Effects of Critical Minimum Depth in the Coastal Region on Storm Surges using a Three-Dimensional Numerical Experiment

Kor J Fish Aquat Sci 47(2),168-173,2014 한수지 47(2), 168-173, 2014

Original Article

168

Copyright © 2014 The Korean Society of Fisheries and Aquatic Science pISSN:0374-8111, eISSN:2287-8815

서 론

해양에서해수순환을모사(simulation)^{할때모델계산임계수} 심(^{이하임계수심}, critical depth) ^{설정과관련하여수치적불안} 정이발생하는경우가있다. ^{물론수치실험에서임계수심을설} 정하는것은수치실험수행상, ^{육지와바다를구분하여수치계} 산의편리성을도모할필요가있기때문이다. 그러나자유표면 을허용할경우, ^{운동계내에서해면변위의진폭의대소와관련} 하여임계수심설정이문제가될수있을것이다. ^{보통광역해양} (^{북서태평양})^{에서의수치실험에서는편의상최저수심으로} 1 m 를설정하는경우도있으나(Hong and Yoon, 2003), ^수심이수 미터에불과한연안역에서는현실적인지형재현측면에서이 런값을설정하는것은곤란할것이다. ^{그럼에도불구하고}, ^적절 한임계수심설정에대한수치실험적조사자료가부족하고, ^이 에대한연구또한매우적은것같다. ^{특히태풍통과시처럼수} 일간의강력한외력이작용할때발생하는수치적불안정에대 해서는국내외적으로거의조사된바가없는것같다.

본연구에서는시험조사해역으로한국남해역완도만(Fig. 1) 을설정하고, 3^{차원원시방정식을이용한} 3D ^모델(the Princ-

eton Ocean Model, POM)^{을사용하여태풍이동경로의다양성}

을고려한 case-study에의해연안역해수순환수치실험에적절

한임계수심을조사하였다. ^{연구주제가연안역수치실험과관} 련, ^{다소세밀한기술적주제이긴하나이분야의연구결과가매} 우적어실제적으로수치실험을수행하는경우참고자료를제 공할수있을것으로예상된다.

자료 및 방법

수치모델

본연구에사용된모델은 Blumberg and Mellor (1987)가개 발한 POM (Princeton Ocean Model)^이며, ^{북태평양에서태풍} Holly에대한해수반응을조사한 Hong and Yoon (2003)(이후 로는 HY^라함)^{과기본적으로같다}. ^다만, ^{본연구목적에맞게}, 연구해역, ^모델태풍, ^{연직레벨수등을변형하여사용되었다}. 그중요부분만간략히정리하면, 연직레벨수는 26개의시그 마층으로서, x, y ^{방향격자간격은각각} 20 km^이다. ^초기조건 에서, 연직수온은표면수온(27℃)로부터지수함수적으로감소 하고, ^{염분은편의상} 34.5 psu^{로일정하게주어진다}. ^남쪽및동

폭풍해일 예측 수치실험에 미치는 연안역 임계최소수심의 영향

홍철훈

부경대학교 해양생산시스템관리학부

Effects of Critical Minimum Depth in the Coastal Region on Storm Surges using a Three-Dimensional Numerical Experiment

Chul-Hoon Hong

Division of Marine Production System Management, Pukyong National University, Busan 608-737, Korea

The effect of critical minimum depth in the coastal region on storm surges was examined using a three-dimensional primitive equation model (POM). Case studies using numerical experiments in a small coastal bay in the southern sea of Korea (Hanam Bay) have examined the ‘critical depth’ (CD) that stabilizes the numerical calculations. De- pendence of the CD of typhoon tracks and tidal components such as M2, S2, O1, and K1 were examined. The model results clearly demonstrated that the numerically unstable state of the calculation was caused by the coarse resolution of sea surface elevation.

Key words: Typhoon, Unstable state, Critical depth, Tidal components, Sea surface elevation

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial Licens (http://creativecommons.org/licenses/by-nc/3.0/)which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

http://dx.doi.org/10.5657/KFAS.2014.0168 Kor J Fish Aquat Sci 47(2) 168-173, April 2014 Received 10 January 2014 Accepted 3 March 2014

*Corresponding author: Tel: +82. 51. 629. 5890 Fax: +82. 51. 629. 5885 E-mail address: [email protected]

수치실험에 미치는 연안역 임계최소수심 169

쪽개방경계에서, ^{내부법선속도는} Sommerfeld ^방사조건, ^수 위는외부개방경계조건, 수온및염분은 slippery 조건에의해 결정된다. ^{모델을단순화하기위해해면을통한열교환은무시} 하고, 또대마난류와같은기본류도무시하였다(POM 모델구 성에대한보다상세한것은 Mellor (1996)^{를참고할것}). ^모델

해역은한국남해역해남만(Fig. 1)^으로서, ^{이해역의주요조석}

은 Table 1과같으며, 최대조류속도는 84.47 cm/s (Jang, 2006), 또 M₂^{조가이해역의조석진폭의약} 70%^를점하며(KORDI, 1996), 실제임계수심은 0.1 m이다. 대기조건에있어, 태풍의 기압은전통적으로흔히사용되고있는 Fujita (1952) ^식, ^바람 은 Miyazaki et al. (1961)^{의식을적용하였다}(^{보다상세한것은} HY 참조). 태풍경로는편의상해남만을중심으로좌, 우및중 앙을통과하는세경우(Fig. 2)^에대해 case-study^{를수행하였} 다. 태풍에대한기상조건은세경우모두동일하게주어진다. 즉최저중심기압(970 hpa), ^이동속도(3.7 m/s, ^상수) ^각경우동

일하게주어지고, ^{제주남방약} 30°N^{에서출발하여} 60^시간뒤

에는소멸한다. 실험수행은, 일정한시간스텝(3 s) 조건하에, 계 의최초임계수심을 0.1 m^{로설정하고수치불안정발생여부를} 점검하면서그수심을 0.1 m 씩증가시켜안정적으로계산이수

행되는적절한임계수심을결정하였다. ^{이러한실험을조석}, ^태 풍의경로등에따라각각수행하였으며, 조석만을고려한경우 (Case I), ^{태풍과조석을동시에고려한경우}(Case II) ^등 Case-

study를수행하였다. 특히, 이러한외력에따른임계수심이변

동되는것은우선적으로실험계에외력이작용할때해면변위

를분해(resolution)^{할수있는적정수심이임계수심과밀접히}

관계될것으로예상된다. 각경우에대한조건들을 Table 2에서

제시하였다. ^{실험은조석의각분조별}, ^{태풍경로별로각각조사} 되었으나분류편의상, 조사한실험을포괄적인그룹으로분류 하여단순화하여표기하였다.

결 과

Table 3^{은조석만고려하면서}, ^{조석분조를순차적으로증가시}

켜얻어진수치적으로안정된수심및시간스텝( 3 s) ^수 의관계를보여준다(Case I). ^예로서, M₂^{조만외력으로사용한} 경우, ^{설정임계수심이} 0.1 m^인경우 2169 ^시간스텝, ^즉수치계 산시간을 1.8시간을채지속하지못하고계산이비정상종료되 었으나임계수심을점차늘려 1.0 m^{에이르자정상종료되었다}.

따라서 M₂^{조만고려한경우는} 1.0 m^{가안정적으로계산이가}

능한임계수심임을보여주었다. ^{또각분조를늘려갈수록임계} 수심은다소증가하여, S₂^{조를추가한조건에서의실험은임계} 수심이 1.3 m로, K₁조 O₁조를추가로포함했을때는 1.4 m가되 Table 1. Principal tidal harmonic constants at Haenam Bay

M₂ S₂ K₁ O₁

A (cm) κ (° ) A (cm) κ (° ) A (cm) κ (° ) A (cm) κ (° )

116.06 297.9 51.44 334.6 24.06 199.6 20.53 178.7

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36 24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step

M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m) ^{1.4 1.5 1.6}

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)

Fig. 1. Model bathmetry (meter). The mimimum depth in the bay is 0.1 m having two open boundaries in the south and the west.

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36 24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step

M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m) ^{1.4 1.5 1.6}

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)

Fig. 2. Tracks of typhoons. Meteorological conditions of typhoons, such as moving speeds, air pressures, and winds are equivalently given in each case (see the contexts for the details).

170 홍철훈

었다. ^즉, ^{조석만을외력으로사용할경우}, ^외력(forcing)^의수가 늘수록안정적인계산임계수심도증가하는경향을보였다. 한 편, ^{본실험에서는} 18,000 ^시간스텝(15^시간)^{이경과되면더이} 상수치적불안정은발생하지않았다.

Fig. 3^은 Table 3^{에서비정상계산종료시간시텝수와임계수}

심과의관계를보다더잘보여준다. ^즉, ^{임계수심을} 0.7 m ^미만 으로설정했을경우는조석외력조건과관계없이 2,000 시간스 텝(100^분)^{을초과하기전에계산이모두도중종료되는경향을} 보여주었으나, 0.9 m^{를상회하면서각분조에대해급격히안정} 된계산모드로전이되는경향을보여주었다. M₂^조의경우, ^임

계수심 0.9 m-1.0 m ^{사이에서안정적인계산모드로급전하였}

으나, 외력(S₂+K₁+O₁)을추가해갈수록, 예를들면 4대분조를 외력으로사용한경우는안정계산모드로다소서서히 (^임계수 심 0.7 m-1.4 m) ^{바뀌는경향을보여주었다}.

다음으로, Fig. 4^에, ^{태풍의경로}(Fig. 2)^별, ^{연구해역의좌편} (Fig. 4a), ^중앙(Fig. 4b) ^및우편(Fig. 4c)^{을통과한태풍에대해},

각각의분조에대한임계수심과시간스텝수의관계를보여준

다(Case II). 태풍과같은강력한외력이작용함으로인해조석

만고려한경우(Fig. 3)^{보다전반적으로임계수심이증가한다}.

조석만고려한경우의임계수심의범위는 1.0 m (M₂)-1.4 cm (M₂+S₂+K₁+O₁) (Table 3)^{이었으나연구해역의좌편및우편} 통과태풍(LHS)^의경우 1.4 m (M₂)-1.6 m (M₂+S₂) (Fig. 4a) ^범

위를, 중앙을통과한경우다소증가해 1.5 m-1.7 m 정도였으

며, ^{전반적조석만고려한경우보다약} 0.4 m ^{정도증가한경향}

을보였다. 이는태풍통과시압력차로인한해수면상승(inverse barometric effect), ^{모멘텀난류점성효과등으로인해해면상승} 이추가반영된결과로해석될수있다.

따라서실험결과는, 조석과태풍을동시에고려할경우는임

계수심을 1.7 m^{로설정하면안정적인계산을수행할수있음}

을보여주었다. 물론본실험에서주어진태풍의조건(중심기압 970 hpa, ^이동속도 3.7 m/s ^등)^{보다태풍의강도가증가하면이} 값은더증가할것이다.

흔히편의상, 조석을고려하지않고태풍만을외력으로실험 을수행하는경우도있다(Konishi and Tsuji, 1999). ^{연안해수순}

환의모사(simulation)보다해수응답에대한이론적연구에주

안점을둔경우이다. Fig. 5^{는각경로별태풍만을외력으로사}

용한경우, ^{임계수심에미치는태풍경로의의존성을보여준다} (Case III). 이경우임계수심은대체로 0.8 m-1 m의범위를보 였다. ^{이는조석과의공명현상등이제거된결과로해석될수있} 을것이다. 또조석을고려한경우(Fig. 4)와같이, 중앙통과태풍 에대해임계수심이다소커지는경향(0.2 m)^을보였다.

이와같이외력에따라임계수심이변동되는것은우선적으로 실험계에서해면변위를분해(resolution)할수있는적정수심이 임계수심과밀접하게관계되기때문일것으로예상된다. ^즉, ^실 Table 2. Factors of each experiment

EXP* ^{Tide (M}_M ^{2, M2+S2, M2+S2+K1,}

2+S₂+K₁+O₁) typhoons (LHS, RHS, CNT)

CASE I involved excluded

CASE II involved involved

CASE III excluded involved

* Note that each experiment represents one group that binds sev- eral experiments implemented with each tide (M₂ only or M₂+S₂ etc.). LHS, RHS, and CNT represent typhoon-track’s types in left hand side, right hand side, and the center over the center of Hanam Bay.

Table 3. A critical depth (CD) and a number of time steps in Case-I

C. depth (m) M2 M2+S2 M2+S2+K2 M2+S2+K2+O2

0.1 2,169 1,988 1,983 2,059

0.2 1,991 1,842 824 681

0.3 1,984 1,848 1,927 1,991

0.4 2,056 1,975 2,082 2,111

0.5 2,240 2,022 2,120 2,216

0.6 2,392 2,081 2,192 2,292

0.7 2,542 2,241 2,409 2,564

0.8 2,665 2,368 2,477 6,312

0.9 2,857 2,381 2,600 10,723

1.0 18,000 (15 h) 2,476 13,961 17,204

1.1 2,657 14,100 17,271

1.2 14,088 17,398 17,358

1.3 18,000 17,568 17,485

1.4 18,000 18,000

수치실험에 미치는 연안역 임계최소수심 171

험계에서해면변위의진폭이해저를느낄만큼커지면제대로 해면변위를분해한다할수없음으로계산불안정이발생하여 정지된다고볼수있을것이다. Fig. 6^{에서이러한추론을확인} 할수있다. ^즉, ^정점 1 (Fig. 1)^{에서각태풍경로별시간스텝수} 와해면변위관계를볼때연구해역의좌측통과태풍(LHS)의경 우(Fig. 6a), ^{임계수심이} 80 cm^{일때끝까지}(18,000 ^시간스텝) 정상적으로계산이수행됨을알수있다. ^{그러나임계수심이이}

보다작을경우(^예를들면, 70 cm)^{는태풍이조사해역에접근해}

옴에따라증가하는해면변위(^{특히음의변위})^{를충분히분해하} 지못하고(12,000 시간스텝부근, 즉계산시간 10시간에서) 수 치적불안정을일으켜계산이종료됨을알수있다. ^{따라서임계} 수심을작게잡을수록수치적불안정이더이른시기에발생된 다. ^{우측통과태풍}(Fig. 6b)^{은태풍이접근할수록해수가만외} 측으로빠져나가게되므로정점에서전반적으로수위가낮아 지는경향을보여해면변위변화양상은좌측통과태풍(Fig. 6a) 과다소다르나임계수심분해와계산불안정발생과정은유사 한양상을보여, ^{임계수심을작게설정할수록계산불안정은이} 른시기에발생하였다. ^한편, ^{중앙통과태풍}(Fig. 6c)^은보다직 접적인태풍의영향을받게되므로해면변위의변화양상이다 소복잡하고, 임계수심도 1.0 m로서다른경로에비해증가하 였다. ^{이상의결과로볼때}, ^{임계수심선정은외력에의해해면} 변위(^{특히음의변위})^{를분해할수있는범위내에서선정되어} 야함을확인할수있었다.

결론 및 고찰

3^차원(3D) ^{원시방정식모델}(POM)^{을이용하여}, ^{수심이수미} 터이내의매우낮은연안내만(^해남만)^{에서태풍통과시해저지}

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36 24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step

M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m) ^{1.4 1.5 1.6}

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)

Fig. 4. Same as Fig. 3 except for experiments driven by both tide and typhoon. a) LHS-type b) RHS-type, and c) CNR (center) in the passage of typhoons.

Fig. 3. Relationship (Case I) between CD and time steps in 3D numerical experiments driven by each tidal forcing, e.g., M₂repre- sents that the model is driven only by M₂; M₂+S₂ driven by M₂+S₂ etc.

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36

24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step

M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m) ^{1.4 1.5 1.6}

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)

172 홍철훈

형과관련, ^{발생하는계산불안정을없애고수치적안정성을확} 보하기위한적정임계수심을조사하였다. ^그결과, 1) ^수치계 산불안정의임계시간은계산수행후 15^시간(18,000 time step;

△t=3 s)이었다. 즉이시간이경과되면계산불안정은발생하

지않았다. 2) ^{외력의조석분조수가증가할수록임계수심도증}

가하는경향을보였다. 3) ^{태풍의경로에도의존하여조사해역}

을정북으로통과하는경우에최대임계수심(1.7 m)^을보였다.

4) ^{계산불안정은실험계에서해면변위를분해하지못함으로} 발생하였다. 따라서임계수심은해면변위를분해할수있는수 심에해당된다.

해수순환수치실험에서수치적계산불안정은다양한형태로

발생한다. ^{가장흔한예는모델격자간격}(△s )이실험계의가장

빠른파(^{보통중력파})^{를분해하지못할때}(^즉 LPL ^{조건을만족} 하지못할때) 발생한다(e.g., Mesinger et al. 1978). 즉, 중력파 의이동으로발생하는에너지전파를실험계가분해할수없다 면분해할수없는만큼실험계의에너지손실이발생, ^결국실 험계에서에너지보존법칙을만족할수없게되므로발생한다. 또유한차분법을이용할경우, ^{고계미분항을무시한차분식만} 을사용하면앞서와같은맥락에서계산불안정이발생한다. 이

외에도본연구에서사용된 3D ^모델(POM)^{에서도열확산에적}

절한경계조건을부과하지않으면발생할수있는계산불안정 도있다(Mellor et al., 1996). ^{모두열역학제}1^법칙(^{에너지보존} 법칙)^{을만족하지못해서이다}.

본연구에서는수치실험상적절한임계수심을조사하였다. 외 양에서의수치실험의경우는임계수심(^보통 1 m-2 m; Hong and Yoon, 2003)^{이수치계산에별영향을미치지않는것같다}.

그러나연안내만의경우는수심이 1-5 m (^예를들면, ^해남만;

Fig. 1)^{로얕은곳이보통이므로}, ^{최적해저지형을표현해야하}

는수치실험목적상, 임계수심을간단히결정하기어렵다. 본 실험을수행하게된동기가여기에있다할것이다.

Fig. 6. Relationship between sea surface elevation and a number of time steps according to typhoon tracks (a) LHS, (b) RHS, and (c) CNR. Numerals represent the minimum depths.

Fig. 5. Same as Fig. 3 except for typhoons only used as forcing.

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36 24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step

M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)

22′N

20′N36′E 38′E 40′E 42′E

34°

126°

24′N 26′N

0 1km

Namchang-ri

Ijin-ri Daldo Is.

Shinheung

Wondong

Dangin-ri

Haenam Gun

Wando Is.

Temperature (°C)

60 48

36

24

12 980

970 970

980 1005

0hr 1005hpa 38

40°N

36 34 32

30

120 123 126 129 132 135°E

M2+S2+K1

M2+S2 M2

0 2,000 6,000 10,000 14,000 18,000

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Depth (m)

Time step M2+S2+K1+O1

0.2

0 0.4 0.6

Depth (m)

0.8 1

0 2,000 6,000 10,000 14,000 18,000

Typhoon, RHS

Typhoon, LHS

Typhoon, Center

Time step

Elevation (cm)

2,000 20

10 30

40 50

60

70 80 cm

0 6,000 10,000 14,000 18,000

0 -60 -40 -20 20 0

(a) 40

Time step

Elevation (cm)

00 2,000 20

10

30 40

50

60 70

80 cm

6,000 10,000 14,000 18,000

-60 -30 0 -10

(b) 10

Time step

Elevation (cm)

00 2,000 2010

30 40

50 60

70 80 90

100 cm

6,000 10,000 14,000 18,000

-60 -40 -20 20 0 40

(c) 60 0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

1.1 1.2 1.3 1.7

Depth (m)

Time step

1.4 1.5 1.6

(a)

1.1

1 1.2 1.3

Depth (m)

1.4 1.5 1.6

Time step

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2 M2

(b)

Time step

1.1

1 1.2 1.3

Depth (m) ^{1.4 1.5 1.6}

0 2,000 6,000 10,000 14,000 18,000

M2+S2+K1

M2+S2+K1+O1 M2+S2

M2

(c)