Over fifty years ago, Carl Eckart described the sequence of processes as a passive scalar is stirred and mixed in a turbulent flow (Eckart, 1948). At first, during the stirring phase, the variance of the scalar gradient is greatly increased, but later, during the mixing phase, the gradients become sufficiently sharp that molecular diffusion becomes important and the gradient variance rapidly decreases. The process is of great practical importance in many engineering situations as well as being familiar from adding cream to coffee.

Müller, P., and C. Garrett. 2002. From stirring to mixing in a stratified ocean. Oceanography 15(3):12–19, https://doi.org/10.5670/oceanog.2002.10.

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