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We introduce a pseudo‐spectral algorithm that includes full compressible dynamics with the intent of simulating near‐incompressible fluids, CaTSM (Compressible and Thermodynamically consistent Spectral Model). A semi‐implicit scheme is used to model acoustic waves in order to evolve the system efficiently for such fluids. We demonstrate the convergence properties of this numerical code for the case of a shock tube and for Rayleigh‐Taylor instability. A linear equation of state is also presented, which relates the specific volume of the fluid linearly to the potential temperature, salinity, and pressure. This permits the results to be easily compared to a Boussinesq framework in order to assess whether the Boussinesq approximation adequately represents the relevant exchange of energy to the problem of interest. One such application is included, that of the development of a single salt finger, and it is shown that the energetic behavior of the system is comparable to the typical canonical development of the problem for oceanographic parameters. However, for more compressible systems, the results change substantially even for low‐Mach number flows.

 

Accurate representation of air‐sea interaction is crucial to numerical prediction of the ocean, weather, and climate. Sea surface temperature (SST) gradients and surface currents in the oceanic mesoscale regime are known to have significant influence on air‐sea fluxes of momentum. Studies based on high‐resolution numerical models and observations reveal that SST gradients and surface currents in the submesoscale regime are much stronger than those in the mesoscale. However, the feedback between the submesoscale processes and the air‐sea turbulent fluxes is not well understood. To quantitatively assess the responses between air‐sea flux of momentum and submesoscale processes, a non‐hydrostatic ocean model is implemented in this study. The inclusion of SST gradients and surface currents in air‐sea bulk fluxes are argued to be significant for modeling accurate wind stress in the submesoscale regime. Taking both into account, this study shows that the linear relationship between wind stress curl/divergence and crosswind/downwind SST gradients existing in the mesoscale regime is not obvious in the submesoscale. Instead, a linear relationship between wind stress curl/divergence and surface current curl/divergence is revealed in the submesoscale. Furthermore, the magnitude of wind stress curl introduced by submesoscale processes is much greater than that presented by mesoscale processes. Another key finding is that tracer subduction and potential vorticity distribution in the submesoscale is susceptible to submesoscale‐modified air‐sea turbulent momentum flux. This study serves as a starting point in investigating the feedbacks between atmospheric and oceanic submesoscale processes.

 

The “eddying” ocean, recognized for several decades, has been the focus of much observational and theoretical research. We here describe a generalization for the analysis of eddy energy, based on the use of ensembles, that addresses two key related issues: the definition of an “eddy” and the general computation of energy spectra. An ensemble identifies eddies as the unpredictable component of the flow, and permits the scale decomposition of their energy in inhomogeneous and non‐stationary settings. We present two distinct, but equally valid, spectral estimates: one is similar to classical Fourier spectra, the other reminiscent of classical empirical orthogonal function analysis. Both satisfy Parseval's equality and thus can be interpreted as length‐scale dependent energy decompositions. The issue of “tapering” or “windowing” of the data, used in traditional approaches, is also discussed. We apply the analyses to a mesoscale “resolving” (1/12°) ensemble of the separated North Atlantic Gulf Stream. Our results reveal highly anisotropic spectra in the Gulf Stream and zones of both agreement and disagreement with theoretically expected spectral shapes. In general, we find spectral slopes that fall off faster than the steepest slope expected from quasi‐geostrophic theory.

 

The thickness‐weighted average (TWA) framework, which treats the residual‐mean flow as the prognostic variable, provides a clear theoretical formulation of the eddy feedback onto the residual‐mean flow. The averaging operator involved in the TWA framework, although in theory being an ensemble mean, in practice has often been approximated by a temporal mean. Here, we analyze an ensemble of North Atlantic simulations at mesoscale‐permitting resolution (1/12°). We therefore recognize means and eddies in terms of ensemble means and fluctuations about those means. The ensemble dimension being orthogonal to the temporal and spatial dimensions negates the necessity for an arbitrary temporal or spatial scale in defining the eddies. Eddy‐mean flow feedbacks are encapsulated in the Eliassen‐Palm (E‐P) flux tensor and its convergence indicates that eddy momentum fluxes dominate in the separated Gulf Stream. The eddies can be interpreted to contribute to the zonal meandering of the Gulf Stream and a northward migration of it in the meridional direction. Downstream of the separated Gulf Stream in the North Atlantic Current region, the interfacial form stress convergence becomes leading order in the E‐P flux convergence.

 

Circulation in the Southern Ocean is unique. The strong wind stress forcing and buoyancy fluxes, in concert with the lack of continental boundaries, conspire to drive the Antarctic Circumpolar Current replete with an intense eddy field. The effect of Southern Ocean eddies on the ocean circulation is significant—they modulate the momentum balance of the zonal flow, and the meridional transport of tracers and mass. The strength of the eddy field is controlled by a combination of forcing (primarily thought to be wind stress) and intrinsic, chaotic, variability associated with the turbulent flow field itself. Here, we present results from an eddy‐permitting ensemble of ocean model simulations to investigate the relative contribution of forced and intrinsic processes in governing the variability of Southern Ocean eddy kinetic energy. We find that variations of the eddy field are mostly random, even on longer (interannual) timescales. Where correlations between the wind stress forcing and the eddy field exist, these interactions are dominated by two distinct timescales—a fast baroclinic instability response; and a multi‐year process owing to feedback between bathymetry and the mean flow. These results suggest that understanding Southern Ocean eddy dynamics and its larger‐scale impacts requires an ensemble approach to eliminate intrinsic variability, and therefore may not yield robust conclusions from observations alone.

 

An important characteristic of geophysically turbulent flows is the transfer of energy between scales. Balanced flows pass energy from smaller to larger scales as part of the well‐known upscale cascade, while submesoscale and smaller scale flows can transfer energy eventually to smaller, dissipative scales. Much effort has been put into quantifying these transfers, but a complicating factor in realistic settings is that the underlying flows are often strongly spatially heterogeneous and anisotropic. Furthermore, the flows may be embedded in irregularly shaped domains that can be multiply connected. As a result, straightforward approaches like computing Fourier spatial spectra of nonlinear terms suffer from a number of conceptual issues. In this paper, we develop a method to compute cross‐scale energy transfers in general settings, allowing for arbitrary flow structure, anisotropy, and inhomogeneity. We employ Green's function approach to the kinetic energy equation to relate kinetic energy at a point to its Lagrangian history. A spatial filtering of the resulting equation naturally decomposes kinetic energy into length‐scale‐dependent contributions and describes how the transfer of energy between those scalestakes place. The method is applied to a doubly periodic simulation of vortex merger, resulting in the demonstration of the expected upscale energy cascade. Somewhat novel results are that the energy transfers are dominated by pressure work, rather than kinetic energy exchange, and dissipation is a noticeable influence on the larger scale energy budgets. We also describe, but do not employ here, a technique for developing filters to use in complex domains.

 

This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist, which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the direction opposite to topographic Rossby waves, steady solutions exist and a semi-analytical method is presented for calculating these solutions. Second, when the modon propagates in the same direction as the Rossby waves, a wave wake is generated. This wake removes energy from the modon, causing it to decay slowly. Asymptotic predictions are presented for this decay and found to agree closely with numerical simulations. Over long times, decaying vortices are found to break down due to an asymmetry resulting from the generation of waves inside the vortex. A monopolar vortex moving along a wall is shown to behave in a similar way to a dipole, though the presence of the wall is found to stabilise the vortex and prevent the long-time breakdown. The problem is equivalent mathematically to a dipolar vortex moving along a density front, hence our results apply directly to this case. 

Analysis of satellite altimetry and Argo float data leads Ni et al. ( J. Geophys. Res. , 125, 2020, e2020JC016479) to argue that mesoscale dipoles are widespread features of the global ocean having a relatively uniform three-structure that can lead to strong vertical exchanges. Almost all the features of the composite dipole they construct can be derived from a model for multipoles in the surface quasi-geostrophic equations for which we present a straightforward novel solution in terms of an explicit linear algebraic eigenvalue problem, allowing simple evaluation of the higher radial modes that appear to be present in the observations and suggesting that mass conservation may explain the observed frontogenetic velocities. 

Abstract Symmetric instability is a mechanism that can transfer geostrophic kinetic energy to overturning and dissipation. To date, symmetric instability has only been recognized to occur at the ocean surface or near topographic boundary layers. Analyses of direct microstructure measurements reveal enhanced dissipation caused by symmetric instability in the northwestern equatorial Pacific thermocline, which provides the first observational evidence of subsurface symmetric instability away from boundaries. Enhanced subsurface cross-equatorial exchange provides the negative potential vorticity needed to drive the symmetric instability, which is well reproduced by numerical modeling. These results suggest a new route to energy dissipation for large scale currents, and hence a new ocean turbulent mixing process in the ocean interior. Given the importance of vertical mixing in the evolution of equatorial thermocline, models may need to account for this mechanism to produce more reliable climate projections.