The nonlinear response of an equatorial ocean to oscillatory forcing (original) (raw)
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Journal of Fluid Mechanics, 1975
The nonlinear response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is re-examined here in part 1 for the case of strong steady forcing. Introduced by Pedlosky & Greenspan (1967), the model consists of a rapidly rotating right cylinder with a planar sloping bottom. The homogeneous contained fluid is driven by the slow rotation of the flat upper lid relative to the rest of the basin. Except in thin Ekman and Stewartson boundary layers on the solid surfaces of the basin, the horizontal flow in the interior and western boundary layer is constrained by the rapid rotation of the basin to be independent of depth. The model thus effectively simulates geophysical flows through the physical analogy between topographic vortex stretching in the laboratory model and the creation of relative vorticity in planetary flows by the β effect.As the forcing is increased, the flow in both the sliced-cylinder laboratory and numerical models first exhibits downstream int...
The response of the equatorial ocean to a moving wind field
Journal of Geophysical Research, 1986
A linear, viscid, continuously stratified model is used to study the response of the equatorial ocean to forcing by a wind patch moving zonally at the velocity U. For simplicity, solutions are found in an unbounded basin, and transient effects are ignored. This problem is mathematically equivalent to one in which the ocean has a uniform background current -U and the forcing is stationary, and it is possible to interpret solutions from either point of view. An important result is that resonant and near-resonant Rossby and Kelvin waves can be preferentially excited over other equatorially trapped waves forced by the wind. For two of the solutions, parameters are set as realistically as the model allows, and the solutions are compared with observations. One of them is forced by an eastward moving wind field like the westerly wind anomaly associated with the 1982-1983 E1 Nifio event. It develops subsurface, anomalously westward flow that is strong enough to eliminate the normal Equatorial Undercurrent. The other is forced by a stationary wind in the presence of a weak, westward background current. It has a current structure in the deep ocean that resembles observations of deep equatorial jets, but the surface currents are not realistic. Near-resonant Kelvin waves contribute significantly to both solutions and are responsible for their interesting properties.
Journal of Physical Oceanography, 2003
Recent numerical experiments indicate that the rate of meridional overturning associated with North Atlantic Deep Water is partially controlled by wind stress in the Southern Ocean, where the zonal periodicity of the domain alters the nature of the flow. Here, the authors solve the cubic scale relationship of Gnanadesikan to find a simple expression for meridional overturning that is used to clarify the relative strength of the windforced component. The predicted overturning is compared with coarse-resolution numerical experiments with an idealized Atlantic Ocean-Southern Ocean geometry. The scaling accurately predicts the sensitivity to forcing for experiments with a level model employing isopycnal diffusion of temperature, salinity, and ''layer thickness.'' A layer model produces similar results, increasing confidence in the numerics of both models. Level model experiments with horizontal diffusivity have similar qualitative behavior but somewhat different sensitivity to forcing. The paper highlights the difference in meridional overturning induced by changes in wind stress or vertical diffusivity. Strengthening the Southern Ocean wind stress induces a circulation anomaly in which most of the water is subducted in the Ekman layer of the wind perturbation region, follows isopycnals down into the thermocline, and changes density again when the isopycnals near the surface in the Northern Hemisphere. Approximating the circulation anomaly by this subduction route allows for a surprisingly accurate prediction of the resulting heat transport anomaly, based on the surface temperature distribution. Some of the induced flow follows a second, near-surface northward route through low-latitude water that is lighter than the subducted flow. Overturning anomalies far from the wind stress perturbations are not completely determined by wind stress in the zonally periodic Southern Ocean: wind stress outside the periodic region strongly influences the transport of heat across the equator primarily by changing the temperature of the flow across the equator.
Dynamics of the Atlantic meridional overturning circulation. Part 1: Buoyancy-forced response
Progress in Oceanography, 2012
Historically, a hierarchy of ocean models have been used to investigate the dynamics of basin-scale, deep, meridional overturning circulations (MOCs). Near the base of this hierarchy are idealized solutions forced only by a surface buoyancy flux. Our goal is to provide a complete dynamical description of such ''base'' solutions, thereby placing the hierarchy on a firmer foundation. For this purpose, we obtain solutions to two types of models: a variable-density, layer ocean model (VLOM) and an ocean general circulation model (COCO), the former allowing for nearly analytic solutions and the latter for more accurate representation of processes. Solutions are obtained in an idealized, flat-bottom basin extending 40°in longitude and from the equator to 60°N, and for simplicity density depends only on temperature. Our standard runs are forced by a surface heating Q, which is spread uniformly throughout layer 1 in VLOM and at depths less than h min in COCO; it quickly relaxes upper-ocean temperature to a prescribed T ⁄ (y) that decreases linearly in the latitude band 30-50°N from 23°C in the south to the temperature of the deep ocean, 3°C, in the north.
Propagation of Meridional Circulation Anomalies along Western and Eastern Boundaries
Journal of Physical Oceanography, 2013
Motivated by the adjustment of the meridional overturning circulation to localized forcing, solutions are presented from a reduced-gravity model for the propagation of waves along western and eastern boundaries. For wave periods exceeding a few months, Kelvin waves play no role. Instead, propagation occurs through short and long Rossby waves at the western and eastern boundaries, respectively: these Rossby waves propagate zonally, as predicted by classical theory, and cyclonically along the basin boundaries to satisfy the no-normal flow boundary condition. The along-boundary propagation speed is cLd/δ, where c is the internal gravity/Kelvin wave speed, Ld is the Rossby deformation radius, and δ is the appropriate frictional boundary layer width. This result holds across a wide range of parameter regimes, with either linear friction or lateral viscosity and a no-slip boundary condition. For parameters typical of contemporary ocean climate models, the propagation speed is coincidental...
Baroclinic and barotropic aspects of the wind-driven ocean circulation
Physica D: Nonlinear Phenomena, 2002
The double-gyre circulation induced by a symmetric wind-stress pattern in a quasi-geostrophic model of the mid-latitude ocean is studied analytically and numerically. The model is discretized vertically by projection onto normal modes of the mean stratification. Within its horizontally rectangular domain, the numerical model captures the wind-driven circulation's three dynamic regimes: (1) a basin-scale double-gyre circulation, cyclonic in the basin's northern part and anticyclonic in the south, which is dominated by Sverdrup balance; (2) a swift western boundary current in either gyre, with dissipation most important near the coast and inertial balance further out; and (3) a strong recirculating dipole near the intersection of the western boundary with the symmetry line of zero wind-stress curl. The flow inside this stationary dipole is highly nonlinear, and equivalent-barotropic. An analytical solution to the potential vorticity equation with variable stratification describes the dipole, and fits well the full numerical model's steady-state solutions. Changes in the numerical model's solutions are investigated systematically as a function of changes in the strength of the wind stress τ and the Rossby radius of deformation L R. The main changes occur in the recirculation region, while the basin-scale gyres and the western boundary currents are affected but little. A unique symmetric dipole is observed for small τ , and agrees in its properties with the analytical solution. As τ increases, multiple asymmetric equilibria arise due to pitchfork bifurcation and are stable for large enough L R. The numerically obtained asymmetric equilibria also agree in their main properties with the analytical ones, as well as with the corresponding solutions of a shallow-water model. Increasing τ further results in two successive Hopf bifurcations, that lead to limit cycles with periods near 10 and 1 years, respectively. Both oscillatory instabilities have a strong baroclinic component. Above a certain threshold in τ the solutions become chaotic. Flow pattern evolution in this chaotic regime resembles qualitatively the circulation found in the Gulf Stream and Kuroshio current systems after their separation from the continent.
Dynamics of Atmospheres and Oceans, 2003
A simplified coupled ocean-atmosphere model, consisting of a one-layer bidimensional ocean model and a one-layer unidimensional energy balance atmospheric model [J. Clim. 13 (2000) 232] is used to study the unstable interactions between zonal winds and ocean gyres. In a specific range of parameters, decadal variability is found. Anomalies, quite homogeneous zonally, show small-scale wavelength in latitude: perturbations emerge and grow at the southern limb of the intergyre boundary and propagate southward before decaying. The wind stress anomalies are proportional to the meridional gradient of the atmospheric temperature anomalies: this ratio acts as a positive amplification factor, as confirmed by a parameter sensitivity analysis. Assuming zonally-averaged anomalies harmonic in the meridional direction, a very simple analytical model for the perturbations is derived, based on forced Rossby wave adjustment of the western boundary current and its associated anomalous heat transport: it accounts for the scale selection, the growth and the southward propagation of sea surface temperature anomalies in the subtropical gyre. The latter is not only due to the slow advection by the mean current, but to a prevailing mechanism of self-advecting coupled oceanic and atmospheric waves, out of phase in latitude. Relevance to the observational record is discussed.
Dynamics of the Atlantic meridional overturning circulation. Part 2: Forcing by winds and buoyancy q
Recently, Schloesser et al. (2012) explored the dynamics of the descending branch of meridional overturning circulations (MOCs), by obtaining analytic solutions to a variable-density, 2-layer model (VLOM) forced only by a surface buoyancy flux. Key processes involved are the poleward thickening of the upper layer along the eastern boundary due to Kelvin-wave adjustments, the westward propagation of that coastal structure by Rossby waves, and their damping by mixing; the resulting zonal pressure gradient causes the surface MOC branch to converge into the northern basin near the eastern boundary. In this paper, we extend the Schloesser et al. (2012) study to include forcing by a zonal wind stress s x (y). Much of the paper is devoted to the derivation and analysis of analytic solutions to VLOM; for validation, we also report corresponding numerical solutions to an ocean general circulation model (OGCM). Solutions are obtained in a flat-bottom, rectangular basin confined to the northern hemisphere. The buoyancy forcing relaxes upper-ocean density to a prescribed profile q ⁄ (y) that increases polewards until it becomes as large as the deep-ocean density at latitude y 2 ; north of y 2 , then, the ocean is homogeneous (a 1-layer system). The wind stress s x drives Subtropical and Subpolar Gyres, and in our standard solution the latter extends north of y 2. Vertical diffusion is not included in VLOM (minimized in the OGCM); consequently, the MOC is not closed by upwelling associated with interior diffusion, but rather by flow through the southern boundary of the basin (into a southern-boundary sponge layer in the OGCM), and solutions are uniquely determined by specifying the strength of that flow or the thermocline depth along the tropical eastern boundary. Solutions forced by s x and q ⁄ differ markedly from those forced only by q ⁄ because water flows across y 2 throughout the interior of the Subpolar Gyre, not just near the eastern boundary. In some of our solutions, the strength of the MOC's descending branch is determined entirely by this wind-driven mechanism, whereas in others it is also affected by Rossby-wave damping near the eastern boundary. Upwelling can occur in the interior of the Subpolar Gyre and in the western-boundary layer, providing ''shortcuts'' for the overturning circulation; consequently, there are different rates for the convergence of upper-layer water near y 2 ; M n , and the export of deep water south of the Subpolar Gyre, M, the latter being a better measure of large-scale MOC strength. When western-boundary upwelling occurs in our solutions, M is independent of the diapycnal processes in the subpolar ocean.
Wind-forced variability of the zonal overturning circulation
Journal of Physical Oceanography, 2022
The mechanisms of wind-forced variability of the zonal overturning circulation (ZOC) are explored using an idealized shallow water numerical model, quasigeostrophic theory, and simple analytic conceptual models. Two windforcing scenarios are considered: midlatitude variability in the subtropical/subpolar gyres and large-scale variability spanning the equator. It is shown that the midlatitude ZOC exchanges water with the western boundary current and attains maximum amplitude on the same order of magnitude as the Ekman transport at a forcing period close to the basin-crossing time scale for baroclinic Rossby waves. Near the equator, large-scale wind variations force a ZOC that increases in amplitude with decreasing forcing period such that wind stress variability on annual time scales forces a ZOC of O(50) Sv (1 Sv ≡ 10 6 m 3 s 21). For both midlatitude and low-latitude variability the ZOC and its related heat transport are comparable to those of the meridional overturning circulation. The underlying physics of the ZOC relies on the influences of the variation of the Coriolis parameter with latitude on both the geostrophic flow and the baroclinic Rossby wave phase speed as the fluid adjusts to time-varying winds. SIGNIFICANCE STATEMENT: The purpose of this study is to better understand how large-scale winds at mid-and low latitudes move water eastward or westward, even in the deep ocean that is not in direct contact with the atmosphere. This is important because these currents can shift where heat is stored in the ocean and if it might be released into the atmosphere. It is shown that large-scale winds can drive rapid cross-basin transports of water masses, especially so at low latitudes. The present results provide a guide on what controls this motion and highlight the importance of large-scale ocean waves on the water movement and heat storage.
Vortex interaction with a zonal Rossby wave in a quasi-geostrophic model
Dynamics of Atmospheres and Oceans, 2006
An analytical theory is presented for the motion of a localized vortex in the presence of a zonal Rossby wave on the β-plane. In the framework of the equivalent-barotropic quasi-geostrophic model, the analytical method developed by Sutyrin and Flierl [Sutyrin G.G., Flierl G.R., 1994. Intense vortex motion on the β-plane: development of the beta gyres. J. Atmos. Sci. 51, 773-790] for intense vortices with piecewiseconstant potential vorticity is generalized to take into account a slowly propagating Rossby wave which modifies the background potential vorticity. The predictions of these asymptotic expansions are compared with the results of numerical simulations. The theory describes the vortex advection by the wave and the vortex drift due to the background potential vorticity gradient. The net vortex drift speed due to the wave is found to be smaller than the maximum wave velocity; this is due to the baroclinic -effect and to the periodic structure of the background potential vorticity gradient. Besides known elliptical core deformations, triangular deformations are generated by the wave on the core boundary. Additionally, the planetary -effect provides a predominantly westward vortex drift with nearly the same speed as the wave propagation speed. The asymptotic theory is shown to agree well the results of a numerical pseudo-spectral, high-resolution biperiodic model when the vortex velocity is much larger than the wave velocity. Both meridional and zonal vortex drifts are slightly overestimated when the wave velocity is comparable with the vortex velocity. Vortex size is shown to be more influential on vortex trajectory than the Rossby wave length. In particular, smaller vortices drift westward farther and faster than large ones. Vortex core deformations typically contain modes 2 and 3 with a stronger mode 3 component for more intense Rossby waves as predicted by theory.