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Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties. 

Abstract Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes. 

Abstract Past studies separately demonstrate that vertical boundary layer turbulence can either sharpen or weaken submesoscale fronts in the surface mixed layer. These studies invoke competing interpretations that separately focus on the impact of either vertical momentum mixing or vertical buoyancy mixing, where the former can favor sharpening (frontogenesis) by generation of an ageostrophic secondary circulation, while the latter can weaken the front (frontolysis) via diffusion or shear dispersion. No study comprehensively demonstrates vertical mixing –induced frontogenesis and frontolysis in a common framework. Here, we develop a unified paradigm for this problem with idealized simulations that explore how a front initially in geostrophic balance responds to a fixed vertical mixing profile. We evolve 2D fronts with the hydrostatic, primitive equations over a range of Ekman (Ek = 10⁻⁴–10⁻¹) and Rossby (Ro = 0.25–2) numbers, where Ek quantifies the magnitude of vertical mixing and Ro quantifies the initial frontal strength. We observe verticalmomentummixing induced, nonlinear frontogenesis at large Ro and small Ek, and inhibition of frontogenesis via verticalbuoyancydiffusion at small Ro and large Ek. Symmetric instability can dominate frontogenesis at very small Ek; however, the fixed mixing limits interpretation of this regime. Simulations that suppress vertical buoyancy mixing are remarkably frontogenetic, even at large Ek, explicitly demonstrating that buoyancy mixing is frontolytic. Application of two scalings to quantify the competition between cross-front buoyancy advection and vertical diffusion identifies practically equivalent controlling parameters (Ro²/Ek, Ro/Ek^1/2); these ratios approximately map regime transitions across simulations with equal vertical eddy viscosity and diffusivity. Significance StatementThis study reconciles competing views on how turbulent vertical mixing on scales of 0.01–1 m controls the sharpening or weakening of upper-ocean fronts characterized by horizontal changes in density and velocity over scales of 100 m–1 km. This sharpening or weakening modulates frontal circulation that acts to bring heat upward. Given the pervasiveness of such fronts, these local dynamics influence upper-ocean heat content globally. Utilizing simulations, we identify a measurable parameter that predicts frontal sharpening or weakening via vertical mixing. This new dynamical framework can better inform the necessary parameterization of these fronts in global climate models. However, future work should interrogate the validity of our simplified model, which unrealistically assumes that the vertical mixing does not evolve. 

Abstract Current-topography interactions in the ocean give rise to eddies spanning a wide range of spatial and temporal scales. Latest modeling efforts indicate that coastal and underwater topography are important generation sites for submesoscale coherent vortices (SCVs), characterized by horizontal scales of (0.1 – 10) km. Using idealized, submesoscale and BBL-resolving simulations and adopting an integrated vorticity balance formulation, we quantify precisely the role of bottom boundary layers (BBLs) in the vorticity generation process. In particular, we show that vorticity generation on topographic slopes is attributable primarily to the torque exerted by the vertical divergence of stress at the bottom. We refer to this as the Bottom Stress Divergence Torque (BSDT). BSDT is a fundamentally nonconservative torque that appears as a source term in the integrated vorticity budget and is to be distinguished from the more familiar Bottom Stress Curl (BSC). It is closely connected to the bottom pressure torque (BPT) via the horizontal momentum balance at the bottom and is in fact shown to be the dominant component of BPT in solutions with a well-resolved BBL. This suggests an interpretation of BPT as the sum of a viscous, vorticity generating component (BSDT) and an inviscid, ‘flow-turning ’ component. Companion simulations without bottom drag illustrate that although vorticity generation can still occur through the inviscid mechanisms of vortex stretching and tilting, the wake eddies tend to have weaker circulation, be substantially less energetic, and have smaller spatial scales.