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Motivated by previous work on kinetic energy cascades in the ocean, atmosphere, plasmas, and other fluids, we develop a spatiotemporal spectral transfer tool that can be used to study scales of variability in generalized dynamical systems. In particular, we use generalized time-frequency methods from signal analysis to broaden the applicability of frequency transfers from theoretical to practical fluids applications such as the study of observational data or simulation output. We also show that triad interactions in wavenumber used to study kinetic energy and enstrophy cascades can be generalized to study triad interactions in frequency or wavenumber frequency. We study the effects of sweeping on the locality of frequency transfers and frequency triad interactions to better understand the locality of spatiotemporal frequency transfers. As an illustrative example, we use the spatiotemporal spectral transfer tool to study the results of a simulation of two-dimensional homogeneous isotropic turbulence. This simulated fluid is forced at a well-defined wavenumber and frequency with dissipation occurring at both large and small scales, making this one of the first studies of “modulated turbulence” in two dimensions. Our results show that the spatiotemporal transfers we develop in this paper are robust to potential practical problems such as low sampling rates or nonstationarity in time series of interest. We anticipate that this method will be a useful tool in studying scales of spatiotemporal variability in a wide range of fluids applications as higher resolution observations and simulations of fluids become more widely available. Published by the American Physical Society2025 

The parameterization of fluxes associated with representing unresolved dynamics in turbulent flows, especially in the atmosphere and ocean (which have a vast range of scales), remains a challenging task. This is especially true for Earth system models including complex biogeochemistry and requiring very long simulations. The problem of representing the dependence of the mean flux of a passive tracer in terms of the mean has a very long history; in this study, we take a somewhat different approach. We use a formalism showing that the mean flux will be a functional of the mean gradients, a formalism that can be used to calculate the structure of the functional which is non-local in both space and time. Two-dimensional turbulent simulations are used to explore the weight of nearby (in space or time) gradients. We also use stochastic velocities and iterated maps to show that the results are similar. The functional formalism provides an understanding of when non-locality needs to be considered and when a local eddy diffusivity can be a reasonably good approximation. Furthermore, the formalism provides guidance for the development of data-driven parameterizations. 

We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to a given flow state. In doing so, we obtain expressions for the turbulent diffusivity as a function of the flow statistics spectrum. When flow statistics are given by a continuous-time Markov process with a finite state space, calculations are amenable to analytic treatment. When the flow statistics are more complex, we show how to approximate turbulent fluxes as hierarchies of finite state space continuous-time Markov processes. The ensemble average turbulent flux is expressed as a linear operator that acts on the ensemble average of the tracer. We recover the classical estimate of turbulent flux as a diffusivity tensor, the components of which are the integrated autocorrelation of the velocity field in the limit that the operator becomes local in space and time. 

We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasigeostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The ‘vortex gas’ scaling predictions put forward in the context of the two-layer QG model carry over to this fully three-dimensional system: the functional dependence of the meridional flux on the control parameters is the same, the two adjustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional heat flux is depth-independent. The vertical heat flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical heat flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical heat fluxes, and of the emergent stratification, without additional fitting parameters. 

Abstract Gulf Stream Warm Core Rings (WCRs) have important influences on the New England Shelf and marine ecosystems. A 10‐year (2011–2020) WCR dataset that tracks weekly WCR locations and surface areas is used here to identify the rings' path and characterize their movement between 55 and 75°W. The WCR dataset reveals a very narrow band between 66 and 71°W along which rings travel almost due west along ∼39°N across isobaths – the “Ring Corridor.” Then, west of the corridor, the mean path turns southwestward, paralleling the shelfbreak. The average ring translation speed along the mean path is 5.9 cm s⁻¹. Long‐lived rings (lifespan >150 days) tend to occupy the region west of the New England Seamount Chain (NESC) whereas short‐lived rings (lifespan <150 days) tend to be more broadly distributed. WCR vertical structures, analyzed using available Argo float profiles indicate that rings that are formed to the west of the NESC have shallower thermoclines than those formed to the east. This tendency may be due to different WCR formation processes that are observed to occur along different sections of the Gulf Stream. WCRs formed to the east of the NESC tend to form from a pinch‐off mechanism incorporating cores of Sargasso Sea water and a perimeter of Gulf Stream water. WCRs that form to the west of the NESC, form from a process called an aneurysm. WCRs formed through aneurysms comprise water mostly from the northern half of the Gulf Stream and are smaller than the classic pinch‐off rings. 

Abstract The distribution of oceanic biogeochemical tracers is fundamentally tied to physical dynamics at and below the mesoscale. Since global climate models rarely resolve those scales, turbulent transport is parameterized in terms of the large‐scale gradients in the mean tracer distribution and the physical fields. Here, we demonstrate that this form of the eddy flux is not necessarily appropriate for reactive tracers, such as nutrients and phytoplankton. In an idealized nutrient‐phytoplankton system, we show that the eddy flux of one tracer should depend on the gradients of itself and the other. For certain parameter regimes, incorporating cross‐diffusion can significantly improve the representation of both phytoplankton and nutrient eddy fluxes. We also show that the efficacy of eddy diffusion parameterizations requires timescale separation between the flow and reactions. This result has ramifications for parameterizing subgrid scale biogeochemistry in more complex ocean models since many biological processes have comparable timescales to submesoscale motions. 

Abstract We describe a process called “squeeze dispersion” in which the squeezing of oceanic tracer gradients by waves, eddies, and bathymetric flow modulates diapycnal diffusion by centimeter to meter‐scale turbulence. Due to squeeze dispersion, the effective diapycnal diffusivity of oceanic tracers is different and typically greater than the average “local” diffusivity, especially when local diffusivity correlates with squeezing. We develop a theory to quantify the effects of squeeze dispersion on diapycnal oceanic transport, finding formulas that connect density‐averaged tracer flux, locally measured diffusivity, large‐scale oceanic strain, the thickness‐weighted average buoyancy gradient, and the effective diffusivity of oceanic tracers. We use this effective diffusivity to interpret observations of abyssal flow through the Samoan Passage reported by Alford et al. (2013,https://doi.org/10.1002/grl.50684) and find that squeezing modulates diapycnal tracer dispersion by factors between 0.5 and 3.