Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number $\mathrm{Re}=\overline{u}L/\nu$ and an active matter Rayleigh number, $R=\left|\zeta \right|S^{2}L/D\overline{u}$. Here $\overline{u}$ is the mean velocity of flow, $L$ is the system size, $\nu$ is the kinematic viscosity, $\zeta$ is the activity coefficient, $S$ is the concentration gradient, and $D$ is the active matter diffusion coefficient. In the mixing limit, $\mathrm{Re}\gg 1,R\ll 1$, we show that the standard Kolmogorov energy spectrum law, $E\left(k\right)\propto k^{-5/3}$, is realized. On the other hand, in the stratified limit, $\mathrm{Re}\gg 1,R\ll 1$, there is a new turbulence universality class with $E\left(k\right)\propto k^{-7/5}$. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.

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• Transition to turbulence
• Turbulence
• Living matter & active matter
• Nonequilibrium systems