On the nonlinear instability and submesoscale turbulence for western boundary currents and undercurrents 

Western boundary undercurrents (WBUCs), present beneath almost all western boundary currents, are significant for transporting subsurface mass and energy and connecting regional circulations. Observations suggest that WBUCs can have strong ageostrophy and intra-seasonal variability, but many dynamic details remain unclear. Here, we analyze a representative model idealized from the Kuroshio Current and Luzon Undercurrent (KC and LUC); other instances like the Gulf Stream and the Deep Western Boundary Current are also feasible. A cross-shore mean flow section, extracted from realistic simulations, serves as the only input. We employ biglobal instability analysis (BIA) and high-resolution (up to 500m) regional simulations to reveal the nonlinear instability of the WBUC, its interaction with the upper-layer, and the induced mesoscale and submesoscale turbulence. First, we solidly verify BIA by showing that the predicted evolution of dominant eigenmodes closely agrees with the model results. Second, an upper-layer (depth < 500m) KC mode and a middle-layer (500 to 1500m) LUC mode are identified. The nonlinear instability of the KC mode leads to strong variability and periodic reversal of the LUC. The subthermocline-eddy-like LUC mode has stronger nonlinearity, but negligibly affects the upper layer. Qualitative and, in some cases, quantitative agreement with observations is obtained. The kinetic energy spectra for the subthermocline can exhibit the k scaling as the upper layer, jointly driven by the KC and LUC instability. Moderate centrifugal instability is identified for the LUC near the topography, leading to locally enhanced submesoscales and eddy fluxes. The present model has the potential to serve as a benchmark for global WBUCs, providing theoretical explanations to observational trends and helping improve the modelling for multi-layer circulations.