Journal of OceanographyVol. 52, pp. 597 to 616. 1996

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments—
XINYU GUO and TETSUO YANAGI
Department of Civil and Ocean Engineering, Ehime University, Matsuyama 790, Japan(Received 29 June 1995; in revised form 22 February 1996; accepted 26 February 1996)

The residual currents in Tokyo Bay during four seasons are calculated diagnostically from the observed water temperature, salinity and wind data collected by
Unoki et al. (1980). The calculated residual currents, verified by the observed ones,
show an obvious seasonal variable character. During spring, a clear anticlockwise
circulation develops in the head region of the bay and a strong southwestward
current flows in the upper layer along the eastern coast from the central part to themouth of the bay. During summer, the anticlockwise circulation in the head region
is maintained but the southwestward current along the eastern coast becomes
weak. During autumn, the preceding anticlockwise circulation disappears but aclockwise circulation develops in the central part of the bay. During winter, thecalculated residual current is similar to that during autumn. As a conclusion, theseasonal variation of residual current in Tokyo Bay can be attributed to thevariation of the strength of two eddies. The first one is the anticlockwise circulationin the head region of the bay, which develops in spring and summer and disappears
in autumn and winter. The second one is the clockwise circulation in the central
part of the bay, which develops in autumn and winter, decreases in spring andnearly disappears in summer.
1. Introduction
Tokyo Bay is a semi-enclosed bay situated at the central part of Japan, which communicateswith the Pacific Ocean through the narrow Uraga Strait (Fig. 1). Field observations (Unoki et al.,1980) show that the residual current in Tokyo Bay has a strong seasonal variable character.
Although many observations about the residual current in Tokyo Bay have been carried out(for a detailed review, see Unoki, 1985), the character of seasonal variation of residual current
has not been known completely yet. On the other hand, a complete numerical calculation about
the residual current system during four seasons in Tokyo Bay has not been found although there
are some numerical researches about the wind-driven current or the formation process of thedensity-driven current in Tokyo Bay (e.g. Endoh, 1977; Ikeda et al., 1981; Guo and Yanagi,1995). Thus, as one of the foundations of the material transport model of Tokyo Bay, thenumerical calculations on the residual current systems during four seasons in Tokyo Bay arecarried out in this paper.
From the viewpoint of physical processes, the seasonal variation of residual current should
be brought by the variations in the river outflow, the heating or cooling through the sea surface,
the prevailed wind field and the sea condition of open ocean. The first two factors can be reflectedby the water density field in each season and the third factor can be considered easily incalculation by giving the wind field above the sea surface. Considering that the mouth of Tokyo
Bay is very narrow and the influence of the open ocean on the residual current in the inner part598

X. Guo and T. Yanagi

Fig. 1. Topography and rivers in Tokyo Bay.

of the bay is very small, we may adopt the diagnostic model to calculate the residual current inTokyo bay.
As the crux of diagnostic calculation, a fine observed density field is necessary. The mostdetailed water temperature and salinity data should be the observed ones by each prefectural
fisheries experimental station around Tokyo Bay. However, in these observations, the current is
not measured at the same time. So the calculated residual current using such water temperatureand salinity data can not be verified appropriately.
In view of verification, the water temperature and salinity data recorded simultaneously withthe current data are preferred. For this purpose, the water temperature, salinity and wind datacollected by Unoki et al. (1980) are adopted in this calculation because they are the most detailed
available data set up to now in which the current was measured simultaneously with watertemperature and salinity. However, these data have obvious weakness, that is, there are only twoor three water temperature and salinity observation points on the vertical direction. As for thisproblem, we will mention its countermeasure later.
In the second section, the numerical model and its application to Tokyo Bay are described.
The third section focuses on the comparison between the calculated and observed results inTokyo Bay. On the forth section, we give some discussions about the seasonal variation
characters of residual current and the forcing balance during each season. Finally, the results are
summarized, the limitation and suggestion for the future work are presented.

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599

2. Numerical Model
2.1 Equations
The governing equations on the Cartesian (x,y,z) coordinate system in which the horizontal
coordinate is laid at the undisturbed sea surface, the vertical coordinate directs upwards, are as
follows:∂u r
1 ∂P ∂  ∂u  ∂  ∂u  ∂  ∂u 
+ u ⋅ ∇u − fv = −+A
 + A +  Av  + Tx∂t
ρ0 ∂ x ∂ x  h ∂ x  ∂ y  h ∂ y  ∂ z  ∂ z (1)

1 ∂P ∂  ∂v  ∂  ∂v  ∂  ∂v ∂v r
+ u ⋅ ∇u − fu = −+A + A +  Av  + Ty∂t
ρ0 ∂ y ∂ x  h ∂ x  ∂ y  h ∂ y  ∂ z  ∂ z (2 )P = ρ 0 g( η − z ) + ρ 0 g ∫z0

ρ − ρ0dz′ ≡ P1 + P2
ρ0(3)

∂η ∂ 0∂ 0+udz +vdz = 0∫−h∂t ∂x
∂ y ∫− h( 4)

ρ = F (T, S )

(5)

where
r

r

r

r

u = ui + vj + wk
r ∂

∇=i

∂x

r ∂

+j

∂y

r ∂

+k

∂z

t = time,u, v, w = the x, y and z components of residual current,
P = pressure,T = observed temperature,S = observed salinity,ρ = observed density,
ρ0 = reference density (the averaged value of all points),
h = undisturbed water depth,η = sea surface elevation,
f = Coriolis parameter (8.469 × 10–5 s–1),
g = acceleration due to gravity (980 cm/s2).
Tx and Ty in Eqs. (1) and (2) are tidal stresses and defined as follows:

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X. Guo and T. Yanagi

Tx = u0∂ u0∂u∂u+ v0 0 + w0 0
∂x
∂y
∂z

(6)

Ty = u0∂ v0∂v∂v+ v0 0 + w0 0
∂x
∂y
∂z

( 7)

where, u0, v0, w0 are the three components of tidal current that have been calculated in advance(Guo and Yanagi, 1994) and 〈 〉 denotes the tidal average. Equation (5) is the well known Knudsen
state equation.
The vertical and horizontal eddy viscosity coefficients Av and Ah are related to the amplitudeof tidal current according to the tidal mixing theory.
2
Av = α Uamp

( 8)

2
Ah = β Uamp

( 9)

where Uamp is the amplitude of tidal current and the parameters α and β are used to adjust the eddy
viscosity coefficients locating in a reasonable range and explained later. By this way, the effectof tidal mixing can be considered partly, i.e., the stronger the tidal current, the larger the eddy
viscosity coefficient.
The boundary conditions on the sea surface and bottom are:z = η: Av∂
1 a a
τx ,τy(u, v ) =∂zρ0z = −h: Av

(

)

∂
1 b b
τx ,τy(u, v ) =
∂z
ρ0

(

(10 )

)

(11)

where, the wind stresses τxa, τya and sea bed stresses τxb, τyb are calculated as:( τ , τ ) = ρ C (u , v ) u + v

2
a

(12 )

( τ , τ ) = ρ C (u , v ) u + v .

(13)

a
x

b
x

a
y

b
y

a

d

b

a

b

a

b

2
a

2
b

2
b

The symbols ua and va denote the eastward and northward components of the wind velocity,
ρa (=1.2 × 10–3 g/cm3) is the density of air, Cd (=1.3 × 10–3) is the non-dimensional drag coefficientat the surface, ub and vb is the velocity above the sea bed, Cb (=2.6 × 10–3) is the drag coefficientat the sea bed.
Along the coastal line, no normal flow and no slip condition are allowed and a sponge
condition is postulated at the open boundary.

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

601

Fig. 2. The calculated tide-induced residual current.

The numerical solving method of above equations is nearly the same as that used in
reproducing the wind-driven current in Tokyo Bay during winter (Guo and Yanagi, 1995). For
the advective terms in Eqs. (1) and (2), we adopt the same difference scheme as that used in the
Oonishi Model (Oonishi, 1978), which can ensure the conservation of the momentum and energy(Arakawa, 1966; Suginohara, 1978). Initially, a state of rest is assumed and the calculation lastsfor 48 hours when the kinetic energy of the whole sea region reaches a steady state.
2.2 Application to Tokyo Bay
The topography of Tokyo Bay is shown in Fig. 1. The maximum depth in this calculation
is taken as 200 m due to the computational economical viewpoint. The horizontal grid size is 1
km × 1 km and the water column is vertically divided into ten layers equidistantly at eachhorizontal grid point. This means that there are ten points on the vertical direction everywhere,no matter what depth they are. The time step is 36 seconds.
As a preparation of the diagnostic calculation, the tide-induced residual currents arecalculated at first and the results at three depths are shown in Fig. 2. The calculated results showthat a clear clockwise circulation is formed near the mouth of Tokyo Bay and the speed of thisclockwise eddy can reach about 5 cm/s in the upper layer behind Futtu-Misaki. Except for thisclockwise eddy, the tide-induced residual current in Tokyo Bay is weak. This calculated result
is consistent with the existing knowledge about the tide-induced residual current in Tokyo Bay(Unoki, 1985). The tide-induced residual current is included in our calculations through tidal
stress of Eqs. (6) and (7).
2.3 The observed water temperature, salinity and wind data
From November 1978 to August 1979, four times observations in Tokyo Bay were carriedout by the Second Port and Bay Bureau, Japan and the observed results were collected andanalyzed by Unoki et al. (1980). In these observations, besides of the current data, the watertemperature and salinity were also measured by the current meter. These data allow us to do thefollowing experiments: reproducing the residual current field through a diagnostic model byusing the observed water temperature, salinity and wind data and verifying the calculated results

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Fig. 3. The representation of stratification by one-third power function.

by the observed current data at the same time.
As a regrettable thing, the above field observation only provides two or three watertemperature and salinity data on the vertical direction (3 meters below the sea surface and 5
meters above the sea bed). If there is no strong stratification such as the case of winter or autumn,
a linear approximation can be used for the interpolation or extrapolation on vertical direction. But
for the case of summer or spring when the density stratification has been formed, a method thatcan give an expression of the stratification effect is preferred than the linear approximation.
Based on the fact that the depth of the pycnocline in most places of Tokyo Bay during summer
has been 10 meters (Unoki, 1985; Yanagi et al., 1991), the one-third power function is adopted
to represent the vertical profile of observed water temperature and salinity as follows:
T = T0 + α T ( z − z0 )

1/ 3

(14)

where z0 is the depth of the pycnocline (10 m in this case), T denotes temperature but can be
replaced by salinity, T0 and αT are determined with the use of the two observed data. An exampleof Stn. D4 in the central part of the bay, whose position is denoted by a black circle in Fig. 1, isgiven by Fig. 3 from which an obvious improvements by Eq. (14) over the linear interpolation
can be seen easily.
In the field observation, there are 8, 22, 9 and 22 observation points on the horizontal planein spring, summer, autumn and winter, respectively. In the report of Unoki et al. (1980), only theaveraged water temperature and salinity data at each point are given. Because there are two setsof observation points in summer and winter whose observation periods are different from eachother (the longer one is about 33 days and the shorter one 17 days), some abnormal distributionof the observed water temperature and salinity can be found in some places, especially insummer. If we interpolate such data without any modification, some local unreal density
distribution and density-driven current will be produced surely. Thus for avoiding such strange

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

603

density current, we delete some temperature and salinity data whose maximum variation is
obviously larger than other points. After this procedure, 8, 14, 8 and 20 points of temperature andsalinity data for spring, summer, autumn and winter, respectively, are kept and interpolated ateach mesh point. The interpolation method is the same as that used by Yanagi and Igawa (1992).
The calculated horizontal distribution of temperature, salinity and density (σt) at three layers(3 m, 10 m and 15 m) in four seasons are shown in Figs. 4(a), (b), (c) and (d), respectively.
The spring case (Fig. 4(a)), whose data are collected from May 2nd to June 7th, 1979, showsthat the water temperature and salinity vary a little in the head region of the bay but largely in thecentral part of the bay. The summer case (Fig. 4(b)), whose data are collected from July 13th toAugust 21st, 1979, shows that in the northern part of Tokyo Bay, an obvious light water mass
exists in the upper layer that should be affected by the Ara, Edo and Tama Rivers (Fig. 1). On
the whole, in the upper and middle layers the water in the western region is lighter than that in
the eastern region but in the lower layer the water gives an opposite distribution with thatmentioned above. The autumn case (Nov. 20th to Dec. 22nd, 1978, Fig. 4(c)) shows that thehorizontal variation of water temperature, salinity is obviously less than those in summer andspring. In the winter case (Jan. 17th to Feb. 22nd, 1979, Fig. 4(d)), the water temperature, salinityand density structure at the mouth of bay is similar to that of the thermohaline front (Nagashima
and Okazaki, 1979; Yanagi et al., 1989) and there is a light water mass in the upper layer of thenorthwestern part of the bay. The common character of the density distributions during four
seasons in Tokyo Bay is that the water in inner part of the bay is lighter than that in outer part ofthe bay.
As mentioned before, the diagnostic calculation result depends on the observed density fieldclosely and as a weak point of this research, only a few observed density data can be used in
calculation, especially in spring and autumn case. However, it must be noticed that the dynamicrole of the density field is manifested by its horizontal gradient, not by the density field itself.
Thus few observed points can also give a basic description of the gradient field if the point’s
positions are arranged well. Basing on this fact, we may believe that the density gradient along
the main axis of Tokyo Bay is well represented by observation, even in spring and autumn case.
The three points around the head region in spring and autumn may also give a basic descriptionof the density gradient field there. The problem exists in the central part of the bay, especiallyin the western side, where the density gradient along the east-west direction can not be obtainedcorrectly from the observation.
The wind data at four stations (Tokyo, Yokohama, Tateyama and Chiba, shown by triangle
in Fig. 1), which were recorded every three hours during the above observation periods, were alsocollected by Unoki et al. (1980). We averaged these data over the observation period andinterpolated them on the horizontal plane. The interpolated results (not shown in this paper
because their spatial variation is very small) tell us that weak south, strong southwest, weak northand strong northwest wind prevails above Tokyo Bay during spring, summer, autumn and winter,
respectively. The averaged wind speed is about 5 m/s in winter and summer, 3 m/s in spring andautumn.
2.4 Determination of eddy viscosity coefficients
Considering that the amplitude of M2 tidal current in Tokyo Bay is almost on the range of
5 and 50 cm/s (Guo and Yanagi, 1994), the parameter α in Eq. (8) is set as 0.06, 0.04, 0.06 and0.08 for the residual current calculation in spring, summer, autumn and winter, respectively. So
the calculated vertical eddy viscosity should be between 1 and 100 cm2 /s in summer, 2 and 200

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X. Guo and T. Yanagi(a)Fig. 4. (a) The horizontal distribution of temperature, salinity and density in spring. (b) The horizontal
distribution of temperature, salinity and density in summer. (c) The horizontal distribution oftemperature, salinity and density in autumn. (d) The horizontal distribution of temperature, salinity anddensity in winter.

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments(b)Fig. 4. (continued).

605

606

X. Guo and T. Yanagi(c)Fig. 4. (continued).

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments(d)Fig. 4. (continued).

607

608

X. Guo and T. Yanagi

cm2/s in winter, 1.5 and 150 cm2/s in spring and autumn. Here its horizontal distribution is notshown because it should be the same as the distribution of M2 tidal current amplitude essentially,
which can be found in our previous paper (Guo and Yanagi, 1994). As used in the real calculation,
its minimum value (1 cm2 /s in summer, 4 cm2/s in winter, 2 cm2/s in spring and autumn) has tobe set to avoid the occurrence of abnormal surface current at the place where the tidal current
amplitude is less than 5 cm/s. Parameter β in Eq. (9) is equated to 4 × 103 in all calculations sothat the horizontal eddy viscosity is on the range of 1.0 × 105 and 1.0 × 107 cm2 /s. Such values
can also be found on other researches (Ikeda et al., 1981; Yanagi and Shimizu, 1993).
3. Results
3.1 Spring
The calculated and observed residual currents during spring are shown in Fig. 5. The
calculated ones show that in the head region of the bay, a clear anticlockwise circulation develops
in the upper layer and expands to the lower layer. In the upper layer of the central part of the bay,
a strong southwestward residual current flows along the eastern coast from the central part to themouth of the bay and turn to northwest partly as being obstructed by the narrow mouth. In the
meanwhile, a northeastward residual current exists in the lower layer of the central part and joins
into the anticlockwise eddy in the head region of the bay.
The observed result seems to be difficult to give a detailed description about the residual
current in Tokyo Bay during spring because there are only nine observation points in the whole
bay and five of them lies at the mouth region. Comparing the calculated and observed results, wewould know that the southwestward flow in the upper layer along the eastern coast from thecentral part to the mouth of the bay and the northeastward flow in the lower layer seem to be

Fig. 5. Comparison between calculated and observed residual current in spring.

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

609

supported partly by the observed result. But the calculated anticlockwise eddy in the head regionof the bay can hardly get some support from the observed result.
Here, we hardly discuss the difference between the calculated and observed results.
However, we can try to give an interpretation on our calculated result. Considering the
topography of the head region of the bay, we think that the calculated anticlockwise circulation
there may be linked to a process similar to the topographic heat accumulation effect, i.e. during
heating period such as spring and summer, the temperature of shallow water becomes higher thanthat of deep water and an anticlockwise circulation may develop in a nearly enclosed bay, where
the water around the bay is shallower than that in the central part. The same mechanism has beenfound to play an important role on the formation and maintenance of the anticlockwise circulationin Lake Biwa during summer (Oonishi, 1975).

Fig. 6. Comparison between calculated and observed residual current in summer. The dot lines in observed
results are the supposed flow pattern and the numbers are the speed of flow expressed in cm/s.

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X. Guo and T. Yanagi

3.2 Summer
The most obvious character of the calculated residual current in the upper layer during
summer (Fig. 6) is the strong southwestward current along the western coast from the head region
to the central part of the bay, which should be brought by the fresh water from Ara, Edo and TamaRivers (Fig. 1). In the meanwhile an anticlockwise circulation develops in the upper layer of thehead region of the bay but does not close in the central part of the bay. The residual current in
the lower layer is very similar to that during spring but stronger than that.
From the observed results, Unoki (1985) concluded that the residual current in Tokyo Bay
during summer as: (i) an anticlockwise circulation exists in the head region of the bay; (ii) asouthward current flows along the western coast; (iii) at the mouth of the bay, the water flow out
at the western side in the upper layer and flow into in the lower layer. Compared with the observed
results, the calculated ones can be said to reproduce the main character of residual current during
summer. The difference in the southwestern coast from the central part to the mouth of the bay
can not be discussed in detail because there is no observation point there. For the difference inthe northwestern region of the bay where the river water concentrates (the calculated residual
current flows southwestward but the observed one northwestward in the upper layer), we
consider that one observed point is not enough to reproduce the density field well.
Although two dimensional numerical calculation shows that the south wind can produce ananticlockwise circulation in Tokyo Bay (Ikeda et al., 1981), the south wind seems not to be themain cause for the anticlockwise circulation in the head region of the bay because the pattern of
the south wind-driven residual current is very different from the observed one (Unoki, 1985).
Considering that the topographic heat accumulation effect can also continue during summer, we
still suggest that this effect should be responsible partly for the anticlockwise circulation in thehead region of Tokyo Bay during summer. As for the fact that this eddy does not close in theFig. 7. Comparison between calculated and observed residual current in autumn.

Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

611

central part of the bay, it should be caused by the different distribution patterns of water density
in the central part of the bay during spring and summer as shown in Figs. 4(a) and (b). Thisdifference should result from the large river outflow during summer. In other words, it may be
the variation of river outflow to induce the anticlockwise circulation to be closed in spring but
to flow southward in summer.
3.3 Autumn
The calculated residual current during autumn (Fig. 7) shows that in the upper layer, a strong
southwestward current flows along the eastern coast from the central part to the mouth of the bay
and another relatively strong southwestward current along the western coast from the head region

Fig. 8. Comparison between calculated and observed residual current in winter. The meaning of dot lines
and numbers in observed results is the same as that in Fig. 6.

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X. Guo and T. Yanagi

to the central part of the bay. At the same time, a northeastward current exists between these twosouthwestward currents. Apart from these characters, a weak clockwise circulation can be foundin the eastern part of head region of the bay. In the lower layer, a branch of narrow and strong
northeastward current exists from the mouth to the head of the bay and in the central part of thebay, a part of this northeastward current turns to the east and forms a clockwise circulation withthe southwestward current along the eastern coast.
Compared with observed results, except for the southwestward current along the western
coast from the head region to the central part of the bay, where no observation point exist, themain characters in the calculated result can almost be supported by the observation. Referring
to other observed data, Unoki (1985) has suggested that the southwestward current along thewestern coast from the head region to the central part of the bay should exist all over the year.
Our calculation is consistent with this suggestion (see Fig. 8 for the winter case).
3.4 WinterOn the whole, the calculated residual current during winter (Fig. 8) is similar to that during
autumn. The difference exists in some local areas, especially in the head region of the bay. For
example, in the upper layer, a branch of southward current appears in the middle of the headregion, where an opposite current exists during autumn.
Unoki (1985) has also given a conclusion about the main characters of the residual current
in Tokyo Bay during winter from the observed results, that is, (i) a clockwise circulation exists
in the upper and lower layers; (ii) the relative strong residual current exists in the upper layer ofthe eastern coast and the lower layer of the western coast, respectively; (iii) in the upper layer asouthwestward current flows along the western coast. Our calculation is consistent with the lasttwo characters basically but shows different pattern in the head part of the bay where theclockwise circulation suggested by Unoki (1985) does not exist. The calculated result shows thata more complicated residual current exists there, which means that in the head region of the bay,especially in the western part of the head region, the influence of fresh water should be great, atleast be the same order as the wind effect.
4. Discussion
4.1 The seasonal variation of residual currents in Tokyo Bay
We choose 10 m as the representative depth in Tokyo Bay and show the residual currents
at this depth during four seasons in Fig. 9. Comparing these results, we attribute the seasonalvariation of residual current in Tokyo Bay to the variation of the strength of two eddies. The firsteddy is the anticlockwise circulation in the head region of the bay, which develops in spring andsummer and disappears in autumn and winter. Such seasonal variation of this eddy can be related
to the alternation of heating and cooling through the sea surface over one year and the variationof the fresh water coming from the rivers at the head of the bay (Fig. 1). During heating period
such as spring and summer, the topographic heat accumulation effect may promote the formationof this eddy and during cooling period such as autumn and winter, the water temperature structurethat the shallow place is warmer than the deep place is destroyed and this eddy can not be
maintained. The second one is the clockwise circulation in the central part of the bay, whichdevelops in autumn and winter, decreases in spring and nearly disappears in summer. This eddy
is considered to be generated mainly by a combined effect of the tide-induced residual current
and the density-driven current. However, the wind field influences greatly on this eddy, that is,Seasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

613

Fig. 9. Seasonal variation of the residual currents at 10 meters.

the north wind during autumn and winter promotes the formation of this eddy and the south windduring spring and autumn hinders the development of this eddy, respectively. In other words, itis the variation of the prevailed wind field to decide the fate of this eddy.
4.2 The forcing balance about the two eddies
The result shown here is that at the nearly steady state. In this case, the time variation terms
in Eqs. (1) and (2) approach to zero and the other terms should balance with each other. In orderto get an insight on the variation of the above two eddies, we plot the distribution of the main terms
in Eq. (1) along the two lines shown in Fig. 10 (the balances in the Y-direction (Eq. (2)) along suchlines are considered having no dynamic meaning to the maintenance of the two eddies). By thisway, we find that the contributions from the advective term, the horizontal and vertical eddy
viscosity terms are smaller than those from the other terms during four seasons and the resultsof spring and autumn case are very similar to those of summer and winter case, respectively.
Thus, only the distribution of relatively large terms in summer and winter case are shown in Fig.
10.

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X. Guo and T. Yanagi

Fig. 10. The main forcing balance about the two eddied during summer and winter.

As expected, the tidal stress has no effect on the eddy existing in the head region of the bay
during summer and the main balance about this eddy is the gradient of water elevation with thesum of Coriolis force and the density pressure coming from the horizontal density difference. The
distribution that the density pressure is negative on the west side and positive on the east sidemeans that the density of water above 10 meters in the middle place of the line is larger than thatat two sides. Noticing that Coriolis force and the density pressure have the same function on theeddy, we suggest that a process similar to topographic heat accumulation effect should beSeasonal Variation of Residual Current in Tokyo Bay, Japan—Diagnostic Numerical Experiments

615

responsible for the formation of this eddy. In fact, to clarify the generation mechanism of thiseddy in detail, a prognostic calculation is needed. But the difference on the dynamic balance insummer and winter is obvious.
As for the eddy existing in the central part of the bay, it is difficult to discuss the detailed
dynamic variation between summer and winter. But the role of tidal stress can be confirmed, i.e.
the tidal stress promote the formation of this eddy, especially in the west side. Such effect should
become strong as the position of the eddy approaches the mouth of the bay.
5. Conclusion and Suggestion(1) The residual currents during four seasons in Tokyo Bay are calculated by a diagnostic
numerical model and the calculated results reproduce the main characters of the observed
residual current system and provide a detailed insight on it.
(2) The data of temperature, salinity and wind used in our calculation are the mean value
over the observed period. In a nonlinear system, the calculated residual currents under thisaveraged data should be different from that obtained by averaging the field current data. Their
good match suggests that the system is controlled mainly by a linear system. This conclusion canalso be supported by the calculated forcing distribution during each season although they are notshown in this paper.
(3) As a limitation of the diagnostic model, we can not separate each process acting on theresidual current system such as the river outflow and heating or cooling process. Thus, we can
not do a deep research on the generation mechanism of the residual current in Tokyo Bay during
each season. This problems will be tried by using a prognostic numerical model in the near future.
Acknowledgements
The authors are grateful to Drs. H. Takeoka and Y. Isoda for their helpful suggestions about
the results of this paper. We thank Mr. H. Akiyama and Dr. S. Takahashi for their useful
discussions during the study. Thanks are also due to the three JO reviewers for their constructive
comments. The calculation was carried out on a FACOM M770 of Ehime University.
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