Long-term Variability and Non-linear Aspects of the Oceanic
Double-gyre
Shinya Shimokawa 1 and Tomonori Matsuura 2
1Storm, Flood and Landslide Research Unit, National Research Institute for Earth Science and Disaster Prevention, Japan
2

University of Toyama, Japan

1. Introduction
The oceanic double-gyre (i.e., sub-tropical and sup-polargyres) is one of the basic configurations of large-scale surface
ocean circulation. Recently, the long-term variability (over adecade) has been studied in relation to climate variability 1).
Firstly, to clarify the long-term variability of the oceanic doublegyre, we investigate Re dependency on the state of the oceanic
double-gyre using a quasi-geostrophic model under constantforcing.
Thus far, however, most studies of oceanic double gyres
using middle-range complexity (e.g., quasi-geostrophic model)
have been conducted under constant forcing. In the real
atmosphere and oceans, wind forcing changes seasonally. Many
problems related to time dependent forcing, especially thosewith nonlinear aspects remain unresolved; for example,entrainment (an adjustment of rhythms of two or more selfsustained oscillating systems) 2) and intermittency (a chaotic
modulation in the transition from laminar flow to turbulentflow) 3). Therefore, it is also important to clarify the nonlinear
interaction between a characteristic oscillation of the ocean itself
and a seasonal oscillation of an external forcing.
2. Numerical model and experimental method
The numerical model used in this study is a 1.5 layer,
reduced-gravity, quasi-geostrophic numerical model with a nonslip boundary condition 4). The model domain is a rectangle of3600 km × 2800 km and the forcing wind has only an east-westcomponent and is north-south varying in space, representing themid-latitude North Pacific. Further details of the numericalmodel are shown in Shimokawa and Matsuura (2010) 5).
Control parameters in the experiments involve Reynolds
number (Re) and the amplitude of seasonal variation α (α=0.0:
no seasonal variation, α=1.0: the amplitude of seasonal variationof wind stress = the average of wind stress). We conducted theexperiments over 250 years for Re = 26, 31, 39, 70, 95,112, 157,
209, and 314 under constant forcing (α＝0.0) and those for
Re=39 and 157 under time-dependent forcing (α＝0.0-1.0).
3. Results
3.1

Constant forcing case
The changes can be classified into four groups as follows: a)
Re = 26, 31, 39, b) Re = 70, 95, 112, c) Re = 157, 209 and d) Re= 314 by the average energy level and the length of the strong
eastward jet (Fig. 1). In particular, the states for Re = 209 and
314 are turbulent, but it can be considered that they are different
qualitatively.
For Re = 209, kinetic energy (KE, Fig. 2b) decreases withthe decrease of available potential energy (APE, Fig. 2a) and thetime lag is only a few months. On the other hand, for Re = 314,
APE (Fig. 2c) shifts to KE (Fig. 2d) over a long-term (about adecade) and then KE oscillates intensely. These differences are

considered to represent differences in the instability. The
instabilities for Re=209 and Re=314 are considered to be related
to oscillation of G-mode 6) and shear instability 7), respectively.
In the unstable state for Re=314, eddy shedding occurs not only
from the easternmost tip of the jet but also in the path of the jet(see Fig. 6a).
3.2

Time dependent forcing case
For Re=39, in α=0.0, only characteristic oscillation (with2.45 years) of the ocean itself can be seen (Figs. 3a, 3g and 4a).
In α=1.0, only seasonal oscillation (1 year) of the external
forcing can be seen (Figs. 3f and 3l). In the intermediate α=0.18,
the oscillation has both aspects (Figs. 3c and 3i). In fact, here,
the entrainment occurs at 2 times the period of the forcing (2years; Fig. 4c).
With increasing α, the intermittency appears (α>0.4; Figs. 3eand 3f). The intermittency has periods from few years to few
decades (i.e., the long-term variability). Intermittent transitions
occur between stable modon-like pattern (alongside path, Fig.
5a) and unstable anti-cyclonic/cyclonic eddy shedding patterns(large meander path, Figs. 5b and 5c). In the unstable state for
Re=157, eddy shedding occurs not only from the easternmost tipof the jet but also in the path of the jet (Fig. 6b), which is similar
to the result for Re=314 under constant forcing (Fig. 6a).
4. Conclusions and Discussions

We found that intermittency (i.e., the long-term variability)
can be generated and eddy shedding occurs not only from theeasternmost tip of the jet but also in the path of the jet for bothconstant and time dependent forcing cases. In addition, theintermittency can be generated at a smaller Re for timedependent forcing case, compared to constant forcing case.
The relation and interaction between the mechanisms of theintermittency for constant and time dependent forcing cases
remain unknown. It, however, can be speculated that only one
mode can’t generate intermittency under constant forcing, but
increasing Re and/or changing forcing to time-variant may occur
two (or multiple) mode nonlinear coupling and then generateintermittency. This needs a further study.
It has often been considered that the long-term variability inthe western boundary current is caused by local instability. An
increasing number of observations, however, indicate that thevariability is also considered to be part of the instability of theentire gyre (i.e., the oceanic double gyre) 8). The phenomena
observed in this study, in particular entrainments andintermittency, are also considered to be related to the entire gyre.
Therefore, these phenomena may be crucial to understanding thegeneration mechanism and characteristics of long-term
variability in the strong current region of sub-tropical/sub-polar
gyres such as the Kuroshio and its extension region.

Figure 3 Time series of total energy for (a) α =0.0, (b) α =0.1,(c) α =0.18, (d) α =0.3, (e) α =0.5, and (f) α =1.0 for 250 years.
Figs. (g) - (l) are the same but during years 100–105.

Figure 4 Power spectra of total energy for (a) α =0.0, (b) α =0.1,and (c) α =0.18.

Figure 1 Average flow patterns (1st layer thickness, upperpanels) and time series of total energy (lower panels) for (a) Re= 26, (b) Re = 31, (c) Re = 39, (d) Re = 70, (e) Re = 95, (f) Re =112, (g) Re = 157, (h) Re = 209 and (i) Re = 314. The periods
indicated by arrows in (h) and (i) are included in those of Fig. 2.

Figure 5 Three typical flow patterns (monthly averaged 1st layerthickness, CI=30m) of double gyres in Q-G model for α = 0.7. (a)Stable modon-like pattern, (b) anti-cyclonic eddy shedding, and (c)cyclonic eddy shedding.

Figure 6 Flow patterns (monthly averaged 1st layer thickness,
CI=20m) for (a) Re=314, constant forcing at 86 years, 11 months
and (b) Re=157, time-dependent forcing at 184 years, 3 months.
Figure 2 (a) Available potential energy and (b) kinetic energy
for Re = 209 during years 176-195 and (c) available potential
energy and (d) kinetic energy for Re = 314 during years 171-190.

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