# Coordinate-free description of corrugated flames with realistic density drop at the front.

@article{Bychkov2003CoordinatefreeDO, title={Coordinate-free description of corrugated flames with realistic density drop at the front.}, author={Vitaly Bychkov and Maxim Zaytsev and V’yacheslav Akkerman}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2003}, volume={68 2 Pt 2}, pages={ 026312 } }

The complete set of hydrodynamic equations for a corrugated flame front is reduced to a system of coordinate-free equations at the front using the fact that the vorticity effects remain relatively weak even for corrugated flames. It is demonstrated how small but finite flame thickness may be taken into account in the equations. Similar equations are obtained for turbulent burning in the flamelet regime. The equations for a turbulent corrugated flame are consistent with the Taylor hypothesis of…

## 13 Citations

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## References

SHOWING 1-2 OF 2 REFERENCES

### Fluid Mechanics

- PhysicsNature
- 1980

Ludwig Krinner (Dated: November 5th 2012) Abstract This is a script made with the help of Landau Lifshitz, Book VI [1] on fluid mechanics, that gives a short introduction to basic fluid mechanics.…