Effects of tidally induced eddies on sporadic Kuroshio-water intrusion (kyucho)

Abstract

The sudden intrusion of Kuroshio warm water into the Bungo Channel (kyucho) occurs mainly at neap tides during summer, suggesting that tidal mixing is one of the essential factors regulating kyucho. In order to clarify the physical mechanisms responsible for the regulation of kyucho, we carry out non-hydrostatic three-dimensional numerical experiments allowing Kuroshio warm water to intrude into a strong tidal mixing region. It is shown that the Kuroshio warm water can (or cannot) pass through the tidal mixing regions off the east coast of the Bungo Channel during neap (or spring) tides. The analysis of the dynamic balance off the east coast of the Bungo Channel shows that tidal residual currents generated by tidal flow interaction with complicated land configurations off the east coast of the Bungo Channel can also play an important role in regulating kyucho. In order to assess separately the effects of tidal mixing and tidal residual currents on kyucho, we incorporate the parameterized vertical mixing and tidal stresses into the numerical model instead of tidal currents. It is demonstrated that tidal mixing cannot by itself block the northward intrusion of Kuroshio warm water, and that an additional effect induced by tidal residual eddies equivalent to horizontal mixing is needed to regulate kyucho. This strongly suggests that the basin–ocean water exchange processes in areas with complicated land configurations can only be reproduced by taking into account the effects of tidal residual eddies on a 1-km scale in addition to tidal mixing effects evaluated by microstructure measurements.

Appendix

1.1 Tidal residual eddies and associated horizontal eddy diffusivity in the Bungo Channel

Figure 8 shows depth- and tidally averaged relative vorticity and barotropic tidal currents, namely, tidal residual currents, obtained from additional numerical experiments in which Kuroshio warm water is not forced at the southern boundary. We can see that strong tidal residual eddies exceeding 0.3 m s⁻¹ with a diameter of a few kilometers are generated off the east coast of the Bungo Channel during spring tides, although they nearly vanish during neap tides. Tidal residual eddies are thought to play an important role in transporting materials in the coastal ocean (Oonishi and Kunishi 1979; Awaji et al. 1980; Zimmerman 1981). It is interesting to note that such small tidal residual eddies are hardly reproduced by low-resolution (∆x = ∆y = 1/100°) numerical models (Fig. 8c). Although the horizontal grid resolution of 1/100° is thought to be, in general, fine enough to model coastal phenomena, it is already too coarse to adequately resolve small residual eddies induced by tidal flow interaction with complicated land configurations.

Fig. 8

Depth- and tidally averaged relative vorticity (color) and corresponding velocity (vector), obtained from the additional numerical experiments during neap (a) and spring (b) tides. c As in (b), but for the numerical experiment with a coarser horizontal resolution of 1/100°

To quantify the effective horizontal diffusivity associated with tidal residual eddies, we now solve a horizontally two-dimensional advection equation for a passive tracer C given by

$$ \frac{\partial C}{\partial t} = - {\mathbf{U}}_{\text{bt}} \cdot \nabla_{H} C, $$

(8)

where ${\mathbf{U}}_{\text{bt}}$ is the barotropic tidal velocity, and $\nabla_{H} = (\partial /\partial x,\partial /\partial y)$ is the horizontal gradient operator. Initially, the passive tracers C1 and C2 with concentration of 1 are placed inside and outside the archipelago area off the east coast of the Bungo Channel, respectively (red box in Fig. 9), and are allowed to spread out in the barotropic tidal velocity field during spring tides obtained from Ex:KYC. As a measure of the spreading of tracer in the oscillatory flow, we define the horizontal eddy diffusivity (K _He),

$$ K_{\text{He}} \left( t \right) = \frac{1}{4} \frac{{\sigma^{2} \left( t \right) - \sigma ^{2} \left( {t - T_{{{\text{M}}2}} } \right)}}{{T_{{{\text{M}}2}} }}, $$

(9)

with

$$ \sigma^{2} = \frac{1}{4}\frac{{\iint {C\left[ {\left( {x - x_{0} } \right)^{2} + \left( {y - y_{0} } \right)^{2} } \right]}{\text{d}}x{\text{d}}y}}{{\iint {C\;{\text{d}}x{\text{d}}y}}}, $$

(10)

(Signell and Geyer 1990; Drinkwater and Loder 2001; Sentchev and Korotenko 2005) where T _M2 and σ indicate the M₂ tidal period and the standard deviation of the tracer location relative to the center of mass (x ₀, y ₀) at time t, respectively.

Fig. 9

Distribution of each tracer concentration (a C1, b C2) at the time of release (red box) and after 3 T _M2 (color)

Figure 9 shows the distribution of each passive tracer after 3T _M2 from the start of calculation, where C2 is advected towards the center of the Bungo Channel without noticeable dispersion, whereas C1 spreads out over a large area while being diluted. Figure 10 shows the time variation of K _He for $T_{{{\text{M}}2}} \le t \le 3T_{{{\text{M}}2 }}$, where the horizontal eddy diffusivity off the east coast of the Bungo Channel (C1) is found to reach K _He ∼ 10² m² s⁻¹, more than ten times that obtained outside the archipelago area (C2, K _He < 10¹ m² s⁻¹). These results clearly indicate that tidal residual eddies generated behind complicated land configurations play a crucial role in the horizontal dispersion processes.

Fig. 10

Time variation of horizontal eddy diffusivity for $T_{M2} \le t \le 3T_{M2}$ (C1 solid line, C2 dashed line)