In the recent preliminary observation of the internal waves in Lake Biwa, the longitudinal inclination of the thermocline due to the wind with the north component and the initial stage of the free oscillation after the wind has ceased, are observed. The period of the first swing was about 56 hours and this period just coincides with the one calculated for a simplified two layer lake. Another small periodic change with the period of 10 hr was also observed. And it is concluded that this oscillation corresponds to the transverse internal seiches under geostrophic effects

KANARI, Seiichi

Kyoto University Research Information Repository

Title Internal Waves in Lake Biwa (I) -The Responses of theThermocline to the Wind Action-Author(s)KANARI, SeiichiCitationBulletin of the Disaster Prevention Research Institute (1970),19(3): 19-26Issue Date1970-02URL http://hdl.handle.net/2433/124777RightType Departmental Bulletin PaperTextversionpublisherKyoto University                                                            51       Errata to "Internal Waves in Lake Biwa (I)  — The Responses of the Thermocline to Wind Action —"                        Presented in Vol. 19, No. 161.                       By Seiichi KANARI                       (Manuscript received July 6, 1970)  Corrections of some numerical errors appearing in the paper "Internal Waves in Lake Biwa  (I)" presented in the Bulletin, Vol. 19, Feb. 1970                                Errata         Page 26, line 3 change 2r  —  6.6 to2r  —  42.0         Page 26, line 7 change about  2.  2 to about  6.  6  Fortunately, in spite of these errors the fundamental results of this study remain  unaffected.Bull.  Naas. Prey. Res. Inst., Kyoto Univ., Vol. 19, Part 3, No.  161, February, 1970           Internal Waves in Lake Biwa  (I)     —The Responses of the Thermocline to the Wind Action—                    By Seiichi KANARI                     (Manuscript receivedOctober 31, 1969)                                 Abstract   In the recent preliminary observation of the internal waves in Lake Biwa, the longi-tudinal inclination of the thermocline due to the wind with the north component and the initial stage of the free oscillation after the wind has ceased, are observed. The period of the first swing was about 56 hours and this period just coincides with the one calculated for a simplified two layer  lake.   Another small periodic change with the period of 10 hr was also observed. And it is  concluded that this oscillation corresponds to the transverse internal seiches under geostro-phic effects. 1. Introduction  In many lakes, the vertical gradients of density are associated with only the  5102  UNA  MA  du:A                               vfre                         01,  .  IP"                       00,•immu.4                                                                                    da4,4.0                                                                   014IKOME  KITAKONA7SU                                                        01.                 *It a                            KATHOA                                                                          •0                                         fq                                           WW1"  EITSU  acteorn                           ,4       Fig.  1 Chart of Lake Biwa and Sugaura Bay. The positions of the three         subsurface buoy-stations are shown by black circles.20 S. KANARI vertical gradients of temperature, and are particularly large in the thermocline-layer. Consequently, internal oscillations involve oscillations of temperature at a fixed depth. From observations of these oscillations of temperature, and from a knowledge of the vertical gradients, it is possible to calculate the amplitude of the oscillations of any particular layer of water. We had a plan for the observation of the internal waves in Lake Biwa using three multi-layered sub-surface buoy-stations in 1969. For this purpose, the preliminary observation was carried out during the period from September 17 to 23, 1968, with three single-layered subsurface  buoy-stations at Sugaura in the nothern part of Lake Biwa.  During the preliminary observation, we confirmed the fact that the longitudinal internal seiches in Lake Biwa are induced by wind with a notherly component.  It has been supposed that the longitudinal internal seiches in Lake Biwa may be induced by  wind". However, this has not been confirmed up to the recent day.  Sugaura-bay (Fig. 1) is situated at the north end of Lake Biwa, and is open towards the south end of the lake. The mean depth of this bay is about 34 meters, and the maximum depth (50 m) is found at the mouth of this bay, which is the same as the mean depth of the whole north basin.  This bay is the most suitable for buoy-stations (Our buoy-stations need elec-tric cables between the buoy and the recorder on the shore.), because large depths can be obtained at short dstances off the shore.  The three stations were set in this bay with intervals of 200 meters from each other. Their situations are shown in Fig. 1, by the black circles with                               the station-number  I, 2 and 3.  V  PILOT  BUOY Of course, the original purposes of the  ? observation withthe three subsurface buoy-            SUBSURFACE BUOY 5 m station were (1) observation of the  progres-           • sive internal waves, (2) observation of the  IT ,5  m standing internal waves and (3) observation                               of the continuance of the progressive in-               .-10mm  Jla  ternal waves. However, in this paper we  SALAN—  ROPE                               will treat the problem concerning the pur-                              pose (2) only. The problems concerning                          — THERMISTER               /THERMOMETER(1) and(3) will be discussed in a future                                  article.                               2. Method of Observation               ELECTRIC  CABLE  —• The structure of the buoy-station is shown                               in Fig. 2. The subsurface buoy is 5 m                                  below the surface, and a thermister thermo-            idiANCHOR BLOCK meter is fixed at the depth of 17.5 m, where                 /c/2°;;;///the thermocline was found at the time of Fig. 2 Schematic structure of the the buoy-stations setting. The thermister   subsurface buoy-stations used in Lake elements at each station are connected with  Biwa. three independent bridge circuits, and their                  Internal Waves in Lake Biwa (1) 21 unbalanced out-put voltages were recorded successively on a three channel recorder. The time interval between adjacent measurements at one station is about 15  sec  ; therefore the period of the measurable fluctuation can not be shorter than 30 sec.  The range of the temperature measurement is from 9°C to 30°C, and the temperature measurement is executed with an accuracy of ±0.1°C in this range. 3. Results of Observation  The temperature fluctuations observed from September 17 to 23, 1968 are shown in Fig. 3 together with the records of the wind direction and wind speed obtained at  Hikone and the Ado-river. During this period, the circuit of station No. 3 was in trouble, so the record is not shown in Fig. 3. The full line (Station No. 1) and the dotted line (Station No. 2) were plotted by reading with intervals of 30 minutes from the continuous records.  As shown in Fig. 3, the maximum temperature change appeared during the time  POOrn to  18h00'n on September 21, and its magnitude reaches 9°C.  Other small periodic changes with an amplitude of 3°C to 4°C are seen all over the record. Its period is about 9 to 10 hours. At a glance, it is clear that the periodic changes with the period shorter than 6 hours can not have any correlation with the wind speed and wind direction shown in Fig. 3 because of the rough plot of the wind with three hours interval. Therefore we cut out the comparatively short period fluctuations by means of the running-mean of 8.5 hours interval. The resulting curves are shown in Fig. 3 by the broken line (Station No. 1) and the dotted broken line (Station No. 2) respectively.  Now let us pay attention to the strong wind that blew on September 21, and the calm weather on September 22 and 23.  The longitudinal motions of the lake water may be affected mainly by the  — WIND  SPUD  AT  Millen                                                   ••••• WINO WAD AT ADO-RIVEN  1  • " .  1 • '        N      I10tit2                           •••ais0 •  ais• te     itI..... 11  -  11"  —  NO  -  Fige  3 Variations of the wind speed and wind direction at Hikone and the  Ado-river,    and water temperature variations obtained from the records of subsurface buoy-stations    No. 1 and No. 2 (full line and dotted line). The broken line and dotted broken line    show the result of the running mean with the time interval of 8.5 hr.22 S. KANARI wind of the N-S component. Consequently, we decomposed the wind speed into the N-S component and E-W component  respectively, and compared the smoothed temperature variation during the period from September 21 to 23, with the N-S component of the wind velocity during the same period.   The broken line in Fig. 4 show the smoothed temperature viriation and wind velocity of the N-S component respectively, in which the wind velocity is averaged between the weather stations at Hikone and the Ado-viver, and the temperature variation is also averaged between Station No. 1 and Station No. 2. 4. Longitudinal Internal Seiche Due to Wind Actions  For the stituation as shown in Fig. 4, we suppose that because of the large wind stresses produced by the north component of the wind along the surface of the lake over about 18 hours, a large amount of lake water in the upper layer was transported towards the south, and water in the lower layer towards the north. Accordingly, the depth of the thermocline will become shallower at the north end and deeper at the south end of the lake.  It is clear that such an inclination of the thermocline will produce a drop in water temperature at the north end of the lake. The full lines in Fig. 4 show such a condition schematically. In spite of the lower velocity of wind during the period from  18b00n 21 st to  12h00m  23rd, the water temperature is going to rise to its maximum at  22"00= 22 nd.  It may be considered that the temperature change on and after  18h00ra on September 21 st was caused by the longitudinal internal seiches due to the wind, and the length of the time between the minimum temperature and the maximum temperature corresponds approximately with half the period of the longitudinal  >TS     6 -    E   - 4   WIND VELOCITY OF N- S COMPONENT  2 2  - 0     0 6 12  1$ is 0 6-.12 ( hr.)t  21 22 23   •  W     20.0 -TEMPERATURE VARIATION  f5•I6.0-   F- bj •16.0 -                                       INITIAL HALF SWING  cr  140-  `, OF FREE OSCILLATIONS 3 12.0-   )11  ( T  56  hr. Fig. 4 Variation of the wind velocity of the N-S component (upper panel) and variation   of the water temperature at the thermocline-layer observed in Sugaura Bay (lower   panel). The full lines show the schematic change of the wind velocity of the N-S   component and temperature variation.                  Internal Waves in Lake Biwa  (I) 23 internal seiches.  From the schematic curve in Fig. 4, we obtain the Period  T  =56 hours of the longitudinal internal seiche as twice the time difference between the minimum temperature and the maximum temperature, if the vertical temperature gradient is invariant.  The 24 hr-observation of the vertical  (  71  -  0.991)(103 temperature distribution was made at Shiozu Bay on September 19,1968, and we  0 TOO 8.00 9.00  1Q00                                       obtained the vertical density distribution curve as shown in Fig. 5. Obviously the  0 •  sharp interface exists at the depth of 17.5m, so we can consider the density  struc-  20   ture of this lake as two layer at that time. From the curve in Fig. 5, we obtained a  30   Soot  19.  1968  density difference between the upper layer  (at  Shiozu  soy) and the lower hlayer as follows :— 40 -   dp=        1Th.h,1ith     ,p(z)dz--.1p(z)dz500 12                   —    of= 2.211 163(vcc)       =2.211 x  10-3  (g/cm3)  60(m)-where  11,  h' denote the thickness of the upper layer and the lower layer respec-                                             Fig. 5 Vertical density distribution                                               at Shiozu Bay calculated from thetively. vertical temperature distribution  The fudamental period of the longitudinal curve. and transverse internal seiches in the two layered rectangular lake are given by the well-known formulas21:—               T1=2L,V p(h +It') (1)  gdp•Ith'                           p(+1f)         T c=2B1h(2)  gdp•hht  The meaning of the symbols in the formulae are shown in Table 1.                   Table 1. Equivalent size of north basin of Lake Biwa.               Latitude Length  I Mean breadth Mean depth Depth of  thermochne   Symbol  Equivalent size  35°20'  50  km  12  km  50  m 17.5  m  When the motion of lake water is under geostrophic effects, it has been said that the period of the internal seiches,  To is given by the following formula  :—         1 1 + 1(3)  TtzT,2 where T, denotes the period of half a pendulum-day.24 S. KANARI  By using the values given in Table 1, we evaluated the periods of the long-itudinal and transverse internal seiches and the period of transverse internal seiche under geostrophic effects in Lake Biwa, with the formulae of (1), (2) and (3). The results are shown in Table 2, together with the period of the inertia circulation in Lake Biwa.  As shown in Table 2, the theoretical period of the longitudinal internal seiche without the geostrophic effects coincides with that of the rough estimation in Fig. 4, and we may conclude that the large temperature variations with long periods in  Fig.  3 are caused by the longitudinal internal seiche due to the wind.  The maximum velocity of water in the lower layer induced by such an internal seiche, will occur in the middlle part of the lake and it will be estimated in the following form :—                             2                IPhiLmast=TzICot I (4) where  Co' is the amplitude of the internal oscillation of the thermocline at both ends of the lake. As described in section 3, the displacement of the thermocline is about 10 m. Then,  Co' takes the value of 5 m. Therefore, we obtain I  U'mari  =8  cm/sec.              Table 2. Periods of various internal seiches in Lake Biwa.                                       I                    Longitudinal TransverseUnderPeriod of                                                         geostrophic  I inertiaSymbol Ti  Tt  To   Calculated period 55.83 hr 13.33 hr 11.20 hr 20.7 hr  Observed period 56 hr 9.5-10.5 hr  — 5. Internal Seiche under Geostrophic Effects  Fig. 6 shows the power spectrum (full line) of the temperature variation, obtained by Fourier's analysis with the fundamental period of 112 hr. In the figure, the higher harmonics are shown by the arrows. Except for the signifi-cant period of 56 hr, the amplitudes of every harmonic uniformly decrease with the increasing frequency, in which only one harmonic component of the period of 28  1m has an extremely low amplitude. The dotted line shows a decreasing curve of the power of these higher harmonics, and we consider that the peaks on and below this curve are insignificant as regards the real motions of the lake water.  The dominant peaks exist at the frequencies of 0.018 c/hr (56  hr) and 0.095 to 0.105 c/hr (10.5 to 9.5 hr). The former obviously just corresponds to the longitudinal internal seiche without geostrophic effects. What kind of motion can be considered for the later  peak  ? The only possibility will be found in the transverse internal seiche under geostrophic effects. In contrast to the longitudinal internal seiche, in which the inertia circle may be restricted by the width of the lake, the transverse internal seiche has no restriction towards the longitudinal direction. Consequently, the assumption,2 with which the formula (3) has been derived, will be satisfied. The calculated period is shown in                  Internal Waves in Lake Biwa  (I) 25  10.0—                          56 hr                                19  ^ en  Sep1.1968  —SUGAURA       w  It        -1 1.0- 27.3 hr  CC  •                    ,  ie  hr                                                           14 hr.      N  Z                                             11216.9.316. "  1.013hr.                              1 o  4  to  26hr.                 0.1 —            I  I     A           0 0.02 0.04 0.06 0.06 030 0.12 0.14 0.16                                      FREQUENCY  ( c/hr)       Fig. 6 Power spectrum of the temperature variation, obtained from Fourier's        analysis method with the fundamental period of 112 hr. The higher harmo-        nics are shown by the arrows. Table 2 as  To. In this case, the maximum velocity in the lower layer is also estimated by the following formula  Uo 2B  =I        gg(5) taking the values of (The amplitude of the transverse internal oscillation of the thermocline on both sides of the  lake.)  -2.5  m,  7  =10  hr,  B=12 km and h' =32.5 m. Then, we obtain I  U,Ciail  =5  cm/sec, which is almost comparable to the maximum velocity of the longitudinal internal seiche without geostrophic effects. 6. Concluding Remarks  From the preliminary investigation of internal waves in Lake Biwa, we ob-served large temperature variations in the thermocline- layer. These variations involve two types of dominant periodic changes of water temperature. One has a period of 56 hr and the other has a period of 10 hr. It was found that the periodic change of the period of 56 hr corresponds to the longitudinal internal seiche of the north basin, caused by the northerly component of the wind, which had blown over the lake during an interval of about 24  hr, and that the periodic change of the period of about 10 hr corresponds to the transverse internal seiche under geostrophic effects (This period does not agree so well with the calculated one).  In section 5, we calculated the maximum velocity of water in the lower layer26 S. KANARI and we obtained  U,'  mar  =5 cm/sec. This means that the ratio of the mean breadth to the diameter of the inertia circle  is  :—                       B                             2r =6'6where r is the radius of the inertia circle.  In formula (3), if we take the period of longitudinal internal seiche for  Tz, then the ratio of the mean breadth and the diameter of the inertia  circle') becomes about 2.2, which is not so large. Smallness of this ratio suggests that the motion of the longitudinal internal seiche under geostrophic effects cannot be free from the width of the lake. Consequently, we concluded that the coexistence of the longitudinal internal seiche without geostrophic effects and the transverse internal seiche under geostrophic effects may be consistent, and, that in narrow lakes of great length, formula (3) should not be applied to the longitudinal internal seiche, but applied to the transverse internal seiche only.                            Acknowledgements  The author wishes to express his sincere appreciation to Professor S. Okuda of Kyoto University for his cordial encouragement, and to Mr. T. Imazato of the Geophysical Institute of Kyoto University, who provided whole-hearted help in the construction of the program for the computation of Fourier's Analysis.  His thanks are also due to Mr. K. Yokoyama of our institute for his sincere help in the field work.  This investigation was partly supported by the Science Research Fund of the Ministry of Education and thanks are due to the Ministry for assisting this investigation.                                References  1) Okamoto,  I.: Time Variation of Water Temperature in Lake Biwa-ko (II), Mem. Fac.      Educ., Shiga Univ., 18, 1968,  pp.  53-64.  2) Proudman,  J.: Dynamical Oceanography, John Wiley and Sons,  Inc, New York, 1953.  3) Mortimer,  C.  H.: Some Effects of the Earth's Rotation on Water Movements in Stratified      Lakes, Proc. of the Intern. Assoc. of Limnology, Vol. XII, 1955.

Internal Waves in Lake Biwa (I) -The Responses of the Thermocline to the Wind Action-

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Internal Waves in Lake Biwa (I) -The Responses of the Thermocline to the Wind Action-

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