Eddies and friction : removal of vorticity from the wind-driven gyre

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2003Inertial terms dominate the single-gyre ocean model and prevent western-intensification when the viscosity is small. This occurs long before the oceanically-appropriate parameter range. It is demonstrated here that the circulation is controlled if a mechanism for ultimate removal of vorticity exists, even if it is active only in a narrow region near the boundary. Vorticity removal is modeled here as a viscosity enhanced very near the solid boundaries to roughly parameterize missing boundary physics like topographic interaction and three dimensional turbulence over the shelf. This boundary-enhanced viscosity allows western-intensified mean flows even when the inertial boundary width, is much wider than the frictional region because eddies flux vorticity from within the interior streamlines to the frictional region for removal. Using boundary-enhanced viscosity, western-intensified calculations are possible with lower interior viscosity than in previous studies. Interesting behaviors result: a boundary-layer balance novel to the model, calculations with promise for eddy parameterization, eddy-driven gyres rotating opposite the wind, and temporal complexity including basin resonances. I also demonstrate that multiple-gyre calculations have weaker mean circulation than single-gyres with the same viscosity and subtropical forcing. Despite traditional understanding, almost no inter-gyre flux occurs if no-slip boundary conditions are used. The inter-gyre eddy flux is in control only with exactly symmetric gyres and free slip boundaries. Even without the inter-gyre flux, the multiple-gyre circulation is weak because of sinuous instabilities on the jet which are not present in the single-gyre model. These modes efficiently flux vorticity to the boundary and reduce the circulation without an inter-gyre flux, postponing inertial domination to much smaller viscosities. Then sinuous modes in combination with boundary-enhanced viscosity can control the circulation

Wind-driven barotropic gyre II : effects of eddies and low interior viscosity

Author Posting. © Sears Foundation for Marine Research, 2004. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 62 (2004): 195-232, doi:10.1357/002224004774201690.Using boundary-enhanced viscosity to control the mean circulation, a simple model can be created and used for study of strong inertial effects in a western-intensified calculation. The simplicity allows for a greater number of strongly-inertial numerical experiments than computationally feasible in a general circulation model. This paper is an introduction to the behavior of this model, covering its general features. Some of the inertial phenomena, including the primary balances of the boundary current and basin interior, the temporal behavior, and the changes in the mean state across parameter space are presented. The analysis of these phenomena focuses on the effects of eddies and the type of eddies present. The low interior viscosity allows for more pronounced eddy effects. As this model is intended for use in future studies, many of the diagnostic tools found to be useful here are likely to be reused effectively

Ocean dynamics

Operational prediction systems must balance conflicting considerations involved in representing the widest possible range of ocean physics, limited by computational constraints. Choices must be made in prediction systems that exclude particular dynamics to enable feasible solutions within defined resources. We examine some of the basic ocean dynamics that ocean prediction systems intend to represent. The two most basic simplifications are the Boussinesq and hydrostatic. Even with these limitations, ocean models represent a vast range of physical processes, and this enables application to many problems. We examine a succinct range of basic dynamics and consider how these affect operational ocean prediction problems

Data-driven versus self-similar parameterizations for Stochastic Advection by Lie Transport and Location Uncertainty

International audienceStochastic subgrid parameterizations enable ensemble forecasts of fluid dynamics systems and ultimately accurate data assimilation. Stochastic Advection by Lie Transport (SALT) and models under Location Uncertainty (LU) are recent and similar physically-based stochastic schemes. SALT dynamics conserve helicity whereas LU models conserve kinetic energy. After highlighting general similarities between LU and SALT frameworks, this paper focuses on their common challenge: the parameterization choice. We compare uncertainty quantification skills of a stationary heterogeneous data-driven parameteriza-5 tion and a non-stationary homogeneous self-similar parameterization. For stationary, homogeneous Surface Quasi-Geostrophic (SQG) turbulence, both parameterizations lead to high quality ensemble forecasts. This paper also discusses a heterogeneous adaptation of the homogeneous parameterization targeted at better simulation of strong straight buoyancy fronts

Adaptive volume penalization for ocean modeling

The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. When penalization methods are coupled with the adaptive wavelet collocation method, the flow near the boundary can be well-resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This paper will give a thorough analysis of these methods applied to the shallow water equations, as well as some preliminary work applying these methods to volume penalization for bathymetry representation for use in either the nonhydrostatic or hydrostatic primitive equations

Adaptive Wavelet Collocation Method on the Shallow Water Model

This paper presents an integrated approach for modeling several ocean test problems on adaptive grids using novel boundary techniques. The adaptive wavelet collocation method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. It is a general method for the solving a large class of partial differential equations, but is applied to the shallow water equations here. In addition to developing wavelet-based computational models, this work also uses an extension of the Brinkman penalization method to represent irregular and non-uniform continental boundaries. This technique is used to enforce no slip boundary conditions through the addition of a term to the field equations. When coupled with the adaptive wavelet collocation method, the flow near the boundary can be well resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow and the boundary is important, thus, those are the test cases presented here

Stochastic transport to quantify errors in geophysical fluid dynamic simulations

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The role of mixed-layer instabilities in submesoscale turbulence

Upper-ocean turbulence at scales smaller than the mesoscale is believed to exchange surface and thermocline waters, which plays an important role in both physical and biogeochemical budgets. But what energizes this submesoscale turbulence remains a topic of debate. Two mechanisms have been proposed: mesoscale-driven surface frontogenesis and baroclinic mixed-layer instabilities. The goal here is to understand the differences between the dynamics of these two mechanisms, using a simple quasi-geostrophic model. The essence of mesoscale-driven surface frontogenesis is captured by the well-known surface quasi-geostrophic model, which describes the sharpening of surface buoyancy gradients and the subsequent breakup in secondary roll-up instabilities. We formulate a similarly archetypical Eady-like model of submesoscale turbulence induced by mixed-layer instabilities. The model captures the scale and structure of this baroclinic instability in the mixed layer. A wide range of scales are energized through a turbulent inverse cascade of kinetic energy that is fuelled by the submesoscale mixed-layer instability. Major differences to mesoscale-driven surface frontogenesis are that mixed-layer instabilities energize the entire depth of the mixed layer and produce larger vertical velocities. The distribution of energy across scales and in the vertical produced by our simple model of mixed-layer instabilities compares favourably to observations of energetic wintertime submesoscale flows, suggesting that it captures the leading-order balanced dynamics of these flows. The dynamics described here in an oceanographic context have potential applications to other geophysical fluids with layers of different stratifications

A tensor-valued integral theorem for the gradient of a vector field, with a fluid dynamical application

The familiar divergence and Kelvin--Stokes theorem are generalized by a tensor-valued identity that relates the volume integral of the gradient of a vector field to the integral over the bounding surface of the outer product of the vector field with the exterior normal. The importance of this long-established yet little-known result is discussed. In flat two-dimensional space, it reduces to a relationship between an integral over an area and that over its bounding curve, combining the divergence and Kelvin--Stokes theorems together with two related theorems involving the strain, as is shown through a decomposition using a suitable tensor basis. A fluid dynamical application to oceanic observations along the trajectory of a moving platform is given, and potential extensions to geometrically complex surfaces are discussed.Comment: 20 page