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Dynamical systems model of entrainment due to coherent structures
Srevatsan Muralidharan1, K R Sreenivas, Rama Govindarajan
1Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
Turbulent shear flow lifetime depends on entrainment. This study models this using two pairs of point vortices, revealing chaotic advection drives entrainment and viscosity reduces it.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Turbulence
Background:
- Turbulent shear flow lifetime is inversely proportional to fluid entrainment.
- A prior dynamical systems model used leap-frogging vortex rings for heated jets.
Purpose of the Study:
- To investigate the two-dimensional equivalent of the heated jet model: two pairs of corotating point vortices.
- To demonstrate entrainment as a result of chaotic advection in this system.
- To analyze the impact of viscosity on entrainment and vortex dynamics.
Main Methods:
- Mathematical modeling of two pairs of corotating point vortices.
- Analysis of system nonintegrability.
- Investigation of chaotic advection.
- Inclusion of core diffusion due to viscosity.
Main Results:
- The two-dimensional vortex pair system is proven nonintegrable for finite separation.
- Chaotic advection naturally leads to fluid entrainment.
- Increased viscosity reduces the entrainment rate by decreasing the vortex leap-frogging frequency.
Conclusions:
- The nonintegrable dynamics of point vortices effectively model turbulent shear flow entrainment.
- Chaotic advection is a key mechanism for entrainment in such flows.
- Viscosity plays a crucial role in modulating entrainment rates by affecting vortex interactions.