Journal of Geoscience and Environment Protection, 2014, 2, 126-134
Published Online June 2014 in SciRes. http://www.scirp.org/journal/gep
http://dx.doi.org/10.4236/gep.2014.23017
How to cite this paper: Zhu, Z. F. (2014). Minimum Wind Stress for the Occurrence of Blue Tide on the Southeast Shore of
Tokyo Bay. Journal of Geoscience and Environment Protection, 2, 126-134. http://dx.doi.org/10.4236/gep.2014.23017
Minimum Wind Stress for the Occurrence of
Blue Tide on the Southeast Shore of Tokyo
Bay
Zhong Fan Zhu
College of Water Sciences, Beijing Normal University, Beijing, China
Email: zhuzhongfan1985@gmail.com
Received March 2014
Abstract
In Tokyo Bay, blue tide is a phenomenon that seawater presents to be milky blue due to reflection
of sunshine off surface water in which a large number of sulfur particles suspend. Its occurrence is
because of coastal upwelling of the oxygen-depleted water at the bottom of the bay induced by the
blowing of a northeasterly wind, consequently leading to many deaths of shellfish and some
aquatic animals in the bay. In this study, an analytical solution of minimum wind stress for the oc-
currence of blue tide on the southeast shore of the bay is presented based on a two-layered model,
and comparison with observation data of blue tide from 2003 to 2010 shows the validity of this
solution. The results of sensitivity analysis to all of parameters involved in this solution were also
found to ag ree with qualitative understandings of blue tide phenomenon.
Keywords
Minimum Wind Stress, Blue Tide, Tokyo Bay
1. Introduction
Tokyo Bay w as subject to the consequences caused by a rapid urbanization and an intensive industrial develop-
ment. Large quantities of untreated domestic sewage and municipal sewage as well as industrial sewage, which
contained large nitrogen and phosphorus loads, were discharged into Tokyo Bay, consequently influencing se-
riously the development of the ecosystem in the bay. The input of these nutrient loads, with available sunlight in
the surface and suitable temperature in spring or summer, promoted the excessive growth of phytoplankton. As a
result, a phenomenon known as red tide (or algal bloom) took place, where the concentration of phytoplankton
was so high that the color of seawater presented to be red. Red tide occurred frequently in Tokyo Bay, and its
occurrence led to decreased biodiversity, toxin production and dissolved oxygen depletion in the bay. When
phytoplankton died and fell into the bottom water due to gravity, some of them were largely decomposed by
bacteria at the bottom. During this process, a large concentration of dissolved oxygen at the bottom was con-
sumed, and consequently the bottom water became oxygen-depleted or even anoxic. On the other hand, fresh
water discharge into the bay from several rivers and intermittent precipitation particularly from summer to au-
Z. F. Zhu
127
tumn, along with seasonal temperature variation caused by surface heating and cooling, resulted in a well-mixed
upper water with high temperature and low salinity and a lower water with low temperature and high salinity in
the bay. As a result, a stable stratification developed, where the lighter upper water covered on the surface of the
heavier lower water. This stable structure prevented a vertical circulation to bring dissolved oxygen from the
surface to the bottom, thus enhancing the oxygen-depleted state of the lower water. Under anaerobic conditions,
sulfate contained in the bottom water will be reduced into hydrogen sulfide. When a northeasterly wind as fre-
quently observed blew on the surface, the well-mixed upper water will follow the wind in the downwind direc-
tion, and the oxygen-depleted lower water will flow in the opposite direction to compensate, finally resulting in
coastal upwelling of the bottom water from the bottom to the surface. During this process, a large amount of hy-
drogen sulfide present in the lower water was oxidized to colloidal sulfur substances when they meet the oxygen
in the atmosphere. When sunshine reflected off the surface water containing these sulfur substances, the color of
seawater presented quickly to be bluegreen, and this phenomenon has been termed as blue tide. Coastal up-
welling of the oxygen-depleted bottom water accompanying the outbreak of blue tide phenomenon caused a
large number of mortalities of fish and shellfish in the upper warm water, consequently resulting in a substantial
economical loss to coastal fisheries in Tokyo Bay.
Plenty of researches concerning blue tide have been carried out in the past from different perspectives (Go-
myo et al., 1998; Ichioka et al., 2009; Kakino et al., 1987; Kataoka et al., 1989; Koibuchi & Isobe, 2007; Ma-
tsuyama et al., 1990; Nakatsuji et al., 1991; Nakatsuji et al., 1995; Otsubo et al., 1991; Sasaki et al., 1993; Sa-
saki et al., 1996). These research results are helpful to understand the mechanism of outbreak of blue tide phe-
nomenon, and, based on them, this study presents the minimum wind stress for the occurrence of blue tide on
the southeast shore of the bay by using an analytical solution in the context of a two-layered model. The layout
of this paper is as follows. Section 2 introduces briefly the engineering background and derivation of the ana-
lytical solution. Comparison with observation data from 2003 to 2010 is provided in section 3, and section 4
presents the sensitivity analysis of the solution to all of the chosen parameters. As a summary, section 5 shows
the concluding remarks.
2. Engineering Background and Derivation of the Solution
As shown in Figure 1, Tokyo Bay is located in the central part of main islands of Japan. Its main axis, mean
width and average water depth are 50 km, 20 km and 15 m, respectively. When a northeasterly-oriented wind
begins to blow on the surface of the bay, blue tide is frequently observed along the coastline from off Funabashi
to off Ichihara.
As described in Zhu and Isobe (2012), although the real coastline of the bay is complicated, we just consider
the research domain to be a rectangular one with the length of 50 km, the width of 20 km and water depth of 15
m, respectively, as shown by real lines and one dashed red line just indicating the imaginary southwest shore in
Figure 1. Figure 2(a) illustrates the dimensions of this domain (
b
is the width, and a right-handed Cartesian
coordinate system is defined as follows: the origin is in the center of domain, the
x
axis follows the northeast-
erly wind, the
y
axis is perpendicular to the length direction of the domain, and the
z
axis is positive upward
above the still surface level.).
Considering that a northeasterly wind is imposed suddenly and uniformly over the surface of the whole water
body, Zhu and Isobe (2012) analyzed the occurrence process of blue tide using a two-layered model which is
consisted of the upper, well-mixed layer and the lower anoxic layer, separated by a density interface. Since the
wind begins to blow on the surface, within a short time, the initial oscillation arising from the Coriolis force due
to the rotation of the Earth does not influence the water body, so that a wind-driven current in the water body
can be simply viewed as being in
z
x
longitudinal section. The wind generates some surface waves and then
these surface waves are reflected by two boundaries of the bay, which forms a standing wave group. Motion of
this standing wave group causes the surface tilt with the southwest boundary up and the northeast shore down,
further causing the surface to oscillate about an equilibrium tilt. Such an equilibrium tilt will be reached when all
wave energy is completely dissipated and, at this point, barotropic pressure on the whole water body caused by
this equilibrium tilt is in balance with surface wind stress. The imposed wind stress also causes the vertical mo-
tions of the water body. Specifically, since the onset of wind stress, the thin layer water beneath the surface will
follow instantly the wind downwind and, as the compensation, the rest layer water between it and density inter-
face will flow upwind, as also schematically shown in Figure 2(b). This opposite motion makes the interface up
Z. F. Zhu
128
Figure 1. Map of Tokyo Bay and the chosen research domain
for the study of blue tide (Zhu & Yu, 2014).
(a)
(b)
Figure 2. Dimensions of the chosen research domain (a) and schematic diagrams of coastal
upwelling (b) and (c), caused by the continual blowing of a northeasterly wind. (b) (The wind
direction is from the left to the right); (c) (The wind direction is perpendicular to the surface of
this paper and inward).
Northeasterly
wind
Northeast Northeast
boundary
Southeast boundary
Northwest boundary
Southwest
boundary
x
y
zb
Z. F. Zhu
129
at the northeast shore and down at the southwest shore of the bay, which is opposite to that of the surface. Simi-
larly, this interface tilt is created by the motion of another standing wave group formed by some internal waves,
thus also oscillating around an equilibrium position at which buoyancy force balances barotropic pressure caus-
ed by the surface set-up. If wind condition is enough, the interface will intersect the surface at the northeast
shore of the bay, and the lower anoxic water begins to touch and interact with dissolved oxygen at the surface, at
this point, blue tide takes place. When the northeasterly wind continuously blows on the surface, the effect of the
Earth’s rotation must be taken into account, and thus velocity direction of the upper layer water in the research
domain is gradually deflected to the right of wind direction. In this case, the thin layer water beneath the surface
will flow towards the northwest shore of the bay while the rest layer water between it and the density interface
will flow in an opposite direction towards the southeast shore. Similarly, this opposite motion causes the corre-
sponding tilt of the interface. If wind conditions are satisfied, the interface will also reach the surface and hence
blue tide will occur on the southeast shore of the bay.
Occurrence of blue tide on the southeast shore is just discussed in this study. In order to simplify the theoreti-
cal method for calculating this case, all of parameters are simply assumed to be uniform along the
x
axis (Zhu &
Isobe, 2012), and we simply analyze the vertical motion in the transverse section of the bay as shown in Figure
2(c).
Governing equations for the upper layer water and the lower one can be expressed as follows:
() ()
''
0
,
sx Ix
uf
thh
ττ
υρζζ ρζζ
−= −
+− +−
(1)
(2)
( )
[ ]
( )
;
''
ty
h
−∂
−=
−+∂
ζζζζυ
(3)
( )
''
'' '
,
Ix Bx
uf
th
ττ
υρζ
−=
+
(4)
() ( )
,
'''
'
'
'
ζρ
ττ
ζζ
ε
ζυ
+
+
−∂
−=+
h
y
g
y
guf
t
ByIy
(5)
( )
'' ''
h
yt
υζ ζ

∂+

= −
∂∂
(6)
Where
()
( )
''
,,,uu
υυ
are vertically-averaged horizontal velocity components in
yx,
directions of the upper and
the lower layers, respectively,
'
,hh
are thicknesses of the upper layer and the lowe-r one, respectively,
'
,
ρρ
are
densities of the upper layer and the lower one, respectively,
0
ρ
is the reference of wa-ter,
'
,
ζζ
are surface dis-
placement and interfacial displacements, respectively,
g
and
ε
are gravitational accele-ration and density con-
trast between two layers (
( )
''
ρρρε
−=
),
sx
τ
is surface wind stress,
() ()
ByBxIyIx
ττττ
,,,
are components of inter-
facial and bottom shear stresses in
yx,
directions, respectively,
f
is the Coriolis coefficient, and
t
is the time.
Considering a specific steady state at which the surface and the interface just intersects on the southeast shor e
when the northeasterly wind lasts for a infinitely long time, there should be a vertical circulation in each layer as
shown by Figure 2(c), so
0
'
==
υυ
. If the interfacial shear stress is simply assumed to be expressed in terms of
the velocity difference between the upper layer and the lower one as,
( )
,
Ix IyI
C
ττ ρ
,
() ()
''' ''
,,
I
uu Cuu
υυ ρυυ
∗−−= −−
, wh ere
'
,
II
CC
are coefficients of interfacial shear stress of the upper layer and
the lower one, respectively, similarly, bottom shear stress being expressed in terms of velocity of the lower layer
as
( )
ByBx
ττ
,
''' ,
υρ
uCB
, where
B
C
is the coefficient of bottom shear stress, it can be found readily that
0==ByIy
ττ
,
( )
'
Ix I
Cuu
τρ
≈−
and
Bx
τ
''
B
Cu
ρ
. At this point, for the upper layer, the force balance along
x
Z. F. Zhu
130
direction is between wind stress
sx
τ
and interfacial shear stress
Ix
τ
, an d the balance of forces along
y
direction
is among the Coriolis force
uf
, pressure gradient due to the surface displacement
y
ζ
∂∂
, as schematically
shown by Figure 3(a); for the lower layer, interfacial shear stress
Ix
τ
simply balances bottom shear stress
Bx
τ
along
x
direction, and the force balance along
y
direction is among the Coriolis force
'
uf
, pressure gradient due
to surface displacement
y
ζ
∂∂
and that due to interfacial displacement
'y
ζ
∂∂
as also schematically shown in
Figure 3(b).
Substituting these expressions in Equation (1)-Equation (6) and considering all parameters at the steady state
can yield
BI
IB
sx
CC
CC
u
'
0
+
=
ρ
τ
,
BI
I
sx
CC
C
u
'
0
'
ρ
τ
=
; (7)
( )
y
CC
CC
g
f
y
BI
IB
sx '
0
+
−=
ρ
τ
ζ
,
( )
( )
' ''
'
0
1
sx BI I
IB
f
yC CCy
g CC
τρ
ζερ ρ

= +−


. (8)
when the surface only intersect the surface on the southeast shore, the following mathematical relation should be
satisfied:
( )( )
'
22ybyb h
ζζ
=+==
. Thus a wind stress can be gotten:
0
2
sx I
gh
Cfb
τε
ρ
=
( 9)
It can be found from Equation (8) that the large parameter
0sx
τρ
results in the larger parameters
'
ζ
and
ζ
at the steady state, indicating that Equation (9) actually represents the minimum wind stress for the occurrence
of blue tide on the southeast shore of the bay.
3. Comparison with Observation Data
As presented in Zhu and Yu (2014), surface wind stress in Equation (9) is generally expressed to be a quadratic
function of surface wind speed (Matsuyama et al., 1990; Wilson, 1960):
22
w
aasx
γρτ
=
, where
a
ρ
is air density
(
a
ρ
= 1.23 kg/m3),
2
a
γ
is surface drag coefficient (here
2
a
γ
= 1.30
×
103 is adopted, as presented in Mat-
suyama et al. (1990) and Wilson (1960), and
w
is the average wind speed measured 10 m above the still sur-
face. Some typical parameter values in Equation (9) in case of Tokyo Bay are as follows:
b=
20 km,
f=
8.47
×
105s1,
0
ρ
=
1000 kg/m3. Especially, a simple estimate regarding
I
C
shows that it should be of the order of
104, so we simply chose the empirical value 104 in this preliminary study.
Observation data sets of blue tide at the head of Tokyo Bay from 2003 to 2010 are available (Zhu and Isobe,
2012), and, among these data sets, those data sets of blue tide observed on the southeast shore of the bay are
only chosen. Wind data set measured at Edogawarinkai shown in Figure 1(a) is simply adopted to represent
wind condition across the whole bay (Zhu and Yu, 2014). By using this raw data set, the average speed of the
northeasterly-oriented wind
w
and the total duration are calculated. The starting point for calculating the wind
duration across which the average wind speed is calculated corresponds to the first appearance of the northeas t-
erly-oriented wind that can directly contribute to outbreak of blue tide, the ending point corresponds to the tim-
ing at which blue tide just happens, as shown in Figure 4 as a typical example.
As introduced in Zhu and Isobe (2012) in detail, for each real case of blue tide, value of minimum wind speed
in Equation (9) should be different, because the density contrast
ε
and thickness of the well-mixed upper layer
h
are closely related to stratification degree and they should differ one case by another case. In order to calcu-
late them, a series of real-time measurement data from Chiba Light Beacon (CLB) also indicated in Figure 1(a)
are used. Densities of the upper and lower layers can be calculated based on the temperature and salinity, and
thickness of the well-mixed upper layer can be estimated from vertical distribution contours of temperature, sa-
linity and dissolved oxygen. Here it needs to be mentioned that this study did not use spatially-averaged wind
data and stratification data across the whole bay because of a lack of a long-term and real-time data measured at
different locations of the bay beyond CLB.
Table 1 summarizes the comparison result of the analytical solution with real cases from 2003 to 2010. The
first big column shows date of the occurrence of blue tide on the southeast shore of Tokyo Bay from 2003 to
2010; the second column presents the calculated average wind speed along the north ea st-southwest direction and
Z. F. Zhu
131
Figure 3. Schematic diagram of the force balance for the upper layer (a), and
that for the lower layer (b) when the two-layered fluid is in the steady state in
the case of blue tide on the southeast shore of Tokyo Bay.
Figure 4. Vector diagrams of surface wind measured at Edogawarinkai in Tokyo Bay in August, 2002. The orientation is as
follows: the up points to the north, the down the south, the left the west and the right the east. The red dashed rectangle
denotes the duration of an observed blue tide: the left dashed line shows the timing of the occurrence of blue tide, and the
right shows the timing of its disappearance. The blue dashed rectangle denotes the duration of the northeasterly-oriented
wind: the left dashed line shows the first timing of the occurrence of the northeasterly-oriented wind, and the right corres-
ponds to the timing of the appearance of blue tide.
wind duration; the third column shows the stratification degree for each case using measurement data sets from
CLB (including densities of the upper and lower layers, thicknesses of the upper and lower layers). Using these
values, the fourth column presents the calculated minimum wind speed fro m Equ ation (9). Whether the wind
speed of each real case exceeds the calculated minimum wind speed is shown in the fifth column, which shows a
good agreement between real cases and the solution. It can be concluded that the analytical solution shows a
certain degree of validity.
4. Sensitivity Analysis
Sensitivity of the analytical solution to all of parameters incorporated into it can be carried out by qualitatively
analyzing Equation (9), and some results can be obtained as follows:
1) When density of the lower layer water with a fixed density for the upper layer water is increased, minimum
wind stress will increase accordingly. This is because a heavy lower water layer has a large gravity against sur-
face wind effect, thereby making coastal upwelling become difficult. This conclusion is consistent with the re-
sults of numerical simulation of Matsuyama et al. (1990), which showed that coastal upwelling is prone to hap-
pen in early autumn because during this period stratification becomes weak. This conclusion is also applicable to
the case in which density of the upper layer water is decreased and density of the lower layer water is fixed.
2) When thickness of the upper layer water is increased, minimum wind stress needed for the occurrence of
coastal upwelling will increase accordingly. This is because increasing thickn ess of the upper layer is equivalent
to lengthening the spatial distance of coastal upwelling, thus making coastal upwelling get more difficult.
3) The wider the research domain is, the easier the occurrence of blue tide gets. This may be interpreted by
virtue of geometry of the research domain: under the circumstance in which all of parameters keep the fixed
Z. F. Zhu
132
Table 1. Comparison of the analytical solution with real cases of blue tide observed on the southeast shore of Tokyo Bay
from 2003 to 2010 (based on measured data from Chiba Light Beacon).
Blue tide on
the southeast
shore of
Tokyo Bay
Northeasterly
wind Degree of stratification
The
analytical
solution
Equation (9)
Does the
average wind
speed exceed
the calculated
minimum
wind speed?
Date of
appearance
Average wind
speed/Wind
duration
(m/s)/(h)
Surface
temperature/
Surface
salinity
(˚C)/(psu)
Bottom
temp e r a ture/
Bottom salin
ity
(˚C)/(psu)
Density of
the upper
layer
(kg/m3)
Density of
the lower
layer
(kg/m3)
The initial
thickness
of the upper
layer (m)
The initial
thickness
of the lower
layer (m)
2003
May 16-
May 19 3.64/45 18/29.8 15.6/33 1021.48 1024.24 5.00 10.00
w
3.1224
m/s
Yes
Sep 22-
Sep 24 5.52/47 22.8/31 20.4/33 1020.99 1023.27 5.00 10.00
w
2.8393
m/s Yes
2004
Jul 28-
Jul 31 6.06/48 26.4/29.8 20.4/33 1019.17 1023.27 5.00 10.00
w
3.8074
m/s Yes
2005
May 31-
Jun 1 5.10/61 18/30.6 16.2/33.40 1022.24 1024.55 5.00 10.00
w
2.8561
m/s Yes
Jun 15-
Jun 17 4.57/68 19.2/32.2 16.8/33.60 1022.71 1024.47 5.00 10.00
w
2.4931
m/s Yes
Sep 6-
Sep 7 4.27/37 25.2/27 21.6/33.0 1017.28 1022.73 2.50 12.50
w
3.1048
m/s Yes
Sep 26-
Sep 30 4.24/138 21.6/31.8 20.4/33.0 1022.08 1023.27 3.00 12.00
w
1.5889
m/s Yes
Oct 12-
Oct 17 3.89/72 21.6/31.8 21.6/33.20 1022.08 1022.88 5.00 10.00
w
1.6822
m/s Yes
2006
Sep 13-
Sep 18 4.15/69 24/31 22.8/32.80 1020.65 1022.29 4.00 11.00
w
2.1548
m/s Yes
2007
Sep 2-
Sep 4 4.08/84 25.8/29.4 21.6/33.00 1018.60 1022.73 4.50 10.50
w
3.6262
m/s Yes
Oct 16-
Oct 18 4.06/48 21/31.8 21/33.00 1022.24 1023.00 4.00 11.00
w
1.4664
m/s Yes
2008
Aug 22-
Aug 28 5.40/40 26.4/29 21.6/32.60 1018.42 1022.42 4.00 11.00
w
3.3651
m/s Yes
Oct 9-
Oct 10 3.33/55 22.2/31 21/33.00 1021.16 1023.00 3.00 12.00
w
1.9760
m/s Yes
2009
May 29-
May 31 2.85/39 18/31 16.8/33.00 1022.24 1024.01 4.00 11.00
w
2.2367
m/s Yes
Aug 31-
Sept 1 4.84/46 24/29 21.6/32.20 1019.14 1022.12 5.00 10.00
w
3.2478
m/s Yes
2010
Sep 9-
Sep 10 3.87/43 27.6/27 25.2/32.20 1016.55 1021.26 5.00 10.00
w
4.0848
m/s No
Sep 15-
Sep 21 3.68/44 26.4/29.8 22.8/33.00 1019.17 1022.45 3.00 12.00
w
2.6389
m/s Yes
Sep 24 4.36/48 24/31 22.8/33.20 1020.65 1022.60 5.00 10.00
w
2.6266
m/s
Yes
constants except the width of the domain, a wide bay should mean a larger displacement of the interface on the
boundary of domain between the upper and lower layers, consequently making coastal upwelling become easier.
4) It is apparent that upwelling can happen more easily in the research domain with a high latitude (that is a
large Coriolis coefficient). This is simply because a high latitude means the larger Coriolis force, which intensi-
fies the vertical motion of the upper layer water and subsequently accelerates the interface tilt on the boundary
of the domain.
5) It can be found that it is difficult for coastal upwelling to happen in the domain with a large coefficient of
interfacial shear stress of the upper layer. This is because the two-layered fluid system with a large coefficient of
Z. F. Zhu
133
interfacial shear stress corresponds to a large production of heat, further implying that a stronger wind is needed
for the occurrence of coastal upwelling on the boundary of the domain.
5. Concluding Remarks
In this study, an analytical solution of minimum wind stress for the occurrence of blue tide on the southeast
shore of Tokyo Bay based on a two-layered model has been derived. Comparison with observation data of blue
tide from 2003 to 2010 showed certain the validity of this analytical solution. The results of sensitivity analysis
to all parameters involv ed in it were also found to agree with qualitative understandings of blue tide phenome-
non.
Acknowledgements
This research is supported by National Key Technology Research and Development Program of the Ministry of
Science and Technology of China (Number: 2013BAB05B04) and “the Fundamental Research Funds for the
Central Universities” in China (Number: 2013NT50).
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