Abstract
The previous analytical developments of slope flows presented by Ellison and Turner (1959) and Manins and Sawford (1979a) are reinterpreted here in terms of a broader viewpoint of entrainment dynamics. The qualitative role of clear air radiational cooling and phase-change are also included. A transformation of variables allows categorization of the flow possibilities into several dynamical regimes.
If the initial flow near the top of the slope is not too stable, entrainment attempts to modify the flow toward a state of turbulence equilibrium while the dynamics drives the flow toward dynamical equilibrium. The interplay between the entrainment and dynamics produces an equilibrium state characterized by a constant bulk Richardson number which is smaller than the critical bulk Richardson number for turbulence.
If the flow is initially very stable, it evolves towards a decelerating and thick slope flow. Weak slopes and strong surface drag or intense clear air radiational cooling can lead to a state which is mathematically, but not physically, similar to the classical hydraulic jump.
Even the sign of the variation of temperature along the slope is found to depend on the particular dynamical regime of the flow which in turn depends on initial conditions, clear air radiational cooling and the geometry of the slope.
If the initial flow near the top of the slope is not too stable, entrainment attempts to modify the flow toward a state of turbulence equilibrium while the dynamics drives the flow toward dynamical equilibrium. The interplay between the entrainment and dynamics produces an equilibrium state characterized by a constant bulk Richardson number which is smaller than the critical bulk Richardson number for turbulence.
If the flow is initially very stable, it evolves towards a decelerating and thick slope flow. Weak slopes and strong surface drag or intense clear air radiational cooling can lead to a state which is mathematically, but not physically, similar to the classical hydraulic jump.
Even the sign of the variation of temperature along the slope is found to depend on the particular dynamical regime of the flow which in turn depends on initial conditions, clear air radiational cooling and the geometry of the slope.
| Original language | English |
|---|
| Place of Publication | Roskilde |
|---|---|
| Publisher | Risø National Laboratory |
| Number of pages | 33 |
| Publication status | Published - 1980 |
| Series | Risø-R |
|---|---|
| Number | R-420 |
| ISSN | 0106-2840 |
Keywords
- Risø-R-420