Linear planetary wave dynamics in a 2.5-layer ventilated thermocline model

Linear planetary wave dynamics in a 2.5-layer ventilated thermocline model is investigated by a local eigenvalue analysis and simple numerical computations. It is known that there are two types of waves in this system; we refer to one of them as the N-mode (Non-Doppler shift mode), which propagates almost westward, and the other as the A-mode (Advection mode), which propagates almost along the second layer basic current. First, we study the local longwave dynamics, assuming that the wavelength is much longer than the deformation radius and shorter than the gyre scale. It is shown that the N-mode and the A-mode cannot neatly be separated in the ventilated zone, and even in the Rhines and Young pool, a compact A-mode disturbance cannot exist by itself. When anomalous Ekman pumping is applied in the ventilated zone, the N-mode is generated in the forcing region, and the A-mode is generated at the wave front of the N-mode. For diabatic forcing, a similar phenomenon occurs. It is also found that the shadow zone is unstable to longwave disturbances. Secondly, the wave behavior in the linear planetary geostrophic model is numerically investigated. The main features can be interpreted by the local wave dynamics, and the disturbances around the maximum amplitudes are dominated by the waves whose wavenumber vectors are perpendicular to the second layer potential vorticity contours. The amplitude changes during the wave propagation are also discussed. Finally, the effects of the finite wavelength are studied. The N-mode is strongly dispersive at the scale of the Rossby deformation radius, while the A-mode is weakly dispersive. It is also shown that the ventilated zone is unstable to shortwave disturbances, although it is stable to longwave disturbances

Interaction between an upper-layer point vortex and a bottom topography in a two-layer system

In this paper, the interaction between an upper-layer vortex and a bottom topography is investigated using an -plane two-layer quasi-geostrophic model with a point vortex and step-like topography. The contour dynamics method is used to formulate the model. A steadily propagating linear solution along the topography, known as the pseudoimage solution, is derived analytically for a weak point vortex, and the nonlinear solution is obtained numerically. Numerical experiments show that the nonlinear pseudoimage solution collapses with time. Saddle-node points in the velocity field are critical in this collapse. Even after the collapse, the point vortex propagates along the topography similarly to in the steadily propagating solution. Numerical experiments with various initial conditions show that the point vortex has two types of motion in this system: motion along the topography and motion away from the topography. In the latter case, the point vortex and lower-layer potential vorticity anomaly form a heton-like dipole structure. The motion classification results show that an anticyclonic (cyclonic) point vortex on the deeper (shallower) side is more likely to form a dipole structure than a cyclonic (anticyclonic) vortex on the deeper (shallower) side when their initial distance from the topography is the same

Latitude of Eastward Jet Prematurely Separated from the Western Boundary in a Two-Layer Quasigeostrophic Model

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

Numerical Study of Eastern Boundary Ventilation and its effects on the Thermocline Structure

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

Linear Response of a Ventilated Thermocline to Periodic Wind Forcing

This article presents a solution for the linear response of a 21/2-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