Microscopic turbulence-flame interactions of thermonuclear fusion flames occuring in Type Ia Supernovae were studied by means of incompressible direct numerical simulations with a highly simplified flame description .
The flame is treated as a single diffusive scalar field with a nonlinear source term .
It is characterized by its Prandtl number , Pr \ll 1 , and laminar flame speed , S _ { L } .
We find that if S _ { L } \geq u ^ { \prime } , where u ^ { \prime } is the rms amplitude of turbulent velocity fluctuations , the local flame propagation speed does not significantly deviate from S _ { L } even in the presence of velocity fluctuations on scales below the laminar flame thickness .
This result is interpreted in the context of subgrid-scale modeling of supernova explosions and the mechanism for deflagration-detonation-transitions .