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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.

 

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.

 

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.

 

A new method for computing the rate at which turbulent mixing builds potential energy in the ocean is described. The traditional approach has focused on the rate of change of the background potential energy associated with an adiabatically leveled state. We argue that when examining mixing events, so‐called “Thorpe” sorting yields a useful and local measure of diabatically generated potential energy and exhibits some advantages relative to adiabatic leveling. Among these, the open question about the leveling domain is avoided, the fate of kinetic energy during a mixing event is clearly defined, and the computational load associated with the leveling is relieved. The resultant kinetic energy equation leads to a natural definition of mixing efficiency and turbulent diffusivity in terms of sign definite viscous and diffusive contributions. Applications to 2‐D Kelvin Helmholtz instability demonstrate the utility of the procedure. We find an integrated efficiency of ≈ 0.15 for a Prandtl number of 1, and of ≈ 0.08 for a Prandtl number of 10. The larger is comparable to the classical value of 0.2 used frequently by the mixing community and smaller than that found in some recent simulations.

 

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. 

Abstract The structure and variations of the North Equatorial Counter Current (NECC) in the far western Pacific Ocean during 2014-2016 are investigated using repeated in-situ hydrographic data, altimeter data, Argo data, and reanalysis data. The NECC shifted ~1 degree southward and intensified significantly with its transport exceeding 40 Sv (1 Sv = 10 6 m 3 s -1 ), nearly double its climatology value, during the developing phase of the 2015/16 El Niño event. Observations show that the 2015/16 El Niño exerted a comparable impact on the NECC with that of the extreme 1997/98 El Niño in the far western Pacific Ocean. Baroclinic instability provided the primary energy source for the eddy kinetic energy (EKE) in the 2015/16 El Niño, which differs from the traditional understanding of the energy source of EKE as barotropic instability in low latitude ocean. The enhanced vertical shear and the reduced density jump between the NECC layer and the subsurface North Equatorial Subsurface Current (NESC) layer renders the NECC–NESC system baroclinically unstable in the western Pacific Ocean during El Niño developing phase. The eddy-mean flow interactions here are diverse associated with various states of the El Niño Southern Oscillation (ENSO).