We study the fundamental problem of mixing and chemical reactions under a Rayleigh‐Taylor‐type hydrodynamic instability in a miscible two‐fluid system. The dense fluid mixture, which is generated at the fluid‐fluid interface, leads to the onset of a convective fingering instability and triggers a fast chemical dissolution reaction. Contrary to intuition, the dissolution pattern does not map out the finger geometry. Instead, it displays a dome‐like, hierarchical structure that follows the path of the ascending fluid interface and the regions of maximum mixing. These mixing and reaction hot spots coincide with the flow stagnation points, at which the interfacial mixing layer is compressed and deformed. We show that the deformation of the boundary layer around the stagnation points controls the evolution of the global scalar dissipation and reaction rates and shapes the structure of the reacted zones. The persistent compression of the mixing layer explains the independence of the mixing rate from the Rayleigh number when convection dominates.

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Viscous fingering and wormhole growth are complex nonlinear unstable phenomena. We view both as the result of competition for water in which the capacity of an instability to grow depends on its ability to carry water. We derive empirical solutions to quantify the finger/wormhole flow rate in single‐, two‐, and multiple‐finger systems. We use these solutions to show that fingering and wormhole patterns are a deterministic result of competition. For wormhole growth, controlled by dissolution, we solve reactive transport analytically within each wormhole to compute dissolution at the wormhole walls and tip. The generated patterns (both for viscous fingering and wormhole growth under moderate Damköhler number values) follow a power law decay of the number of fingers/wormholes with depth with an exponent of −1 consistent with field observations.