Eigenanalysis of the two-dimensional wind-driven ocean circulation problem

A barotropic model of the wind-driven circulation in the subtropical region of the ocean is considered. A no-slip condition is specified at the coasts and slip at the fluid boundaries. Solutions are governed by two parameters: inertial boundary-layer width; and viscous boundary-layer width. Numerical computations indicate the existence of a wedge-shaped region in this two-dimensional parameter space, where three steady solutions coexist. The structure of the steady solution can be of three types: boundary-layer, recirculation and basin-filling-gyre. Compared to the case with slip conditions (Ierley and Sheremet, 1995) in the no-slip case the wedge-shaped region is displaced to higher Reynolds numbers. Linear stability analysis of solutions reveals several classes of perturbations: basin modes of Rossby waves, modes associated with the recirculation gyre, wall-trapped modes and a “resonant” mode. For a standard subtropical gyre wind forcing, as the Reynolds number increases, the wall-trapped mode is the first one destabilized. The resonant mode associated with disturbances on the southern side of the recirculation gyre is amplified only at larger Reynolds number, nonetheless this mode ultimately provides a stronger coupling between the mean circulation and Rossby basin modes than do the wall-trapped modes

Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part II.

This paper is a continuation of Part I of the suggested study of the barotropic model of the subtropical gyre for finite Reynolds numbers. The statement of the problem, the motivation of the analysis, and the description of the general properties of the solution are presented in Part I (Kamenkovich et al., 1995). Here, in Part II of the study, the detailed investigations of the peculiarities of the solution are offered. The most striking feature of the solution is the formation of a recirculation gyre in the northwest corner of the basin. To study the gyre structure for various Reynolds numbers the time-averaged fields of the stream function, and that of the relative and potential vorticity are thoroughly examined. The role of the eddies, appeared within the boundary layer, in the transfer of positive vorticity from the west coast is clarified. The analysis of the energy characteristics of the system is presented and the vorticity balance both integral and regional (within a closed streamline) is elucidated. Finally, the consistent discussion of the process of the formation of the recirculation gyre for different Reynolds numbers is suggested

Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part I

A barotropic time-dependent model of the wind-driven currents in the subtropical region of the ocean was considered taking both nonlinearity and lateral friction into account. The boundary conditions are the impermeability at all boundaries, no-slip at the coasts and slip at the fluid boundaries. It is shown that the solution of the problem is characterized by two nondimensional parameters ε (the ratio of width of the inertial boundary layer to a basin dimension) and R (Reynolds number for the boundary layer). A series of numerical experiments is discussed with fixed ε = 0.01 and varying R to analyze the joint effect of nonlinearity and lateral friction for a wide range of the coefficient of the horizontal friction. The spin-up and quasistationary regimes in the evolution are identified. The most striking feature of the solution for finite R is the formation of a permanent intensive recirculation gyre. The periodic formation of the northward moving eddies in the boundary current is also observed during the quasistationary regime. A Fourier analysis of the energy oscillations as well as the time records of the stream function at certain points during the quasistationary regime is presented and the time-averaged solution of the problem is introduced. The basic result of the analysis is the proof of the existence of two critical values RC and RL of the Reynolds number R. For R \u3e RC the time-dependent solution of the problem does not stabilize as time proceeds (RC = 0.38). For R \u3e RL the structure of the solution is changed drastically: the motion becomes substantially more chaotic both in the interior and in the boundary layer (RL = 1.6). It will be shown in Sheremet et al. (1996, hereafter will be called SIK) that for R \u3e RC the steady solution still exists but it appears to be unstable, while for R \u3e RL the steady boundary-layer-type solution of the problem ceases to exist. The main feature of the time-averaged solutions for R \u3e RL is a rapid increase of a recirculation gyre in the northwest corner of the basin

Ray-based description of normal mode amplitudes in a range-dependent waveguide

An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations. This analytical description accounts for mode coupling and remains valid in a nonadiabatic environment. It has been used to investigate the applicability condition of the adiabatic approximation. An applicability criterion is formulated as a restriction on variations of the action variable of the ray.Comment: 11 pages, 5 figure

Future effects of ozone on carbon sequestration and climate change policy using a global biogeochemical model

Author Posting. © The Authors, 2004. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Climatic Change 73 (2005): 345-373, doi:10.1007/s10584-005-6776-4.Exposure of plants to ozone inhibits photosynthesis and therefore reduces vegetation production and carbon sequestration. The reduced carbon storage would then require further reductions in fossil fuel emissions to meet a given CO2 concentration target, thereby increasing the cost of meeting the target. Simulations with the Terrestrial Ecosystem Model (TEM) for the historical period (1860-1995) show the largest damages occur in the Southeast and Midwestern regions of the United States, eastern Europe, and eastern China. The largest reductions in carbon storage for the period 1950-1995, 41%, occur in eastern Europe. Scenarios for the 21st century developed with the MIT Integrated Global Systems Model (IGSM) lead to even greater negative effects on carbon storage in the future. In some regions, current land carbon sinks become carbon sources, and this change leads to carbon sequestration decreases of up to 0.4 Pg C yr-1 due to damage in some regional ozone hot spots. With a climate policy, failing to consider the effects of ozone damage on carbon sequestration would raise the global costs over the next century of stabilizing atmospheric concentrations of CO2 equivalents at 550 ppm by 6 to 21%. Because stabilization at 550 ppm will reduce emission of other gases that cause ozone, these additional benefits are estimated to be between 5 and 25% of the cost of the climate policy. Tropospheric ozone effects on terrestrial ecosystems thus produce a surprisingly large feedback in estimating climate policy costs that, heretofore, has not been included in cost estimates.This study was funded by the Biocomplexity Program of the U.S. National Science Foundation (ATM-0120468), the Methods and Models for Integrated Assessment Program of the U.S. National Science Foundation (DEB-9711626) and the Earth Observing System Program of the U.S. National Aeronautics and Space Administration (NAG5-10135). The IGSM has been developed as part of the Joint Program on the Science and Policy of Global Change with the support of a government-industry partnership including in addition to the above the US Department of Energy (901214-HAR; DE-FG02-94ER61937; DE-FG0293ER61713), the US Environmental Protection Agency (X-827703-01-0; XA-83042801-0), the National Aeronautics and Atmospheric Administration (NA16GP2290) and a group of corporate sponsors from the United States, Japan, United Kingdom, Germany, France, and Norway

On the evolution of Rossby waves, generated by wind stress in a closed basin, incorporating total mass conservation

The evolution of Rossby waves generated in a closed basin by applied stationary wind stress is considered, taking into account the total mass conservation constraint. The behavior of the wave field for large time t and the formation of a Sverdrup regime in the open ocean are analyzed by neglecting the frictionally induced wave decay. The consistent quasigeostrophic formulation of the problem is developed and the conditions are found for the applicability of relations derived. Using the vertical mode expansion reduces the 3D problem to a set of 2D problems. A method of solving the forced 2D problem with the mass constraint is suggested. The method consists of solving several particular problems, the most important of which are the forced problem for the auxiliary stream function Ψ τ with zero boundary values and the Volterra integral equation of the second kind for time-dependent boundary values of the stream function Ψ. To simplify the analysis, the 1D model of the forced problem considered is offered. The analytical solution of the problem with zero boundary values of the stream function Ψ is found. It is known that, in general, such a solution does not stabilize with time but for large values of m (the ratio of the basin dimension to the Rossby radius of deformation) and t it tends to the Sverdrup solution in the open ocean. The time-averaged stream function Ψ is introduced, which tends to the Sverdrup solution in the open ocean for all m. A solution of the consistent problem satisfying the total mass conservation constraint is obtained and analyzed. It is pointed out that the stream function Ψ does not tend to the Sverdrup solution outside the western boundary layer for large values of m and t, which differs drastically from the corresponding behavior of Ψ in the problem with zero boundary values. This demonstrates the failure of the solution of the inconsistent problem with zero boundary values to describe the wave motion for large t. It is shown that the establishment of the Sverdrup solution for large t can be seen only if the time-averaged stream function Ψ is considered. It is proved for all m that outside the western boundary layer Ψ tends to the Sverdrup solution (minus the integral of Ψ in x over the whole basin) for large t. The evolution of the total energy is also discussed

Simulation of Subantarctic Mode and Antarctic Intermediate Waters in Climate Models

Abstract The Southern Ocean’s Subantarctic Mode Water (SAMW) and Antarctic Intermediate Water (AAIW) are two globally significant upper-ocean water masses that circulate in all Southern Hemisphere subtropical gyres and cross the equator to enter the North Pacific and North Atlantic Oceans. Simulations of SAMW and AAIW for the twentieth century in eight climate models [GFDL-CM2.1, CCSM3, CNRM-CM3, MIROC3.2(medres), MIROC3.2(hires), MRI-CGCM2.3.2, CSIRO-Mk3.0, and UKMO-HadCM3] that provided their output in support of the Intergovernmental Panel on Climate Change’s Fourth Assessment Report (IPCC AR4) have been compared to the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Atlas of Regional Seas. The climate models, except for UKMO-HadCM3, CSIRO-Mk3.0, and MRI-CGCM2.3.2, provide a reasonable simulation of SAMW and AAIW isopycnal temperature and salinity in the Southern Ocean. Many models simulate the potential vorticity minimum layer and salinity minimum layer of SAMW and AAIW, respectively. However, the simulated SAMW layer is generally thinner and at lighter densities than observed. All climate models display a limited equatorward extension of SAMW and AAIW north of the Antarctic Circumpolar Current. Errors in the simulation of SAMW and AAIW property characteristics are likely to be due to a combination of many errors in the climate models, including simulation of wind and buoyancy forcing, inadequate representation of subgrid-scale mixing processes in the Southern Ocean, and midlatitude diapycnal mixing parameterizations

Stability of Baroclinic Vortices on the β Plane and Implications for Transport

Abstract This paper explores stability of and transport by baroclinic vortices on the β plane using a two-layer, quasigeostrophic model. The study adapts a wave–mean flow formalism and examines interactions between the axisymmetric flow (“the vortex”) and residuals (“the waves”). Unlike baroclinically unstable vortices on the f plane, such vortices on the β plane can be also vulnerable to barotropic instability as revealed by the globally integrated energy balance analysis. The spatial structure of energy fluxes shows the energy leakage inside the vortex core when its breakdown occurs. Mixing by stable and unstable vortical flows is quantified through the computation of finite-time Lyapunov exponent (FTLE) maps. Depending on the strength of wave radiation, the upper-layer FTLE maps of stable vortices show either an annulus or volute ring of vigorous mixing inside the vortex interior. This ring region is disrupted when the vortex becomes unstable. Both stable and unstable vortices show the wavy patterns of FTLE in the near and far fields. Despite the fact that the initial vortex resides in the top layer only, significant FTLE patterns are observed in the deep layer at later times. Lagrangian analysis of the vortex-induced change of large-scale tracer gradient demonstrates significant effects of vortex instability in the top layer and the importance of the wavelike anomalies in the bottom layer