Understanding the statistics of ocean geostrophic turbulence is of utmost importance in understanding its interactions with the global ocean circulation and the climate system as a whole. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. Entropy is a concept of fundamental importance in statistical physics and information theory; motivated by equilibrium statistical mechanics theories of ideal geophysical fluids, we consider the effect of forcing and dissipation on eddy-mixing entropy, both analytically and numerically. By diagnosing the time evolution of eddy-mixing entropy it is shown that the entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability, formation of large scale structures and steady state fluctuations. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced-dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance entropy and statistical mechanics in the study of geostrophic turbulence.
"Eddy saturation" is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic …
This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments to the model. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind fo…
The global ocean overturning circulation, critically dependent on the global density stratification, plays a central role in regulating climate evolution. While it is well-known that the global stratification profile exhibits a strong dependence to Southern Ocean dynamics and in particular to wind and buoyancy forcing, we demonstrate here that the stratification is also acutely sensitive to the mesoscale eddy energy dissipation time-scale. Within the context of a global ocean circulation model with an energy constrained mesoscale eddy parameterization, it is shown that modest variations in the…
This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It turns out that energy is transferred via local triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale. From there it is then transferred to the large-scale barotropic modes via a nonlocal inverse transfer. Using scale separation a sys- …
The linear response function (LRF) of an idealized GCM, the dry dynamical core with Held-Suarez physics, is used to accurately compute how eddy momentum and heat fluxes change in response to the zonal wind and temperature anomalies of the annular mode at the low-frequency limit. Using these results and knowing the parameterizations of surface friction and thermal radiation in Held-Suarez physics, the contribution of each physical process (meridional and vertical eddy fluxes, surface friction, thermal radiation, and meridional advection) to the annular mode dynamics is quantified. Examining the…
The global stratification and circulation of the ocean and their sensitivities to changes in forcing depend crucially on the representation of the mesoscale eddy field. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies --- termed GEOMETRIC --- is proposed and implemented in three-dimensional primitive equation channel and sector models. The GEOMETRIC framework closes mesoscale eddy fluxes according to the standard Gent--McWilliams scheme, but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, prov…
Explicit filtering in large eddy simulation (LES) of a turbulent barotropic flow on the sphere in spectral space is studied and compared to implicit filtering. Here, a smooth filter is applied to the nondivergent barotropic vorticity equation (BVE) on the rotating sphere to divide the flow field into resolved scale (RS) and subfilter scale (SFS) motions. A portion of the SFS motions are reconstructed theoretically using the approximate deconvolution model (ADM). While the unreconstructed portion consists of the subgrid scale (SGS) motions and needs to be modeled separately. In order to investi…
We present an approximate deconvolution (AD) large eddy simulation (LES) model for the two-layer quasigeostrophic equations. We applied the AD-LES model to mid-latitude two-layer square oceanic basins, which are standard prototypes of more realistic stratified ocean dynamics models. Two spatial filters were investigated in the AD-LES model: a tridiagonal filter and an elliptic differential filter. A sensitivity analysis of the AD-LES results with respect to changes in modeling parameters was performed. The results demonstrate that the AD-LES model used in conjunction with the tridiagonal or di…
Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, and so large eddy simulation (LES) is the preferred approach to study these models. In LES a low-pass filter is applied to the flow field to separate the large and small scale motions. In implicitly filtered LES the computational mesh and discretization schemes are considered to be the low-pass filter while in the explicitly filtered LES approach the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of t…
Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the unresolved small scales of motion on the explicitly resolved large scale motions. Complimentary to this mainstream physics-based perspective, we propose to address this failure from the dynamical systems point of view, namely, as the persistent tendency of phase space trajectories representing the low-resolution solution to escape the right region of the correspond…
Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit at least two timescales; an Eulerian lifetime associated with persistent identifiable signatures in gridded fields such as vorticity or sea-surface height, and multiple Lagrangian or material coherence timescales that are typically much shorter. We propose a method to study the multi-timescale material transport, leakage, and entrainment by eddies with their surroundings by constructing sequences of…
We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure's subgrid spectral transfers and flux. We apply this method to 6 different closures for forced-dissipative simulations of the barotropic vorticity equation on a f-plane (2D Navier-Stokes equation). Using a high-resolution benchmark, we compare each closure's model of energy and enstrophy transfer to the actual transfer observed in the benchmark run. The error-landscape norms enable us to both make objective comparisons between the closur…
The mean state of the atmosphere and ocean is set through a balance between external forcing (winds, radiation, heat and freshwater fluxes) and the emergent turbulence, which transfers energy to dissipative structures. The forcing gives rise to jets in the atmosphere and currents in the ocean, which spontaneously develop turbulent eddies through the baroclinic instability. A critical step in the development of a theory of climate is to properly include the resulting eddy-induced turbulent transport of properties like heat, moisture, and carbon. The baroclinic instability generates flow structu…
Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke down-gradient mixing, or diffusion, of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from unfiltered fluxes are thus contaminated by the presence of these rotational components. Here a new methodology is applied whereby eddy diffusivities are diagnosed directly fro…
In this paper, a stabilized proper orthogonal decomposition (POD) reduced-order model (ROM) is presented for the barotropic vorticity equation. We apply the POD-ROM model to mid-latitude simplified oceanic basins, which are standard prototypes of more realistic large-scale ocean dynamics. A mode dependent eddy viscosity closure scheme is used to model the effects of the discarded POD modes. A sensitivity analysis with respect to the free eddy viscosity stabilization parameter is performed for various POD-ROMs with different numbers of POD modes. The POD-ROM results are validated against the Mu…
Observational studies of a planetary boundary layer (PBL) are difficult. Ground-born measurements usually characterize only a small portion of the PBL immediately above the surface. Air-born measurements cannot be obtained close to the surface and therefore cannot capture any significant portion of the PBL interior. Moreover, observations are limited in choice of instrumentation, time, duration, location of measurements and occasional weather conditions. Although turbulence-resolving simulations with a large-eddy simulation (LES) code do not supplant observational studies, they provide valuabl…
Wind forcing injects energy into the mesoscale eddies and near-inertial waves (NIWs) in the ocean, and the NIW is believed to solve the puzzle of mesoscale energy budget by absorbing energy from mesoscale eddies followed by a forward cascade of NIW energy which finally dissipates at the ocean interior. This work studies the turbulent energy transfer in the NIW--quasigeostrophic mean mesoscale eddy coupled system based on a previously derived two-dimensional model which has a Hamiltonian structure and inherits conserved quantities in the Boussinesq equations (Xie \& Vanneste, \textit{J. Fluid M…
Diapycnical eddy diffusivities are formulated from physical relations according to a simple fact that the different formulas are identical for the same parameter. It is found that the dispassion ratio Γis a crucial parameter. When it is above a critical value (about 0.2), the flow is salt finger type; otherwise, it is turbulence. All the density ratio $R_ρ=1/(1-Γ^2)$, eddy flux ratio $γ=1/(1+Γ)$, and eddy diffusivity ratio $R_k=1-Γ$ are simply dependent on the dispassion ratio gamma Γ. We apply these relations to the measurement data in the western tropical Atlantic Ocean. The effective diapyc…
The present study gives an overview and emphasizes principal moments of the applications of the turbulence-resolving modeling with large-eddy simulation (LES) numerical technique to planetary boundary layer (PBL) research and climate studies. LES proved to be very useful in understanding of the atmospheric and ocean turbulent exchange and ultimately in parameterization improvement in traditional meteorological models. LES have played a key role in recognizing the importance of previously ignored self-organized structures in the geophysical turbulence. LES assisted theoreticians and weather/cli…
Jets coexist with planetary scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary scale waves requires adopting the perspective of statistical state dynamics (SSD) which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work the S3T implementation of SSD for barotropic …
The Lagrangian-Averaged Navier-Stokes alpha (LANS-alpha) model is a turbulence parameterization that has been shown to capture some of the most important features of high resolution ocean modeling at lower resolution. Simulations using LANS-alpha in the POP primitive-equation ocean model resemble doubled-resolution simulations of standard POP in statistics like kinetic energy, eddy kinetic energy, and potential temperature fields. The computational cost of adding LANS-alpha is only 27% for our most efficient implementation, as compared to a factor of 8-10 for a doubling of resolution. The LANS…
Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e. surface and bottom boundary layers, separated by an interior stratification.…
While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first-order closure schemes such as the K-Profile Parameterization (KPP) lack energetic constraints; two-equation models like $k-ε$ directly solve an equation for the turbulent kinetic energy but do not account for non-local fluxes, and high-order closures that include the non-local transport terms are computationally expensive. To address these, here we extend the Assumed-Distribution Higher-Order Closure (ADC) framework originall…
We develop a numerical method for simulating coupled interactions of complex floating structures with large-scale ocean waves and atmospheric turbulence. We employ an efficient large-scale model to develop offshore wind and wave environmental conditions, which are then incorporated into a high resolution two-phase flow solver with fluid-structure interaction (FSI). The large-scale wind-wave interaction model is based on the two-fluid dynamically-coupled approach of Yang and Shen (2011), which employs a high-order spectral method for simulating the water motion and a viscous solver with undulat…
A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions…
