Abstract

Weakly nonlinear longwaves in a horizontally sheared current flowing along a longitudinal boundary in a two-layer ocean are investigated by using a quasi-geostrophic β-plane model. Under the assumptions that the depth ratio of two layers is small, the β effect is weak and the waves are almost stationary, we obtain a set of coupled equations similar to that derived perviously by Kubokawa for a coastal current with a surface density front on an f-plane. This set of equations contains soliton and cnoidal wave solutions and allows baroclinic instability to occur.

Considering a perturbation around the marginally stable condition, we obtain an analytic solution of a growing solitary disturbance with an amplitude larger than a certain critical value in a linearly stable eastward current. This disturbance propagates eastward, and grows by a baroclinic energy conversion. A numerical computation on its further evolution shows that after the amplitude exceeds another certain critical value, the disturbance begins to propagate westward and to radiate Rossby waves. This Rossby wave radiation causes the disturbance to decay and the propagation speed approaches zero. Nonlinear evolution of linearly unstable waves in an eastward current is also briefly discussed. The theory is applied to the Kuroshio Current in a qualitative way.

Abstract

The mixed layer thickness generally increases in the northward direction, but its change seems to occur rather sharply in a narrow transition zone, referred to as a mixed layer front here. The author investigates the effects of the mixed layer front on the ventilated thermocline structure, especially focusing on the generation mechanism of the subtropical countercurrent. If the mixed layer front is not parallel to the surface density contour, the fluid with minimum isopycnal potential vorticity is formed around the intersection of the mixed layer front and outcrop line. If the mixed layer front slants northeastward and surface density is zonally uniform, as seen in a numerical experiment carried out by Kubokawa and Inui in which the subtropical countercurrent was reproduced, the minimum potential vorticity on a high-density isopycnal occurs in the east, while that in a low-density isopycnal occurs in the west. In the present study, analytic solutions for a simple three-layer model are presented first to demonstrate that such an inhomogeneous distribution of isopycnal potential vorticity can generate a subtropical countercurrent. Then, a multilayer ventilated thermocline model coupled with the mixed layer is solved numerically. For the northeastward slanting mixed layer front, as advected southward, the low potential vorticity fluids in different layers converge in the horizontal plane, forming a thick ventilated layer in the central western region of the subtropical gyre. This thick ventilated layer lifts the base of the surface layer and generates a subtropical countercurrent along the southeastern edge of this region. On the other hand, a southeastward slanting mixed layer front can also generate a countercurrent.

Abstract

This article presents a solution for the linear response of a 2½-layer ventilated thermocline to large-scale periodic wind forcing, with a fixed outcrop latitude. At the eastern boundary, a Rossby wave whose vertical structure is similar to the first baroclinic mode is generated and propagates westward in the shadow zone. Meanwhile, the wave is unstable and amplified westward in the southern region. In the ventilated zone, in addition to the first-mode Rossby wave generated at the eastern boundary, two waves with second mode–like vertical structures are generated. One wave is generated directly by the wind over the outcrop. This wave has a zero zonal wavenumber and southwestward group velocity, such that the eastern edge of the wave migrates westward as it propagates southward. The other wave is generated by interaction between the westward-propagating, first-mode Rossby wave and the outcrop. The zonal wavenumber is the same as that of the first mode at the outcrop, and the phase of the wave propagates southwestward. The crests and troughs of this wave extend across the ventilated zone from the outcrop to the internal boundary between the shadow zone and the ventilated zone.

Abstract

Western boundary currents (WBCs) under no-slip boundary conditions tend to separate from the coast prematurely (without reaching the intergyre boundary) and form eastward jets. This study theoretically considers the meridional structure and location of a prematurely separated WBC extension jet using a two-layer quasigeostrophic model. Assuming homogenized potential vorticity (PV) regions on both sides of and below the jet, we constructed a simple model for the meridional profiles of the zonal flows in the western subtropical gyre. This work clarifies that the meridional structure can be determined if two variables, such as the strength of the PV front (difference in PV across the jet) and the value of the streamfunction at the jet’s center, are given in addition to the meridional profile of the Sverdrup zonal flow and the vertical stratification. The zonal velocity profiles in both layers agreed well with those obtained by numerical experiments. When the jet is close to the intergyre boundary, the meridional location of the jet depends only on the front’s strength. When the northern recirculation gyre is detached from the intergyre boundary and the local wind effect on the jet is negligible, comparisons with the numerical experiments suggest that the jet’s central streamline connects to the central streamline of the eastward Sverdrup flow. We also found that a downward Ekman pumping velocity shifts the jet southward.

Abstract

In the North Pacific, there is a shallow eastward current called the subtropical countercurrent, which flows across the central subtropical gyre. The present article studies the generation mechanism of the subtropical countercurrent reproduced in an ocean general circulation model (GCM) with a simple geometry, driven by surface wind stress and surface buoyancy forcing.

In the ocean GCM, the deep mixed layer occurs in the northern part of subtropical gyre and shoals abruptly in the central subtropical gyre. The mixed layer front, the narrow transition zone of the mixed layer depth, slants from the western central subtropical gyre to the northeast, and the low potential vorticity fluid is formed at the intersection of the mixed layer front and the outcrop line. Since the surface density is almost zonally uniform and the mixed layer front slants northeastward, the minimum potential vorticity fluids on denser isopycnals are formed in the northeastern region, while those on lighter isopycnals are formed in the western region. Subducted and advected southwestward, the low potential vorticity fluid in each isopycnal overlaps that on another isopycnal and makes a thick low potential vorticity pool in the western central subtropical gyre. It is found that the model subtropical countercurrent occurs along the southern edge of this pool.

Abstract

Numerical experiments with idealized OGCM are carried out to investigate the oceanic eastern boundary problems. The experimental results indicate that the eastward flow due to the north–south gradient of the surface density returns to the interior region through the lower half of the mixed layer, and this return flow generates a density jump just above the thermocline. Formulation for the mixed layer depth distribution at the eastern boundary is also presented, which is derived only from the geostrophy and no-normal flow condition. This formulation agrees well with the numerical experiment, and can be an appropriate eastern boundary condition for theoretical ventilated thermocline model with no deficiency of the mass balance on the boundary. Furthermore, the effects of such eastern boundary structure on the subtropical thermocline are studied. On the shallow thermocline in the subtropics, eastern boundary ventilated region emerges, which is identified as a region of high potential vorticity. In the deep thermocline, which does not outcrop in the subtropics, a cross-gyre ventilation occurs. This cross-gyre ventilation is caused by the density structure along the eastern boundary.

Abstract

The relation between lens translation speed and potential thickness anomaly in the second layer is investigated in a 2½-layer β-plane primitive model in the case of southward movement of lens-shaped eddies. The trapped dipole in the second layer under the lens generated by the initial westward movement of the lens drives the first-layer lens southward. The subsequent southward translation has an almost steady stage before the lens succumbs to baroclinic instability, and the lens in the first layer and a negative potential thickness anomaly in the second layer remain coupled. It is shown that the translation speed is related to the potential thickness anomaly and that the β effect in the first and second layers plays an important role in sustaining the steady translation. To examine this relation and discuss the dynamic balance of the steadily translating eddy, an analytic solution in a 2½-layer f-plane model is derived, assuming that the relative vorticity in the second layer is negligible. The solution shows the following: 1) If the translation speed is not zero, the area integral of the potential thickness anomaly in the second layer is constant irrespective of the translation speed. 2) The lens speed is related to the area average of the potential thickness anomaly in the second layer. 3) For steady translation, the area average of the potential thickness anomaly must be larger than a certain value. On the β plane, Rossby wave radiation, leakage of the potential thickness anomaly, and meridional displacement of the vortex structure lead to a transformation of the potential vorticity anomaly, and the constraints of the f plane are thus difficult to hold. From the comparison between the f-plane theory and the numerical experiments, however, these constraints are found to be almost satisfied on the β plane if the effect of the relative vorticity is included in the f-plane theory. This suggests that the increasing of the potential thickness anomaly due to the second-layer β during the southward translation balances the leakage of the potential thickness anomaly from the lens region, with the result that the constraints obtained by the f-plane theory hold.

Abstract

This paper investigates the formation of eastward jets extended from western boundary currents, using a simple two-layer quasigeostrophic (QG) model forced by a wind stress curl consistent with the formation of a subtropical gyre. The study investigated the dependency of the latitude of the eastward jet on various parameters and on the meridional distribution of the Ekman pumping velocity. The parameters considered in the present study included the viscous and inertial western boundary layer width, the parameter representing the degree of the partial-slip boundary condition, the ratio of the upper- to lower-layer depth, and the bottom friction. With the parameters used, two types of stable structures are found in the time-mean field. One type of structure represented the “prematurely separated jet case,” in which the eastward extension jet was located far south of the northern boundary of the subtropical gyre, as is the Kuroshio Extension; the other type was the “gyre boundary jet case,” in which the eastward jet occurred along the northern boundary. The initial condition decides which type of structure would occur. When the prematurely separated jet case occurred, the authors found that the latitude of the eastward jet depended very little on the parameters. In addition, this study also observed that the latitude was determined by the meridional distribution of the Ekman pumping velocity. The eastward extension jet was usually located near the latitude that was half of the maximum value of the Sverdrup streamfunction and satisfied an integral condition derived from the QG potential vorticity equation.

Abstract

The nonlinear evolution of linearly unstable barotropic boundary currents, consisting of three piecewise uniform vorticity regions, was investigated using the contour dynamics method. A physical interpretation of the nonlinear behavior of the unstable currents is also presented. The contour dynamics experiments reveal that the nonlinear behavior can be classified into three regimes dependent on the vorticity distribution of the basic flow and the wavelength of the unstable wave. In the first breaking wave regime a regular wave train appears with crests breaking on their upstream side. In the second vortex pair regime the unstable wave evolves into a mushroomlike shape consisting of two vortices having opposite signs, which, due to self-induced flow, advect coastal water far away from the boundary. In the third boundary trapped vortex regime the vortices generated in both the offshore and coastal shear regions remain trapped near the coastal boundary. Differences among the three regimes are mainly governed by the temporal change of the phase relationship between the vorticity centers in the piecewise uniform vorticity regions. The important point to note is that the nonlinear evolution exhibits qualitatively different behavior at different wavelengths, even if the basic currents have the same velocity profiles. In the real ocean, due to coastal topography or external disturbance, the scale of the disturbance is not always determined by the fastest growing mode. Therefore, the nonlinear behavior of an unstable current, which affects the mixing and transport processes, should be studied with attention focused on various wavelengths of the disturbance.

Abstract

The appropriate lateral boundary condition for an oceanic general circulation model is not yet well determined. A large-scale current is inhibited from ascending the continental slope because of the restriction of the potential vorticity conservation. As a consequence the current may never be in contact with a side boundary that has vertical walls; nevertheless, side boundaries have always been assumed in the formulation of general circulation models. In the true situation the western boundary current associated with a midlatitude, wind-driven gyre may be located on the continental slope. Since the streamfunction tends to follow the ambient potential vorticity contours, there will be an equatorward tail to the gyre that also occurs on the slope.

Here a linear barotropic theory is developed for the following three cases: 1) a quasigeostrophic model with Rayleigh friction, 2) a quasigeostrophic model with lateral viscosity, and 3) an equatorial β-plane model with Rayleigh friction. These can be viewed as generalizations of Stommel and Munk solutions for an oceanic basin with a vertical side boundary. The general characteristics of the solutions and the dependence on the parameter representing the slope and/or the friction are studied. It is found that in the steep-slope limit the solutions in the flat region for 1) and 2) approach the Stommel solution and the Munk solution, respectively. In the former case, the streamfunction at the outer edge of the slope decreases as (slope)^−1/2 and the current velocity suddenly vanishes in the slope region in this limit; in the latter case, the streamfunction there also decreases as (slope) ^−1/2, while the velocity varies as (slope) ^−1/4. From the solution for 3), it is found that the WI decays rapidly in low latitudes and cannot cross the equator. It is also found that if the frictional torque is stronger than the effect of the vortex stretching over the slope, the tail length is significantly reduced, even if the friction coefficient is not large.