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Rotational flow in gravity current heads.
1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, UK. jnm11@damtp.cam.ac.uk
Summary
This study analyzes gravity currents and plumes on slopes, finding a constant Froude number of radical2 and a 60-degree front angle. These findings explain avalanche pressures and extend prior research to various slope angles and velocities.
Area of Science:
- Fluid dynamics
- Geophysics
Background:
- Gravity currents and plumes are common phenomena in nature and industry.
- Understanding their behavior on slopes is crucial for predicting events like avalanches.
Purpose of the Study:
- To analyze the structure of gravity currents and plumes on slopes of arbitrary angles.
- To extend the theoretical understanding of these flows, particularly near the front.
Main Methods:
- Utilizing inviscid, rotational flow solutions in a wedge geometry.
- Applying these solutions to model the flow near the front of a gravity current.
Main Results:
- Derivation of a constant Froude number (radical2) for these flows.
- Determination of the angle of the flow front to the slope as 60 degrees.
- Extension of von Kármán's (1940) results to arbitrary slope angles and high internal velocities.
Conclusions:
- The theoretical predictions align with experimental observations.
- The model successfully explains the significant negative pressures observed in avalanches.
- This research provides a more comprehensive understanding of gravity-driven flows on inclined surfaces.