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Abstract 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 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. 

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 A current along a sloping bottom gives rise to upwelling, or downwelling Ekman transport within the stratified bottom boundary layer (BBL), also known as the bottom Ekman layer. In 1D models of slope currents, geostrophic vertical shear resulting from horizontal buoyancy gradients within the BBL is predicted to eventually bring the bottom stress to zero, leading to a shutdown, or “arrest,” of the BBL. Using 3D ROMS simulations, we explore how the dynamics of buoyancy adjustment in a current‐ridge encounter problem differs from 1D and 2D temporal spin up problems. We show that in a downwelling BBL, the destruction of the ageostrophic BBL shear, and hence the bottom stress, is accomplished primarily by nonlinear straining effects during the initial topographic encounter. As the current advects along the ridge slopes, the BBL deepens and evolves toward thermal wind balance. The onset of negative potential vorticitymodes of instability and their subsequent dissipation partially offsets the reduction of the BBL dissipation during the ridge‐current interaction. On the upwelling side, although the bottom stress weakens substantially during the encounter, the BBL experiences a horizontal inflectional point instability and separates from the slopes before sustained along‐slope stress reduction can occur. In all our solutions, both the upwelling and downwelling BBLs are in a partially arrested state when the current separates from the ridge slope, characterized by a reduced, but non‐zero bottom stress on the slopes.