Mesoscale horizontal stirring (MHS) is ubiquitous in the oceans, influencing heat and carbon transport, phytoplankton blooms and fish larvae dispersal. The current generation of Earth system models lacks sufficient resolution to properly resolve MHS-relevant small-scale phenomena, such as oceanic mesoscale eddies, leaving it largely unknown how MHS will change in response to greenhouse warming. Here we determine how CO2 doubling and quadrupling will change the surface MHS statistics in Community Earth System Model simulations with 1/10-degree ocean resolution. MHS is analysed using the finite-size Lyapunov exponent, a Lagrangian diagnostic that measures the separation of close trajectories. Projected increases in MHS are expected in the Arctic Ocean and coastal Antarctic regions, driven by enhanced time-mean ocean flow and turbulence which predominantly result from sea ice reduction. The enhanced horizontal stirring in polar oceans implies substantial yet uncertain consequences for tracer transport, nutrient supply and ecosystems under higher CO2 conditions.
Stirring is a turbulent process that deforms and stretches fluid elements into elongated filaments, thereby dispersing fluid properties and generating sharp gradients. These gradients are smoothed by diffusion and, together with stirring, this leads to irreversible homogenization (mixing). In the ocean, where horizontal velocities dominate over vertical ones across most scales, mesoscale horizontal stirring (MHS) is the primary dynamical process. MHS is closely linked to mesoscale features such as eddies, meanders, fronts and filaments, which span tens to hundreds of kilometres and persist for days to months. It plays a pivotal role in regulating the transport of heat, carbon and other tracers, phytoplankton blooms, the dispersal of larvae and fish eggs and broader ecosystem interactions.
Given the wide-ranging impacts of MHS, understanding how MHS will respond to future climate change is particularly important in high latitudes, where warming is most strongly amplified. Recently, rapid sea ice decline due to greenhouse warming has driven major environmental changes in polar oceans, altering ocean temperature, salinity and surface momentum flux, with potential consequences for diverse physical and biological processes. Recent studies using state-of-the-art climate models have reported marked changes in upper-ocean circulation and a substantial increase in eddy activity in the Arctic under warming scenarios. Notably, a kilometre-scale high-resolution simulation showed a threefold increase in eddy kinetic energy (EKE) in the upper Arctic Ocean under a 4 °C-warmer climate, associated with enhanced baroclinic instability driven by sea ice loss. Such dynamical changes are expected to markedly influence MHS. While a Lagrangian-based network theory study linked increased kinetic energy to stronger horizontal stirring in the Mediterranean under a warmer climate, comparable analyses in polar regions are still lacking. Addressing this gap is crucial to improve understanding of oceanic responses to greenhouse warming in the most rapidly changing regions of the world.
Here focusing on the polar oceans, we explore spatiotemporal changes in surface MHS under varying CO conditions. To characterize and assess changes in MHS, we use the finite-size Lyapunov exponent (FSLE), a Lagrangian diagnostic which measures the continuous exponential rate of separation between nearby particle trajectories, indicating how quickly a patch of passive tracers is stretched (Methods). The FSLE provides spatially and temporally resolved estimates of transport and mixing, revealing fine-scale features such as filaments and spirals that are often overlooked by Eulerian methods. In this study, FSLE is calculated as the time-based growth rate of separation from an initial distance (δ) to a final distance (δ), defined as a tenfold increase. To target mesoscale structure, δ and δ are set to 0.1° and 1.0°, respectively. This choice of δ aligns with the 0.1° horizontal resolution of the ocean model, while δ is set to a scale comparable to that used in previous studies for consistency (see Supplementary Information for δ-δ sensitivity tests). The FSLE technique has been successfully applied to identify complex spatial and seasonal patterns of surface MHS in both the Mediterranean and global ocean under present-day conditions.
To investigate how future greenhouse warming affects MHS, we analyse idealized century-long time-slice simulations conducted using the fully coupled ultra-high-resolution Community Earth System Model v.1.2.2 (CESM-UHR), with horizontal resolution of 0.25° for the atmosphere and 0.1° for the ocean. Notably, in the Arctic the ocean model uses a tripolar grid with 2.5-km eddy-permitting resolution. The three experiments use constant atmospheric CO concentrations of 367 ppm (present-day, PD), 734 ppm (2 × CO) and 1,468 ppm (4 × CO) (Methods). Daily FSLEs, a measure of MHS, are analysed at each grid point over 10 years in each simulation. This approach enables evaluation of MHS changes under different CO conditions within a fully coupled ocean-sea ice-atmosphere framework. FSLEs from the CESM-UHR PD simulation closely match ocean reanalysis in both magnitude and spatial distribution (Supplementary Information), supporting the suitability of the model for this study.