The Damkohler number is used in turbulent combustion and corresponds to the ratio of chemical time scale and turbulent time scale . This turbulent scale is usually taken as the integral scale.
Damkohler number measures how important is the interaction between chemistry and turbulence. Most combustion models are placed in the extremes of Damkohler.
If the turbulence is much faster than the chemistry. This regime is the "well-stirred reactor", where products and reactants are rapidly mixed. The Karlovitz number is linked to the Damkholer number.