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Humio Mitsudera

Abstract

Localized baroclinic instability in a weakly nonlinear, long-wave limit using an Eady model is studied. The resulting evolution equations have a form of the KdV type, including extra terms representing linear coupling. Baroclinic instability is triggered locally by the collision between two neutral solitary waves (one trapped at the upper boundary and the other at the lower boundary) if their incident amplitudes are sufficiently large. This characteristic is explained from the viewpoint of resonance when the relative phase speed, which depends on the amplitudes, is less than a critical value. The upper and lower disturbances grow in a coupled manner (resembling a normal-mode structure) initially, but they reverse direction slowly as the amplitudes increase, and eventually separate from each other.

The motivation of this study is to investigate a type of extratropical cyclogenesis that involves a preexisting upper trough (termed as Type B development) from the viewpoint of resonant solitary waves. Two cases are of particular interest. First, the author examines a case where an upper disturbance preexists over an undisturbed low-level waveguide. The solitary waves exhibit behavior similar to that conceived by Hoskins et al. for Type B development; the lower disturbance is forced one sidedly by a preexisting upper disturbance initially, but in turn forces the latter once the former attains a sufficient amplitude, thus resulting in mutual reinforcement. Second, if a weak perturbation exists at the surface ahead of the preexisting strong upper disturbance, baroclinic instability is triggered when the two waves interact. Even though the amplitude of the lower disturbance is initially much weaker, it is intensified quickly and catches up with the amplitude of the upper disturbance, so that the coupled vertical structure resembles that of an unstable normal mode eventually. These results describe the observed behavior in Type B atmospheric cyclogenesis quite well.

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Humio Mitsudera and Roger Grimshaw

Abstract

The resonant interaction of a longshore baroclinic current with a topographic feature is investigated, using a quasi-geostrophic two-layer model, where the lower layer is assumed to be deep but is not stagnant. In this model the current may be baroclinically unstable. When a long-wave phase speed is close to zero (in a fixed reference frame), which is found to be realized when the current has almost zero velocity at the coast, there is an enhanced generation of mesoscale variability due to a combination of resonant topographic forcing and baroclinic instability. A forced evolution equation of the KdV-type, which includes an additional coupling term with the lower-layer equation, describes the behavior of the upper layer. On the other hand, the lower-layer motion is governed by a linear vorticity equation, which in turn is coupled to the upper-layer equation.

A stability analysis shows that a solitary wave is unstable when a parameter Γ (the phase speed in the absence of any coupling between the two layers) takes values in a certain range determined by considering a linear stability problem. A variety of numerical solutions are presented, covering stable and unstable cases, characterized by the property of the baroclinic current and the forcing mechanism, which is due either to a coastline perturbation or to bottom topography. It is found that upstream and downstream nonlinear waves are generated due to resonant forcing and may be further amplified by baroclinic instability if the wave parameter Γ meets the instability criterion. These destabilized nonlinear waves show very complicated interactive behavior.

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Humio Mitsudera and Roger Grimshaw

Abstract

The authors have demonstrated that a large amplitude, nearly stationary solitary wave can be induced either by direct resonant forcing or by the capture of a traveling wave over the forcing region, using a two-layer model in a weakly nonlinear, long-wave limit. This two-layer model consists of a thin upper layer (where the motion is relatively strong) and a deep lower layer. From this system, an evolution equation of the KdV-type is derived to describe the upper-layer motion, while the deep lower-layer motion is described by a linear long-wave vorticity equation. The authors are particularly interested in the role of baroclinic instability in the evolution of solitary waves, as well as the effects of topographic forcing and frictional dissipation.

Resonant forcing occurs within a bandwidth of a detuning parameter that scales with the square root of the (nondimensional) forcing amplitude. On the other hand, the capture of traveling waves, whose amplitude is larger than a critical value, occurs when the detuning parameter is outside the resonant band, and it is in this range that multiple equilibria (coexistence of the large and small amplitude stationary states for a given parameter set) can be realized. Whether the large amplitude stationary state appears upstream or downstream from the forcing region depends on the relative importance of baroclinic energy conversion, topographic forcing, and frictional dissipation. Further, a topographic feature can trigger baroclinic instability, which can then induce not only large amplitude stationary waves but also large amplitude traveling waves going away from the forcing region. The model results are suggestive of the bimodality of Kuroshio upstream from the Izu Ridge.

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Hajime Nishigaki and Humio Mitsudera

Abstract

The dynamics of subtropical western boundary currents over slopes detaching from coasts with inshore pool regions, where the water of the subtropical gyre does not enter and the velocity is small, are investigated. This study is intended to understand the dynamics of the nearshore path of the Kuroshio, which has a distinct boundary between the boundary current and the coastal water. Numerical experiments under idealized conditions are made. The results show flow patterns with pool regions similar to the Kuroshio under simple conditions. A deep countercurrent is present on the lower bottom slope, which represents observed deep currents. This is part of a deep cyclonic recirculation north of the jet, which extends to the lower bottom slope despite steep topography. This extension can be explained by the geostrophic contours. In this region, the upper boundary current feels the bottom slope and the westward intensification is blocked. In the other region, where the bottom-layer velocity is very small, the upper boundary current is free from the bottom slope and westward intensification occurs at the coast. The sensitivity to the volume transport of the boundary current is investigated by case studies. The pool regions are broken in cases with large volume transports. It is indicated that these unsteady inshore regions are produced by instability caused by an outcrop of the upper isopycnal, which is led by a large baroclinic volume transport.

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Humio Mitsudera and Roger Grimshaw

Abstract

In this paper, the effects of bottom and interfacial friction on localized baroclinic instability are discussed in the weakly nonlinear, long-wave limit. Using a quasigeostrophic two-layer model in which the lower layer is assumed to be deep, we have derived a coupled evolution equation set that consists of a KdV-type equation for the upper layer and a linear long-wave equation for the lower layer. A perturbation theory reveals that there are multiple equilibria in this system, where baroclinic energy conversion and frictional dissipation are in balance; the flow is not forced externally, and multiplicity here refers to the presence or absence of solitary waves propagating steadily on a zonal flow. Further, direct numerical calculations show a rich variety of behavior of solitary waves, including steady, periodic, and complicated interacting evolutions. For a two-layer model to have multiple steady or oscillatory states, both bottom and interfacial friction should be included because if one of these vanishes, friction destabilizes rather than damps the otherwise neutral waves. The localized baroclinic instability is highly suggestive of the dynamics of the Kuroshio large meander.

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Ryu Saiki and Humio Mitsudera

Abstract

Ice bands are frequently observed over marginal ice zones in polar seas. A typical ice-band pattern has a regular spacing of about 10 km and extends over 100 km in the marginal ice zone. Further, the long axis of an ice band lies to the left (right) with respect to the wind direction in the Northern (Southern) Hemisphere. Here, the study shows that the resonance between ice-band pattern propagation and internal inertia–gravity waves below the sea ice well explains the ice-band pattern formation. Internal waves are generated by the difference between the stress on the open water and the stress on ice-covered water. This in turn reinforces the formation of an ice-band pattern with a regular band spacing. Specifically, the authors have found the following: 1) A band spacing on the order of 10 km is selected by the resonance condition in which the ice-band pattern propagation speed coincides with the phase speed of internal inertia–gravity waves. 2) The ice bands tend to develop favorably when the wind direction and the band propagation direction are nearly parallel. The velocity acceleration caused by the periodic differential stress associated with the ice bands, driven by the wind parallel to the band propagation direction, is important. The wind direction may turn to the left (right) slightly in the Northern (Southern) Hemisphere as a result of the Coriolis force acting on ice. Satellite images confirmed that the band spacing of the ice-band pattern in the polar seas is consistent with this theory.

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Tangdong Qu, Humio Mitsudera, and Bo Qiu

Abstract

Time-averaged structure of the Kuroshio/Oyashio system east of Japan was examined using historical hydrographic data. Unlike most of the earlier climatological analyses, the data were averaged along isopycnal rather than pressure surfaces in a 0.5° × 0.5° grid. As a result, most of the detailed phenomena associated with the narrow western boundary currents were revealed. Water from the Oyashio is seen to overshoot the zero zonally integrated wind-stress-curl line by more than 5°, approaching as far south as 36°–38°N at the western boundary. Water from the Kuroshio Extension, by contrast, tends to feed into the Oyashio Front in the interior ocean. This exchange of waters leads to a zero of zonally integrated (western boundary–180°) meridional transport at about 44°N, reasonably coinciding with the zero of zonally integrated wind stress curl in the western North Pacific. A well-defined double-front structure is seen at depths of the thermocline, but it does not appear to have a strong signature in the surface dynamic topography. Though always accompanied by strong temperature and salinity gradients, water density changes little across the Oyashio Front near the surface. Both the Kuroshio Extension and Oyashio Front have a significant deep component, but below 1000 m the former seems to be dominated by eddy features associated with the Kuroshio Extension recirculation gyre.

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Humio Mitsudera, Keisuke Uchimoto, and Tomohiro Nakamura

Abstract

The Soya “Warm Current” (SWC) flows through a shallow strait between the Japan Sea and the Sea of Okhotsk. The SWC has a jet structure downstream of the strait along the northern coast of Hokkaido with a maximum speed exceeding 1 m s−1 at its axis in summer and fall. A surface cold belt with a subsurface doming structure forms offshore of the SWC axis. Mechanisms of the cold belt formation are discussed from a point of view of resonant interaction between a barotropic stratified flow and a shallow sill and subsequent baroclinic adjustment along the SWC. When a stratified current rides a slope upstream, the thermocline displaces upward greatly and outcrops owing to resonant generation of internal Kelvin waves if the upper layer is thinner than the lower layer. The control section, where a Froude number is unity, occurs “upstream” from the sill crest when the ambient inflow has a barotropic flow component. These upwelling features closely resemble those along the southwestern coast of Sakhalin Island. The SWC then flips from an upwelling-type to a downwelling-type structure; in doing so, it transits from the west coast of Sakhalin to the east coast of Hokkaido. It is this transition that leads to the offshore doming structure, which propagates downstream as a vorticity wave, manifesting the cold belt at the surface.

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Ming Feng, Humio Mitsudera, and Yasushi Yoshikawa

Abstract

Four years of mooring array measurements in Tokara Strait, south of Kyushu, Japan, from 1992 to 1996 are used to analyze the structure and temporal variability of the Kuroshio Current. The mean Kuroshio current in Tokara Strait shows a nearly permanent subsurface double-core structure, possibly due to topographic blockage effects.

The dominant variations of the Kuroshio in Tokara Strait are separated into long-term variability (typically 100-day period) and short-term variability (10 days to 1 month) according to spectrum and wavelet analysis. The long-term variability has a large horizontal scale across the strait, with a striking twofold banded structure in spatial correlations. This is due to the north–south Kuroshio axis shift that advects the double-core structure of the mean current. The axis shift can be indexed with the northeastward current velocity at the northernmost station; a composite analysis using this index shows well-defined northward and southward axis shift structures of the Kuroshio current. From the composite of the TOPEX/Poseidon sea level anomaly in terms of this index, the Kuroshio axis shift and the current structure change are associated with a dipole-shape sea level anomaly east of Tokara Strait. On the other hand, the short-term variability of high kinetic energy only has a small horizontal scale within the northern part of the current, which is related to frontal variability.

There exists a deep southwestward undercurrent below 600 m in the northern part of Tokara Strait, flowing along the isobaths. The undercurrent becomes stronger during the northward shift of the Kuroshio axis, while it almost disappears during the southward shift.

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Leland Jameson, Takuji Waseda, and Humio Mitsudera

Abstract

The second generation of a new approach to data assimilation where wavelet analysis is used for error estimation is presented here. The first generation is known as EEWADAi. This modified and optimized method uses wavelet analysis to not only estimate numerical error but to also acquire an estimate of the variation at various scales of the model simulation. In the original EEWADAi, wavelet analysis on the finest scale was used to estimate numerical error. In the second-generation version, called SUgOiWADAi, wavelet analysis is used on a variety of scales to not only obtain an estimate of numerical error, finest-scale information, but to also obtain an estimate of model variation, information from coarser scales. This new algorithm is computationally very inexpensive and is very effective.

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