The Origin of Life in the Vortex Reactor: A Hydrodynamic Theory of Prebiotic Compartmentalisation and the Origin of Protocells on the Early Earth's Ocean Surface

We present a rigorous hydrodynamic theory of the first stage of abiogenesis: the concentration and compartmentalisation of prebiotic organic molecules into protocellular structures on the early Earth’s ocean surface. The theory is founded onthe recently proved inverse cascade theorems for Navier–Stokes flows, which es-tablish that the wind-driven ocean surface decomposes into isolated Morse–Smalevortex cells—quasi-two-dimensional microreactors bounded by separatricial surfaces of measure zero. These separatrices are identified as hyperbolic Lagrangian Coherent Structures, and the confining KAM tori in the vortex cores as elliptic LCS,connecting the theory to experimentally measurable diagnostics of transport barriers.Within each vortex cell, the inverse Kraichnan cascade transports passive scalars (organic molecules) from small to large scales, concentrating them against diffusive dilution by a factor of 102–104. This prediction is in quantitative agreement with the observed enrichment of the sea surface microlayer (SML), for which the theory provides a dynamic rather than static mechanism. The closed topology of Lagrangian trajectories provides a geometric template for the elongation of molecular chains along streamlines and their subsequent cyclisation into rings—the fundamental building blocks of purines, pyrimidines, and porphyrins. We derive the advection-diffusion-reaction equation for a passive scalar in the Morse–Smale geometry, using streamline averaging techniques from the theory of reaction-advection-diffusion (RAD) systems, and obtain rigorous estimates for the concentration enhancementfactor as a function of the P´eclet number.The vortex reactor is shown to function as a kinematic compartment—a bounded volume defined by flow topology rather than by a phase boundary—duringthe early stages of molecular concentration and polymerisation. This resolves the chicken-and-egg problem of prebiotic compartmentalisation: the confinement necessary for chemistry exists before the lipid membranes that later replace it. At laterstages, concentrated lipid precursors self-assemble into bilayer membranes, which undergo shear-induced tubulation and closure into spheroidal protocells. This transition from kinematic to physical compartmentalisation is the decisive step in the emergence of life-like entities.The stability of each vortex reactor is governed by the KAM winding index K. For K < 28, the reactor is stable and accumulates reaction products. WhenK reaches the critical threshold of 28, the confining KAM tori are destroyed in a homoclinic explosion, releasing the accumulated protocells into the surrounding medium. This cycle of accumulation and release provides a physical basis for pre-Darwinian natural selection among vortex reactors. We establish the correspondence between our theory and six foundational frameworks: Prigogine’s dissipative structures, Braun’s thermophoretic pore accumula-tion, Michaelian’s thermodynamic dissipation theory of life, England’s dissipation-driven adaptation, the theory of Lagrangian Coherent Structures, and the physics of chemically active droplets and coacervates. The vortex reactor is shown to bethe hydrodynamic realisation of the physical reactor that these theories postulate but do not construct from first principles.The theory contains no adjustable parameters. The value Kcrit = 28 is the Lorenz homoclinic explosion threshold. The concentration factor is determined bythe P´eclet number of the vortex flow. All predictions are in principle testable in laboratory experiments with thin fluid layers subjected to controlled wind stress, indirect numerical simulations of the 2D Navier–Stokes equations with passive scalars, and in field observations of the sea surface microlayer.