, the computation of the fluxes as variances and covariances will induce some conspicuous kinks in vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. For computing turbulent fluxes as appearing in the prognostic equations the computed fluxes in the advection routines are buffered and reused also for the statistics. For getting only the turbulent, not the mean signal and to remove the influence of Galilei transformation, the flux F_i has to be multiplied with a factor … and the dissipative flux with … . Furthermore the turbulent fluxes are evaluated on each Runge-Kutta substep and weighted with the respective Runge-Kutta coefficients, to remove dependencies of the Runge-Kutta substep. The interpretation of the turbulent fluxes as variances and covariances is no longer valid when using WS5. For other advection schemes like the PW scheme the interpretation of turbulent fluxes as co/variances is still valid, because the discretization is alike the computation of the co/variances. |
| | 79 | The evaluation of turbulent fluxes should be consistent to the discretization in the prognostic equations, else some unphysical effects will occur. For example, the computation of the fluxes as variances and covariances will induce some conspicuous kinks in vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. For computing turbulent fluxes as appearing in the prognostic equations the computed fluxes in the advection routines are buffered and reused also for the statistics. For getting only the turbulent, not the mean signal and to remove the influence of Galilei transformation, the centered flux F,,i+1/2,, has to be multiplied with a factor |
| | 80 | {{{ |
| | 81 | #!Latex |
| | 82 | \[ \frac{u_{i+\frac{1}{2}} - 2 \overline u}{u_{i+\frac{1}{2}} - u_{i, Galilei}} \] |
| | 83 | }}} |
| | 84 | and the dissipative flux with a factor |
| | 85 | {{{ |
| | 86 | #!Latex |
| | 87 | \[ \frac{|u_{i+\frac{1}{2}} - 2 \overline u|}{|u_{i+\frac{1}{2}} - u_{i, Galilei}|}, \] |
| | 88 | }}} |
| | 89 | where u denotes the respective velocity component. Furthermore the turbulent fluxes are evaluated on each Runge-Kutta substep and weighted with the respective Runge-Kutta coefficients, to remove dependencies of the Runge-Kutta substep. The interpretation of the turbulent fluxes as variances and covariances is no longer valid when using WS5. For other advection schemes like the PW-scheme the interpretation of turbulent fluxes as co/variances is still valid, because the discretization is alike the computation of the co/variances. |
