Studies on the assessment of the allowable stocking capacity of yellowtail cultured in the Fukaura fish farm (I) Field observations on tidal current-香川大学学術情報リポジトリ

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Tech. Bull. F a c . Agr.. Kagawa Univ",Vol.. 37, No. 1 , 41-53, 1985

S T U D I E S ON T H E A S S E S S M E N T O F T H E ALLOWABLE STOCKING CAPACITY

O F YELLOWTAIL CULTURED IN T H E FUKAURA F I S H FARM

( I )

F i e l d obsevations on tidal c u r r e n t

Takashi

SASAKI

and Hiroo

INOUE

In seeking the best strategies for management of marine culture farms, it i s necessary to understand the allowable stocking capacity of fishes cultured in the basins and to control the fish population s o a s not to exceed the stocking capacity.

With this in mind, research efforts on assessments of stocking capacity in marine culture farms have been undertaken in Fukaura-wan located in Wakamatsu-seto, Nagasaki-ken. In the present paper, the tidal current data observed in and out of the bay a r e analyzed.

We made the following findings..

(1) North-Southward flows a r e predominant at both Stn.1 (the main stream) and S t n . 2 (the mouth of the bay). East-Westward flows a r e extremely small a t both stations..

(2) The M2 tidal current consitituent has the largest magnitude a t both stations.. (3) The power spectrum on the raw data has predominant peaks a t the semidiurnal.

(4) The power spectrum on the fluctuation excluding (M2

+

S 2 ) consitituent flows is approximated by the Kolmogoroff (- 5/3) spectrum law in a restricted frequency range.

(5) Horizontal eddy diffusivities a r e 2 . 2 X 10" cm2/sec (North-Southward component ) and

1..2

X

l o G

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Tech. Bull.. Fac. Agr Kagawa Univ.,Vol.. 37, No. 1, 1985

Introduction

The eutrophication of sea waters caused by leftover food and excrement of fishes cultured i s deteriorating marine culuture farms around our country, doing damages to fishes, such a s low growth,

disease and sometimes death due to serious red tide and oxygen deficit

Hereafter, in seeking the best strategies for management of marine culture farms, it i s essential to under stand the allowable stocking capacity of fishes cultured in the basins and to contr 01 the fish populati- ons so a s not to exceed the basin's stocking capacity.

For that reason, it i s urgently necessary to develop techniques for assessing the ability of the marine culture environments to purify sea waters without unacceptable consequences and to determine the criteria

for stocking capacity in order to maintain the stability of fishery production

With this in mind, we have undertaken research on assessments of stocking capacity in the marine culture farm in Fukaura-wan located in Wakamatsu-seto, Nagasaki-ken

The present paper reports on part of that research, and its purpose is to make clear hydraulic characteristics on the basis of the observation data obtained in and out of the bay

Fig..l Location of the moored current meters (Stn..l and Stn..2).

Method

Wakamatsu-seto, about 1 4 km long, is extremely narrow and has a very complicated shoreline with some bays and many inlets, extending from the northwest to the south a t the northern part of the Goto islands, Nagasaki-ken..

S e a water flows into Wakamatsu-set0 through the mouth of the s t r a i t between Nokubinohana and Hitotsunose a t the northeast part,the mouth being about 1.5 km wide and 56 m deep.. The waterway curves near Ogushisaki and also a r e connected with another mouth between Shinosaki and Kazurato, about 1.6 km wide and 51 m deep, a t the southern part.

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T. SASAKI and

H.

INOUE : ALLOWABLE STOCKING CAPACITY

43

The type of tide i s regular with high or low tides two times a day in Wakamatsu-set0 The times of high and low tide a t Wakamatsu port and Arakawa near the central part of the strait a r e 20 min later than those a t Sasebo port, the reference station for tides

The time of high tide a t Sao near the southern mouth of the strait is faster than that a t Yakisaki r e a r the northern mouth Therefore, the northward components of the tide currents during flood tide a r e dominant in the main stream around the bay mouth of Fukaura.wan which i s located in the southern part of the straits, a s a r e the southward components during ebb tide The tidal currents in the main stream a r e extremely fast, about 4 8 kn a t the eastern waterway past Shimonakashima, opposite the bay mouth of Fukaura-wan. However, the tidal currents in the inlets and the bays a r e weak enough to permit culture

farming

Taking into account the general features stated above,we carried out the tide current obsevations over 1 5 days, from July 26 to August 12, in 1982, to clarify the hydraulic characteristics in and around Fukaura.wan The tide currents were measured by using two One-type current meters, a t 2 5 m depth below the sea surface a t S t n 1 and S t n 2 a s shown in Fig 1

Analysis end results

Mean tidal currents obtained at Stn..l and Stn..2 a r e divided into N-S components and E-W components over the period observed, respectively(Fig.. 2 and Fig. 3).. Using these results, we conducted harmonic analysis, autocorrelation analysis and power spectrum analysis, and an estimation of eddy diffusivity.

WAKAMATSU SET0 STN 1

1982 7/27 16 : 00 --8/12 11 : 10

- (N-S) CURRENT ( E W ) CURRENT

- 1 . 5 L

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Tech. Bull.. Fac. Agr.. Kagawa Univ.,Vol.. 37, No. 1 , 1 9 8 5

WAKAMATSU S E T 0 S I N 2 1 9 8 2 7 / 2 7 1 5 : 00

-

8 / 1 1 1 5 : 00

- (N-S) CURRENT (E-W) CURRENT

Fig..3 Variations in tidal current velocity observed a t Stn..Z..

(a) Harmonic analysis of tidal currents,

T h e tidal c u r r e n t s a t any place can be express'ed in t e r m s of a sum of harmonic t e r m s a s follow^.^^)

where

U : the speed of current a t any time Uo : the constant flow

,f

: the node factor, modifying UH for the year under consideration U,, : the mean amplitude of the consituent during the 18.6 year period Vo

+

u : the value of the equilibrium argument of consitituent n , when t ;;0

Vo : the unifying changing p a r t of the phase of the constituent according to the equilibrium u : the correction f o r V,, determined by the position of line of nodes

K : the lag of the phase of tidal constituent behind the phase of corresponding equilibrium constituent a t Greenwich

n : the degrees per mean solar hour t : the time

In Eq,(l), amplitude and phase lag a r e s o called harmonic constants.. In the present paper, these values a r e estimated by means of Darwin's meth~d.!~' T h e r e s u l t s of harmonic analysis obtained from the observed data aresummarized in Table..2.. The data observed a r e compared with the tidal current curve using the four major tidal c u r r e n t constituents a s shown in Fig..4 and Fig..5..

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T

SASAKI and H INOUE : ALLOWABLE STOCKING CAPACITY I I I * I I (I I * I U I I I (I I ( I . * 10.0 ,. 'b1.6 I I * . I e . I * I

.

I # I

..

I I

.

I

.

I

.

I I I I I I I I * I I * I

.

I I

.

I

wakamatsu weto stn.2 (spring tide) I

I I982 1/27 I5:OO

---

8/11 15:oO I I

I I

I + north flow I

I

-

south flow I

I observed I

I

.

predicted 1

time step I0 min. unit ; cm/sec

Fig.4 Comparison of the predicted curve with the raw data on currents observed at Stn..2 ; N-S component flow

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Tech. Bull Fac Agr Kagwa Univ.,Vol 37, No. 1, 1985 -2.3 ,-8.1 I -0.2 ,-R.9 I - 5 . 5 ,-911 1 -,0.8 - 9 . 3 1 -5.5 -9.5 1 - 3 . 1 -9.7 1 - 4 , 9 -9.8 I - 9 . 9 1 - 3 - 1 .-1o.n I - 3 . 1 - 1 n . n I -2.5 - 1 n . n I 0.0 -10.n I - 4 0 1 - 1 n . n I - 1 - 2 - 1 n . n I -1.8 - 9 . 9 1 -0.7 -9.8 I - 4 . 1 - 9 . h I - 3 . 8 - 9 , 5 1 7 1 9 .-9.1 1 2 0 2 -9.1 I 0 . 0 - 8 . 9 I - 0 . 4 - 8 . 1 I 0.8 -0.4 I -0.3 - 8 . 7 I -1.3 -7.P I - 2 . 6 - 7 . 6 I -6.4 - 7 . 1 1 - 3 , b - 7 . n I - 2 - 8 , - h a 1 I -4.6 - h a 4 I - 9 . 4 - 6 . 1 I -11.1 -5.8 I -14.5 - 5 . 5 1 - 1 4 . 6 - 5 0 7 1 -5.9 - 4 1 9 1 -5.3 - & , A I -3.6 -4.3 1 - 1 4 . 6 -4.1 1 -13.2 - 3 . 1 1 -5.4 - 3 . h I - 5 1 1 - 3 . 4 1 -2.4 .-?a7 I 1.8 - 3 . n I - 2 . 6 -7.R I 2 , 5 -7.7 1 0.2 -7.5 1 0 - 2 -7,4 1 1.7 -7.3 I - 0 . 1 - 7 . 1 I -0.6 -7.7 I -3.7 -7.7 I -2.0 - 7 . 7 I -0.8 -7.7 I -0.8 -7.7 I - 1 1 3 - 7 1 1 I - 1 1 3 - 7 1 1 1 '-2.4 - 7 1 4 1 - 1 3 - 7 s I - 1 6 7 I - 0 - 6 - 7 0 8 I - 2 . 0 -?.'I r - 5 1 I -0.2 - 3 . 7 I - 4 . 1 -3.c I - 0 8 2 - 3 . h I -0.7 -3.R I -4.6 - 4 , n 1 -1.4 '4,? 1 0 1 - 4 I 0 . 7 - 4 . h I - 2 - 6 - 4 . 1 I - 1 1 4 - 4 0 9 1 , - 1 . 4 -5.1 1 -0.2 - 5 . 1 1 -2.6 - 2 0 4 1 .-0.2 - 5 . h I

Fig..5 Comparison of the component flow.

' wakamatsu e e t o s t n . 2 ( e p r i n e t i d e )

:

.

1

I982 7/27 1g:OO

---

8/11 1g:OO

.

+ weet flow

.

* I

-

eltat flow . * I obuervod a * I

.

predicted . * I time o t e p ' I0 min. u n i t ; cm/Leo

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T..

SASAKI and H. INOUE : A L L O W A B L E STOCKING C A P A C I T Y

₄₇

(b) Autocorrelationand spectrum analysis

F r o m the r e s u l t s of the harmonic analysis, taking

(Mz

+

S Z ) tidal current constituents a s the mean velocity, and excluding the low frequency components from the observed data to find the instantaneous fluctuation velocity, we estimated the autocorrelation coefficient and the power spectrum. T h e instantaneous fluctuation velocity i s given by

where u

'

(t),

v' (t) : the instantaneous fluctuation velocities in 3 and y-directions denoting horizontal Cartesian

coordinates

- -

U(t),

V(t)

: the time averaged velocities in the 3 and y-directions a t any point in the flowing fluid

U(t), V(t)

: the instantaneous velocities in the 3 and y-directions

F o r a continuous function

u"(t),

the autocorrelation covariance function

C(r)

i s given by(3)

T h e autocorrelation coefficient i s

Since the s e r i e s should not change with time, the autocovariance function i s distributed a s shown in the following.

C

( 5 ) = U'

(t)~'

( t

+

r)

= U' (t' -

r)ur

(t'

)

A s shown by Biackman and Turkey, i t may also be written a s the F o u r i e r transform of a distribution function

PU).

If

u'(t)

i s real,

C(r)

i s r e a l and symmetric around r = 0. Hence

C(r)

and

P(f)

may be expressed more simply a s a two-sided cosine transformation :

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48

Tech. Bull. Fac.. Agr.. Kagwa Univ.,Vol. 37, No.. 1, 1 9 8 5

With r = 0, we will get

From this equation,P(f) may be shown to represent the contribution t o the variance of

d

(t) from the frequency between f and f

+

df Most of the energy that i s exchanged a c r o s s a given wave number apparently comes from the next l a r g e r eddies and goes to the next smaller eddies I t seems fair to describe the energy t r a n s f e r a s a cascade, much like a s e r i e s of waterfalls, each one filling a pool that overflows into the next one below.(4)(5) In an inertial subrange of the equilibrium spectrum, the spectrum function should be independent of the fluid viscosity. Therefore,

where

C

: the absolute constant of order one

E : the dissipation r a t e

f : the wave number

These equations may be rearranged for numerical analysis a s follows.(6) a.) Intensity of the turbulence fluctuation

where

N

: the number of data

b..) Autocorrelation c..) P o w e r spectrum nhk P(h) = A t [ R(0)

+

2 5 ' R(k)cos7 k= 1

+

( - l ) k ~ ( m ) l where h = 0,1,2

;...

,m

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T SASAKI and H INOUE : ALLOWABLE STOCKING CAPACITY

where

a1 (0) = 0..5, a, (-1) = 0.25, al(2) = a,(--2) = 0, %(O) = 0..625, a, (1) = a,(-1) = 0.25, a2(2) = a2(-2) = -0..0625.

These results are shown in Figs. 6-7.. Fig.6 shows the autocorrelation coefficients on the raw data of tidal current observed at Stn..l and on the fluctuation, excluding (M2

+

S2) constituent flows.. Similarly, the power spectral density functions are shown in Fig.7 and Fig.8.. The power spectral density is smoothed

by Eq.113)

LAG TIME, min

LAG TIME, min LAG TIME, min

Fig.6 Autocorrelation coefficients of tidal current observed a t Stn..l ;

(a) N-S component of the raw data..

(b) N-S component of the fluctuation excluding( Mz

+

Sz ) constituent flows.. (c) E-W component of the raw data

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50

Tech.. Bull.. F a c . Agr. Kagwa Univ.,Vol.. 37, No. 1 , 1 9 8 5

( c ) Eddy diffusivity

From the Eulerian velocity correlation, the horizontal eddy diffusivities can be estimated a s follows (7x8)

P E R I O D , hr PERIOD , hr PERIOD , hr PERIOD , hr 24 12 6 3 0.6 0.3 24 12 6 3 0.60.3 P: b 0 W a lo2

-

rn FREQUENCY, l / s e c FREQUENCY. l / s e c

F i g 7 P o w e r stectrum of the r a w data on the tidal c u r r e n t observed a t Stn.1 ; (a) N-S component of the tidal c u r r e n t (W1)

(b) N-S component of the tidal c u r r e n t (W2). (c) E-W component of the tidal c u r r e n t (W1) (d) E-W component of the tidal c u r r e n t (Wz).

P: W

g

lo1

a

lo0 . '

lo-'lO-e io-6 i0-4

low3

lo-2

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T. SASAKI and

H..

INOUE : ALLOWABLE STOCKING CAPACITY

where

K ~ , K y : the horizontal eddy diffusivities in

x-

and y directions, respectively

gZ(t),

v k 2 ( t ) : the intensities of turbulence fluctuation in x and y- directions, respectively

R,,, RL2 : Eulerian autocorrelation coefficients in P and y- directions

P I ? P2 : _{the non -dimensional par amenters in}

x-

and y- directions

T,,,

T,,

: the integral time scales in 1.and y- directions, respectively These results are summarized in Table. 1.

PERIOD, hr PERIOD, hr 24 12 6 3 0.6 0.3 24 12 6 3 0 . 6 0.3 0 W a cn lo2 - Cr: W Cc:

a

lo0

-

10-l- 10-e 1 0 4 1 0 10-3 10-2 FREQUENCY, l / s e c FREQUENCY, l / s e c PERIOD, h r PERIOD, hr

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Tech.. Bull.. Fac.. Agr. Kagwa Univ.,Vol.. 37, No., 1, 1985

Table,, 1, Eddy diffusivities and characteristic values of turbulence.

Discussion

The largest values of observed tidal currents a t Stn..l a r e about 70..2 cm/sec (westward flow) in the E-W components and about 133..1 cm/sec (northward flow) in the _{- .} S-N components. Constant flows a r e 14.,4 cm/sec and 4.4 cm/sec, respectively Those values a t Stn.2 a r e 14,6 cm/sec (eastward flow) and 61.7 cm/sec (southward flow) Constant flows in the flow a r e 5.2 cm/sec (westward) and 12.3 cm/sec (southward flow) North-Southward flow i s predominant a t both Stn.1 and S t n 2 East-Westward flow i s extremely small Northward currents a r e larger than the southward currents a t both stations It seems

to be an asymmetrical flow probably because both of them a r e complicated by geometry fi

0 3 0 2 0 5 0 5

Table.2. Harmonic constants for the four major constituents, M2, S 2 , 0 1 , and K1

U (cm/sec) 14 5 3 9 12 4 5.5 Date 1982 7 27- 8 11 15days

0

(cm/sec) 41 4 15 5 19 4 8 . 3 K (cm2/sec) 2 2X106 1 2x10" 1 0 X 1 0 6 1.6X106 *E (hr) 1 2 0 7 1 5 1.2 S tn 1 2

In Table &harmonic constants of the four major tidal current constituents a r e cited from the observed data They a r e dominant over other constituents, and the M, tidal current has the largest magnitude a t both S t n 1 and a t Stn 2, From the spectr um analysis, both spectrum have predominant peaks at the semidiurnal, a s expected.. Therefare, the M2 and Szconstituents can be chosen a s 'representatives of the mean velocity.. The maximum level of the N-S spectrum i s one order of magnitude higher than that of the E-W spectrum.. The spectrum has a peak near the frequency, f = 6.7

x

10-5 Hz. Each spectrum has a slope of - 5 / 3

for periods shorter than about 1 2 hours.. Horizontal eddy diffusivities calculated by Eq.(l4 a r e 2.2 X 10' cm2/ sec (N-S ward) and 1.2 X l o 6 (E-W ward) a t Stn.. 1, and 1..O X l o 6 cm2 / sec and 1.6 X 10' cm2 sec,

DEPTH (m) 2 5 2 5 PERIOD 1 9 8 2 7 2 7 - 8 11 a t Stn.2, respectively. DIREC N-S E-W N-S E-W CONSTANT FLOW (cm /sec ) 1 4 4 4.4 12 3 5 2

The eddy diffusivity of the N-S component is one order of magnitude higher than that of the E-W Stn

1

2

component.. It seems that flow patterns a r e nonisotropic a t both Stn.1 and Stn.2 DIREC N-S E-W N-S E-W IEPTH (m) 2.5 2 5 Acknowledgments

This work was supported by the Nagasaki Fishery Experimental Station, Nagasaki-ken.. The data analysis in the present paper was carried out on a FACOM 230-45s in the data station of Kagawa University.. The

HARMONIC CONSTANT

K 1 AMPLI

-

PHASE

TUDE LAG (an /sec ) (deg)

4 9 131 3 1 2 265.0 2.8 3198 2 2 3252 M2 AMPLI

-

PHASE TUDE LAG (cm /sec ) (deg ) 29 5 114 2 6.2 211.4 1 4 9 3151 5 4 3223 s2 AMPLI

-

PHASE TUDE LAG

(em /sec ) (deg ) 10 1 147 8 2.1 222.1 9 3 3517 3 4 244 0 , AMPLI

-

PHASE TUDE LAG (cm /sec ) (deg ) 2.6 15.7 0 5 108.7 2.5 2318 1.1 241.9

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T . SASAKI and H.. INOUE : ALLOWABLE STOCKING CAPACITY

53

authors wish to thank the scientists and the staffs of these stations for helping in the field surveys and the data analyses The authors also would like to thank Mr.. Hiroshi Tanaka, an undergraduate student, in Depertment of Agricultural Engineer.ing,Kagawa University, in 1982, for his cooperation in this study.

References

(1) J.J.. DRONKERS : Tidal computations, 88-126, Amsterrdam, Nor thholland Publishing Company (1964).

( 2 ) S.OGINO : Bulletin of the National Research Insititute of Agricultural Engineering, F(6), 97-118(1971)..

(3) M.HINO : Spectral analysis, 25-51, Tokyo, Asakura-shoten (1977).

( 4 ) J..O.. HINZE : Turbulence, 142-246, New York, McGrow-Hill Book Company (1959).

(5) H,TENNEKES and J.L. LUMLEY : A first course in turbulence, 248-287, Massachusetts, 'The

MIT P r e s s (1973).

(6) H.AKAIKE and T..NAKAGAWA : Statistical analysis and optimal control on dynamic systems, 36-50, Tokyo, Science Company (1972)..

(71 A..WADA and M..KAKUIA : Proceedings of Coastal Engineering in Japan, 21th, 297-302 (1974)..

(8) T.SASAKI and H.. INOUE : Technical Bulletin of Faculty of Agriculture, Kagawa University, 31-38 (1984).