Open Access
Table 1.
Glossary of the notations used in this paper.
| Symbol | Definition |
|---|---|
| f0 | Time-averaged equilibrium value of the quantity f |
 |
Instantaneous Reynolds average of f |
 |
Instantaneous Favre average of f |
| ⟨f⟩L | Lagrangian-mean of f |
| f1 | Fluctuation of f around f0 |
| f′ | Fluctuation of f around  |
| f″ | Fluctuation of f around  |
| ai, bij | Drift and diffusion coefficients in velocity stochastic |
| differential equation (SDE) | |
| C0 | Kolmogorov constant |
| c0 | Equilibrium sound speed |
| ϵ | Turbulent dissipation rate |
| ηi | Time derivative of Wiener process |
| gi | Gravitational acceleration |
| Gij | Drift tensor in velocity SDE |
| γ | Polytropic exponent |
| Γ1 | First adiabatic exponent |
| k | Turbulent kinetic energy |
| K | Kernel weighting function in SPH formalism |
| p | Gas pressure |
| ρ | Gas density |
| ui | Flow velocity in Eulerian frame |
 |
Fluid particle velocity in Lagrangian frame |
| ui, t | Turbulent part of ui |
| ui, osc | Oscillatory part of ui |
| Wi | Wiener process |
| xi | Eulerian average position of fluid particle |
| (used as Eulerian space variable) | |
 |
Fluid particle position in Lagrangian frame |
| Xi | Instantaneous fluid particle position, as a |
| function of Eulerian average position | |
| ξi | Fluctuation of Xi around xi |
| ξi, t | Turbulent part of ξi |
| ξi, osc | Oscillatory part of ξi |
| ωt | Turbulent frequency |
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.