* ᖙ᳦ݡ⦺Ʊ Õᖅ⪹ĞŖ⦺ŝ ၶᔍŝᱶ ([email protected])
*** (ᵝ)ݡᩢᨵḡܩᨕย ⧎อᇡ ݡญ ([email protected])
Received November 20 2012, Revised February 15 2013, Accepted May 22 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵ǤͶǤͳͶͶ Ǥ ǤǤ
≾⟖⢪⮎⛚ⴖ#㬫⺺㣊#㣊㯓#⯆㏟#⇍#IORZ06G⮎#ⴖ㬚#ሾ⽛
ଲࣦ ȵଲఢผ ȵ୍ ȵճֈૈ
Lee, Byeong Wook*, Lee, Changhoon**, Kim, Yong Jae***, Ko, Kwang Oh****
Prediction of ship wave Crests on Varying Water Depths and Verification by FLOW-3D
ABSTRACT
In this study, we developed the equation of ship wave crests in intermediate as well as deep waters by extending Kelvin’s (1887) theory using the recursive relation for the dispersion relation. The present equation can be applied for varying water depth as well as constant water depth. Using FLOW-3D we conducted numerical experiments to verify analytical prediction. The ship wave crest patterns became asymmetric on a plane slope when the ship propagates alongshore direction. That is, in shallower side, wave crests tend to be parallel to the coastline due to refraction and, in deeper side, wave crests tend to be orthogonal due to reverse refraction.
Key words : Ship wave crest, Cusp locus angle, Intermediate water depth, Varying water depth, Dispersion relation, FLOW-3D
Ⅹಾ
ᅙᩑǍᨱᕽᖁ⩶ᇥᔑšĥ᮹ᙽ⪹šĥෝᯕᬊ⦹ᩍKelvin (1887)᮹ᯕುᮥ⪶ᰆ⧉ᮝಽ៉ᝍ⧕ᐱอᦥܩᵲeᙹᝍʭḡᱢᬊa܆⦽⧎ᵝ❭
᮹❭⩶ᮥᩩ⊂⦹۵ᯕುᮥ}ၽ⦹ᩡ݅. ᅙᯕುᮡᯝᱶᙹᝍᐱอᦥܩ᪥Ğᔍ᮹ᄡᙹᝍᨱࠥᱢᬊa܆⦹݅. ᅙᩑǍ᮹⧕ᕾ⧕ෝá᷾⦹
ʑ᭥⦹ᩍFLOW-3D༉⩶ᮥᯕᬊ⦹ᩍᙹ⊹ᝅ⨹ᮥᙹ⧪⦹ᩡ݅. ᙹ⊹⧕᪡ᯕು⧕ෝእƱ⧕ᅙđŝ, ᅙᩑǍ᮹ᯕು⧕۵ᯝᱶᙹᝍᐱอᦥܩ
ᄡᙹᝍᨱᕽࠥ⧎ᵝ❭᮹ᱥ❭᧲ᔢᮥᰍ⩥⦹ᩡ݅. ⠪໕Ğᔍ໕᭥ಽ႑a⧕ᦩᖁŝӹ⦹íᱥ❭⦹۵Ğᬑ⧎ᵝ❭᮹ᱥ❭᧲ᔢᯕእݡ⋎ᯕࡹ
ᨩ݅. ᷪ, ᙹᝍᯕ᧶ᮡŔᮡǕᱩಽᯙ⦹ᩍ❭⨆ᖁᯕ⧕ᦩᖁŝӹ⦽Ğ⨆ᯕᯩŁ, ᙹᝍᯕʫᮡŔᮡᩎǕᱩಽᯙ⦹ᩍ❭⨆ᖁᯕ⧕ᦩᖁᨱᙹḢᯙ
Ğ⨆ᯕᯩᨩ݅.
áᔪᨕ ⧎ᵝ❭❭⩶, ↽ݡ❭⨆b, ᵲeᙹᝍ, ᄡᙹᝍ, ᇥᔑšĥ, FLOW-3D
1. ᕽು
Ł·ᗭ⩶ᖁၶ᮹᷾aಽᯙ⦽⧎⧪ኩࠥ᮹᷾a, ʑᚁಆ᮹ၽݍಽᯙ⦽ᖁၶ᮹⧎⧪ᗮࠥ᮹᷾a, əญŁĞᱽᖒᰆŝᇩᨕ༉░ᅕ✙ӹ
✙॒᮹ษญӹ⪹Ğ᮹᳑ᖒ॒ᮝಽᗭ⩶ᖁၶŝᱲᦩ⦹ᩍ⦹ᩎᵲᯙᖁၶ᮹ᦩᱥྙᱽ, ⧎อᖅ᮹❭ᗱ॒᮹ྙᱽaၽᔾ⦹Łᯩ݅.
ᦩᱥᖒ ⪶ᅕ᪡ ⧎ԕ ᱶ᪉ࠥ ᮁḡෝ ᭥⦹ᩍ ⧎ᵝ❭ ᱥ❭ᨱ ݡ⦽ ᩑǍa ⦥⦹݅.
⧎ᵝ❭۵ᖁၶᯕᯕ࠺⧁ভၽᔾ⦽❭௲ᮝಽ❭⨆ᮥᖁၶ᮹᳭ᬑಽᱥ❭⦹۵᳦❭(diverging wave)᪡ᖁၶ᮹अᨱᕽ⧎ᱢᵲᝍᖁᮥ
aಽḡ۵⩶┽ಽᱥ❭⦹۵⬂❭(transverse wave)ಽǍᇥ⧁ᙹᯩ݅. ⧎ᵝ❭᮹❭Ł۵ᙹᝍ, ᖁၶ᮹Ⓧʑ, ᖁၶ᮹ᗮ॒ࠥᨱ
३؋ф२χėॡ
Fig. 1. Ship wave pattern (Kelvin, 1887)
݅໑ ❭⨆ᮡ ᙹᝍ, ᖁၶ᮹ ᗮࠥ ॒ᨱ ݅݅.
⧎ᵝ❭ᨱš⦽ᩑǍ᮹ݡᇡᇥᮡ᳑ᖁŖ⦺ᇥᨱᕽᙹᝍᯕᯝᱶ
⦽᳑Õ⦹ᨱᯕᨕᲭ݅. ⧎ಽ᮹ᙹᩎᯕմᮡĞᬑ⧎ᵝ❭᮹ᨱթḡ aᬱᱱ(source point)ᨱᕽᵝ᭥ಽ⟝ḡ໕ᕽᨱթḡaqᗭ⦹ᩍ
ᦩᱥᖒᨱྙᱽaᨧ݅. ⦹ḡอ⧎ԕӹ᳢ᮡᙹಽ॒ᨱᕽ۵ᦩᱥᖒᨱ
ྙᱽa ၽᔾ⧁ ᙹ ᯩ݅. ᕽ, ᙹᝍᯕ ᧶ᮝ໕ᕽ ᭥⊹ᨱ
ᄡ⦹۵Ğᬑ᮹⧎ᵝ❭᮹ᱥ❭✚ᖒᨱݡ⦽ᩑǍa⦥⦹݅. ḡɩʭ ḡ⧎ᵝ❭ෝ⧕ᕾ⦹۵ᙹ⊹༉⩶ᨱݡ⦽ᩑǍaᯩᨩḡอᄡᙹᝍᨱ ᕽ ⧎ᵝ❭᮹ᱥ❭ ✚ᖒᨱ ݡ⦽ᯕುᱢᯙ ᩑǍa ᨧᨩäᮝಽ
Łᯩ݅. ↽ɝᨱLee et al. (2011)ᮡᯝᱶᙹᝍᨱᕽ⧎ᵝ❭᮹
ᱥ❭᧲ᔢᮥ ᩩ⊂⦹ᩡ݅.
ᅙᩑǍᨱᕽᇥᔑšĥ᮹ᙽ⪹šĥෝᯕᬊ⦹ᩍKelvin (1887) ᮹ႊჶᮥ⪶ᰆ⦽⧎ᵝ❭᮹ᯕುᮥᱽᦩ⦹ᩡ݅. ᷪ, ᝍ⧕ᐱอ
ᦥܩᵲeᙹᝍᨱᕽᱢᬊࡹŁ, ᯝᱶᙹᝍᐱอᦥܩᄡᙹᝍᨱᕽ
ࠥᱢᬊࡹ۵ ⧎ᵝ❭᮹⩶ᔢᨱݡ⦽ ᯕುᮥᱽᦩ⦹ᩡ݅. ੱ⦽, ᅙᩑǍ᮹ᯕುᨱ᮹⦽⧕ෝFLOW-3D᮹ᙹ⊹⧕᪡እƱၰ
á᷾⦹ᩡ݅. ᱽ2ᰆᨱ⧎ᵝ❭᮹❭⩶ᨱݡ⦽ᯕುᮥᱽᦩ⦹ᩡ݅.
ᱽ3ᰆᨱFLOW-3D᮹⧎ᵝ❭᮹ᰍ⩥ᖒᮥá᷾⦹ʑ᭥⦹ᩍ⧎ᵝ❭
᮹↽ݡ❭⨆bᮥᰍ⩥⦽अHavelock (1908)᮹ᯕುŝእƱ⦹ᩡ
݅. ᱽ4ᰆᨱᄡᙹᝍᨱᕽ⧎ᵝ❭᮹❭⩶ᨱݡ⦽ᯕುᮥᙹ⊹⧕᪡
እƱ⦹ᩡ݅. ᱽ5ᰆᨱᩑǍԕᬊᮥᱶญ⦹Ł⨆⬥ᩑǍŝᱽෝᱽ⦹
ᩡ݅.
2. ⧎ᵝ❭᮹❭⩶ᨱݡ⦽ᯕು
⧎ᵝ❭۵ᖁၶᯕ⧎⧪⧉ᮝಽ៉ᙹ໕᮹Ʊᯕၽᔾ⦹۵❭௲ᮝ ಽᖁၶ᮹ᗮࠥၰᙹᝍᨱəⓍʑ᪡⩶ᔢᯕ݅݅. ⧎ᵝ❭᮹
ᬱᱱ(source point)ᮡᖁၶᯕᬡḢᯕ۵อⓝzᯕᯕ࠺⦹အಽ
ᖁၶᯕ⧎⧪⦹۵⧎ᱢᵲᝍᖁᮡᙹฯᮡᬱᱱᮝಽᯕᨕḥᖁᯕ
݅. ⧎ᵝ❭ᨱ۵ᖁၶᮥʑᵡᮝಽᖁၶ᮹अᅕ݅۵᳭ᬑႊ⨆ᮝಽ
ᱥ❭⦹۵᳦❭ॅ᮹❭ᅪŝ ᖁၶ᮹अᨱᕽᱥ❭⦹۵⬂❭ॅ᮹
❭ᅪᮝಽᯕᨕᲙᯩ݅. ᯕ్⦽❭௲ॅᮡ⩥ᰍᱱᨱᕽ⩶ᖒࡽ
❭ᅪॅᯕ ᯕᱥ᮹ ᕽಽ ݅ෙ bᨱ ᕽಽ ݅ෙ ᬱᱱᮝಽᇡ░
ᱥ❭⦹ᩍ⩶ᖒࡽ݅. Figure 1ᨱᕽ❭௲ᯕᬱᱱᮝಽᇡ░❭ᅪʭḡ
ᨕਜíᱥ❭⦹۵ḡᙹᯩ݅. ༉ु❭⨆ᖁॅᮡ⬂❭ੱ۵᳦❭᮹
❭ᅪᖁᨱᙹḢᮝಽอӽ݅. ᩍʑᕽ, ľ۵⧎ᱢᵲᝍᖁŝ❭⨆ᖁᔍᯕ ᮹bࠥෝ᮹ၙ⦹໑,ķ۵↽ݡ❭⨆b(cusp locus angle)ᮝಽ᳦❭
᪡⬂❭aอӹ۵ᱱŝᖁၶᮥᯕᮡᖁ(cusp locus line)ŝ⧎ᱢᵲᝍ ᖁ ᔍᯕ᮹ bࠥෝ ᮹ၙ⦽݅. ᳦❭۵ ⬂❭ᨱ እ⧕ ᖁၶŝ ᳡
aʭᬕᬱᱱᨱᕽᱥ❭⦽äᮥᅝᙹaᯩ݅. ᩩෝॅᨕ,ľ á Ö×Ţ ᮹᳦❭۵⩥ᰍ᮹ᬱᱱᨱᕽၵಽᱥ❭⦽äᯕŁ,ľ á ×Ţ᮹⬂❭
۵ ᪅ e ᱥᨱ ᬱᱱᨱᕽ ⇽ၽ⦹ᩍ ᱥ❭⦽ äᯕ݅.
Kelvin (1887)ᮡᝍ⧕ᨱᕽᱢᬊa܆⦽⧎ᵝ❭᮹❭⩶ᮥ݅ᮭ
ᮝಽ ᱽᦩ⦹ᩡ݅.
ćƖƗ á à ćÎ â ľ ľ á Þņàķß á àķÏľ (1)
ᩍʑᕽ,Ɩ᪡Ɨ۵bbᖁၶᮥʑᵡᮝಽ⧎⧪ႊ⨆ŝəḢbႊ⨆᮹
⇶ᮥ᮹ၙ⦽݅. ᭥ᮡ⧎ᵝ❭a⧎ᱢᵲᝍᖁᮥʑᵡᮝಽ❭⨆bᯕ
ľ á ×Ţ g Ö×Ţᔍᯕᨱ⧎ᵝ❭᮹᭥⊹ෝđᱶ⦹۵ᯕ݅. ᯕᮥ
ᔍᬊ⦹໕Figure 1ŝzᮡ⧎ᵝ❭᮹(ᝅᖁᮝಽ⢽ࡽ) ❭ᅪᖁᮥ
əตᙹᯩ݅. ੱ⦽⬂❭۵❭⨆bᯕľ á ×Ţ g ÐÒíÏÓŢᨱᇥ⡍⦹
Ł᳦❭۵❭⨆bᯕľ á ÐÒíÏÓŢ g Ö×Ţᨱᇥ⡍⧕ᯩ݅. ⬂❭᪡
᳦❭a อӹ۵ ḡᱱᮡ ❭⨆bᯕľ á ÐÒíÏÓŢᯕŁ, ᯕভ ᖁၶᮥ
ʑᵡᮝಽ❭⨆bᯕ↽ݡaࡹŁ(ᷪ, ķ á ÎÖíÑÔŢaࡹŁ) ⧎ᱢᵲᝍ ᖁᨱᕽ aᰆ ມญ ਉᨕᲙ ᯩ݅.
ᅙᩑǍᨱᕽKelvin᮹ႊჶᮥᔍᬊ⦹ᩍᝍ⧕ᐱอᦥܩᵲeᙹ ᝍᨱᕽࠥᱢᬊࡹ۵⧎ᵝ❭᮹❭⩶ᨱݡ⦽ᯕುᮥᱽᦩ⦹ᩡ݅.
ᖁၶᯕᯝᱶ⦽ᗮࠥ®ಽ⧎⧪⧁ভ⧎ᵝ❭۵⧎ᱢᵲᝍᖁᨱᯩ۵
ᬱᱱᨱᕽľ ႊ⨆ᮝಽᱥ❭⦹۵Ǒ❭ᯕ݅. Ǒ❭ᯙᯕᮁ۵⦽
ၵ݅ᨱᕽ❭௲ᨱթḡaᱥ❭⦹ʑভྙᯕ݅. ⧎ᵝ❭۵ᵝʑ᪡ႊ⨆
ᯕ ᕽಽ ݅ෙ ᩍ్ ᖒᇥᮝಽ Ǎᖒࡹᨕ ᯩ݅. ᕽ, ⧎ᵝ❭᮹
ᗮࠥ⡍▱ᖽᮥ ݅ᮭŝ zᯕ ⢽⩥ ⧁ ᙹ ᯩ݅.
ŋ á à ƇćſƅŎ
ć ƉÞƆ â ³ß ƃ ƉƆ Ƈ ãŎƒ à ƉÞ±ľ â ² ľ ßä (2)
ᩍʑᕽ,Ɖ۵⧎ᵝ❭᮹❭ᙹᯕŁ, Ɔ۵ᱶḡᙹᝍᯕ݅. Figure 2ᨱᕽ Þ±ì ²ì ³ß, Þ Ɩì Ɨì Ƙ ß۵ bb Łᱶࡽ ḡᱱŝ ᖁၶᮥ ʑᵡᮝಽ
⦽᳭⢽ᯕ݅.± á Ɩ â® ƒì ² á Ɨ ì ³ á Ƙ ᯥᮥᙹaᯩ݅.
(2)ෝᖁၶᮥʑᵡᮝಽ⦽᳭⢽ಽ⢽⩥⦹໕݅ᮭŝzᮡ⧎ᵝ❭᮹
ᗮࠥ⡍▱ᖽᯕ ᱶ᮹ࡽ݅.
ŋ á à ƇćſƅŎ
ć ƉÞƆ â Ƙß ƉƆ ƃƇ ãÞŎ à Ɖ® ľßƒàƉÞƖ ľ â Ɨ ľ ß ä(3)
Fig. 2. Coordinates to express ship wave pattern ᖁၶᮥ ʑᵡᮝಽ ⧎ᵝ❭᮹ ❭⩶ᮥ ᅕ໕ eᨱ ḡӹࠥ ᄡ⦹ḡ
ᦫᮝအಽ(stationary) ݅ᮭŝ zᮡ šĥᮥ ᮥ ᙹ ᯩ݅.
ƕ á Ɖ® ľ (4)
᭥ᮥ❭௲᮹ᖁ⩶ᇥᔑšĥᨱݡ᯦⦹໕݅ᮭŝzᮡ⧎ᵝ❭᮹
ᇥᔑšĥᮥ ᮥ ᙹ ᯩ݅.
Ɖ á ćÞ® ľßÏ
ƅ ƉƆ (5)
ᯕ ᮡ ᝍ⧕ᨱᕽ ݅ᮭŝ zᯕ ࡽ݅.
Ɖ×á ćÞ® ľßÏ
ƅ (6)
Kelvin (1887)ᮡᝍ⧕ᨱᕽ᮹❭ᙹƉ×ෝᔍᬊ⦹ᩍ⧎ᵝ❭᮹❭⩶ᮥ
ᱽᦩ⦹ᩡ݅. Łᱶᱱၹᅖჶᮥᔍᬊ⦹ᩍᙽ⪹šĥᨱ᮹⦽⧎ᵝ❭᮹
❭ᙹෝ ݅ᮭŝ zᯕ Ǎ⦽݅.
ƉƇá Ɖ×ÞƉƇ àÎƆß ì Ƈá Îì Ïì z (7)
᮹ ᱥ❭ෝ ݅ᮭŝ zᯕ ⢽⩥⧁ ᙹ ᯩ݅.
Ł(4)ෝ(8)ᨱݡ᯦⦹ŁƉÞľßᨱݡ⧕ᩑᘥჶ⊺ᮥᱢᬊ⦹໕
݅ᮭ ᯕ ᮁࠥࡽ݅.
ćƂľƂ ãƉÞƖľ â Ɨľßä á × (9)
᭥ᮥƗîƖᨱݡ⧕ᱶญ⦹໕݅ᮭŝzᮡᯝၹ⪵ࡽᮥᮥ
ᙹ ᯩ݅.
ćƖƗ á ć
Ɖľ â ćƂľƂƉ ľ Ɖľ à ćƂľƂƉ ľ
(10)
᭥ ᨱᕽ ❭ᙹƉᨱ ᝍ⧕ᨱᕽ᮹ ❭ᙹƉ×ෝ ݡ᯦⦹໕ (1)ᮥ
ᮥᙹᯩ݅. (6)ᮥ(10)ᨱݡ᯦⦹໕ᅙᩑǍᨱᕽ}ၽ⦽
ᝍ⧕ᐱอᦥܩᵲeᙹᝍʭḡᱢᬊa܆⦽↽ݡ❭⨆bᯕುᮥ
ᮥ ᙹ ᯩ݅.
ÞćƖƗßƇá ćÏľ âÏÏľÞÎ âƌƇß
ľľ à ÏľľÞÎ âƌƇß
áà ķ ì (11) Ƈ á Îì Ïì z
ᩍʑᕽ,
ƌƇá Ē ē Ĕ
ĕ ĕ
ćÏƉ×ƆÏƉ×Ɔ
ì Ƈ á Î
ćÞÏƉƇ àÎƆß ÏƉ×Ɔ ÞƉƇ àÏƆß
ÞÎ â ƌƇ àÎß ì Ƈ á Ïì Ðì z (12)
᳦❭᪡⬂❭aᱥ❭⦹۵❭⩶ᮥᱶ⪶⯩⢽⩥⦹ʑ᭥⧕ᕽ(11)ᮥ
Ɩ᪡Ɨᨱ ݡ⦽ ݅ᮭ ᮝಽ ⢽⩥⦹ᩡ݅.
ƖƇá ćÑÎ
ÞƉƇ àÎƆß
Òľ à Ðľ â ÏÞľ à Ðľß ƌƇ
ì (13) Ƈ á Îì Ïì z
ƗƇá ćÑÎ
ÞƉƇ àÎƆß
à Þľ â Ðľß à ÏÞľ â Ðľß ƌƇ
ì (14) Ƈ á Îì Ïì z
ᩍʑᕽ, ᔢᙹ۵⧎ᵝ❭᮹Ⓧʑෝđᱶ⦽݅. Havelock (1908)ᮡ
Froudeᙹෝ ݅ᮭᮝಽ ⢽⩥⦹ᩡ݅.
Ɛá ćöćƅƆ
® (15)
⧎ᵝ❭᮹ᇥᔑšĥᯙ(5)ෝ(15)ᨱݡ᯦⦹໕ᔢݡᙹᝍŝ
Froudeᙹ᮹ šĥෝ ᙹ ᯩ݅.
(a)Fr < 1 (b) Fr > 1 Fig. 3. Ship wave patterns in theory (upper) and by FLOW-3D (lower)
Ɛá ćö® áćƅƆ ćľÎ öććƉƆÎ ƉƆ (16)
ᩍʑᕽ,
Ɛá Ē ē Ĕ
ĕ ĕ
ćľÎ öććƉƆÎ ì ƉƆ ð ņ
ćľÎ
ì ƉƆ ï ćÎ×ņ (17)
᭥ ᨱᕽ ⧕(ƉƆ ï ņîÎ×)᮹ Ğᬑ Froudeᙹa ⧎ᔢ 1ᅕ݅ ⓑ
äᮥᙹᯩŁ, ᝍ⧕᮹(ƉƆ ð ņ)Ğᬑ݅ᮭŝzᯕᥙᙹᯩ݅.
ƉƆ á ćƐÏ Î ćÏľ
Î ð ņ (18)
᭥ᮥᅕ໕ᝍ⧕ᨱᕽᯥ᮹᮹Froude ᙹᨱݡ⧕ľa᷾a⧁ᙹಾ
ƉƆa᷾a⦽݅. ᷪ, ľa×ŢᯝভƉƆaaᰆ᯲ᮝအಽᝍ⧕ᨱᕽ Froudeᙹaᱢᬊa܆⦽ჵ᭥۵ƐïöćÎîņ á ×íÒÓÑaࡽ݅.
(13), (14)ᨱᕽƇ á Îᯝভᝍ⧕᪡⧕᮹Ğᬑᨱᇥ༉abb
1ŝƉ×ƆaࡹŁ, ၹᅖ⬀ᙹƇa᷾a⧁ᙹಾᝍ⧕᮹Ğᬑᇥ༉۵
1ᯕḡอ⧕᮹Ğᬑᨱᇥ༉۵ÞƉ×ƆßƇಽɪĊ⦹í᯲ᦥᲙ⧕ᕾ⧕a
ᙹಕ⦹۵äᨱ⦽ĥaᯩ݅. ᕽ, ᅙᩑǍᨱᕽ}ၽ⦽ᯕು
(11)ᮡ ⧕ᩢᩎᮥ ᱽ⦽ ᝍ⧕᪡ ᵲeᙹᝍᨱᕽ ᱢᬊ a܆⧉ᮥ
ᩩ⊂⧁ᙹᯩ݅. Havelock (1908)ᮡFroudeᙹa1ᅕ݅ⓑĞᬑ(ᷪ,
⧕᮹Ğᬑ) ⬂❭۵ᔍḡ໑᳦❭อᯕ᳕ᰍ⦽݅Łᙹ⦺ᱢᮝಽ
ၾ⩵݅.
(11)ᮡᯝᱶᙹᝍᨱᕽᱢᬊࡹ۵ᯕḡอᄡᙹᝍᨱᕽTaylor ɪᙹ᮹0₉ɝᔍsᮝಽ⢽⩥ࡽᯕʑࠥ⦹݅. ᱽ4ᰆᨱᕽᝍ⧕ᐱอ
ᦥܩᵲeᙹᝍʭḡᱢᬊa܆⦽⧎ᵝ❭᮹❭⩶ᮥFLOW-3D᮹ ᙹ⊹ᝅ⨹đŝ᪡እƱ⦹ᩍᄡᙹᝍᨱᕽ⧎ᵝ❭᮹❭⩶ᮥá᷾⦹ā݅.
3. FLOW-3Dෝᔍᬊ⦽↽ݡ❭⨆bᰍ⩥
Kelvin (1887)ᮡᝍ⧕ᨱᕽ᮹↽ݡ❭⨆bᮥ(1)ᮥᔍᬊ⦹ᩍ
ᱽᦩ⦹ᩡ݅. Havelock (1908)ᮡᝍ⧕ᐱอᦥܩᵲeᙹᝍ⧕,
⧕(Froudeᙹa1ᅕ݅ⓝ)ʭḡᱢᬊࡹ۵↽ݡ❭⨆bᮥ݅ᮭŝ
zᯕ ᱽᦩ⦹ᩡ݅.
Ïķ á Ē
ē
Ĕ
ĕ ĕ
ćÞÐ à ćÏƉƆÏƉƆ ßÏÕÞÎ à ćÏƉƆÏƉƆ ßì
Ɛï Î
Î à ƐÏì Ɛð Î
(19)
᭥ ᮥ ᇥᕾ⧕ᅕ໕ ↽ݡ❭⨆bᮡ ᖁᗮŝ ᙹᝍᮝಽ ᱶ᮹ࡹ۵
Froudeᙹᨱ݅᧲⦹í ӹ┡ӹ۵äᮥᙹᯩ݅. Froudeᙹa
0.4ᯕ⦹᮹ Ğᬑ ↽ݡ❭⨆bᯕ Kelvinᯕ ᱽᦩ⦽ äŝ zᯕķ á
Fig. 4. Variation of cusp locus angle with Froude number (solid line: theory, dot: FLOW-3D)
Fig. 5. Cross section of bottom to simulate ship wave propagation on varying water depth
Fig. 6. Ship wave patterns suggested in this study (U = 8m /s, hc = 10m) : solid line = constant water depth, dashed line = slope of 1/100, dotted line = slope of 1/61
ÎÖíÑÔŢಽ ᯝᱶ⦹݅. Froudeᙹa0.4ᇡ░1ಽ᷾a⦹۵Ğᬑ↽ݡ
❭⨆bࠥ⧉̹ķ á ÎÖíÑÔŢᨱᕽķ á Ö×Ţಽ᷾a⦽݅. Froudeᙹ a1ᅕ݅ⓑĞᬑ(ᷪ, ⧕᮹Ğᬑ) ↽ݡ❭⨆bᯕķ á Ö×Ţᅕ݅
᯲ᦥḥ݅. ᅙᩑǍᨱᕽ۵FLOW-3Dෝᯕᬊ⦽ᙹ⊹ᝅ⨹᮹đŝಽ ᇡ░↽ݡ❭⨆bᮥ⊂ᱶ⦹ᩍHavelock (1908)ᯕᱽ⦽ᯕುsŝ
እƱ·á☁⦹ᩡ݅.
⧎ᵝ❭ᙹ⊹༉⩶ᝅ⨹ᮥ᭥⧕Ɩì Ɨì Ƙႊ⨆᮹ĥᔑᩢᩎᮥÎì×××Ƌ Z ÏÒ×Ƌ Z Ð×ƋಽࢱŁ, ĊᯱeĊᮥĢƖ á ĢƗ á ÏƋ,ĢƘ á ÎƋ əญŁ ᙹᝍᮥƆ á Ï×Ƌಽ ࢱᨩ݅. ᖁၶ᮹ ᗮࠥ۵ Froudeᙹa
0.5~3.0ჵ᭥a ࡹࠥಾ ᖅᱶ⦹ᩡ݅. Figure 3ᨱ ᅕ۵ ၵ᪡ zᯕ
↽ݡ❭⨆bᮡFroudeᙹa1ᅕ᯲݅ᮝ໕᳦❭᪡⬂❭aƱ₉⦹໑
ӹ┡ӹ۵↽ݡ❭Łၽᔾḡᱱᮥᩑđ⦽ᖁᯕ⧎ᱢᵲᝍᖁŝᯕ۵
bࠥෝ⊂ᱶ⦹ᩡᮝ໑, Froudeᙹa1ᅕ݅Ⓧ໕⬂❭aᔍḡŁ
᳦❭อšₑࡹအಽℌჩṙ᳦❭᮹❭ᅪᖁᯕ⧎ᱢᵲᝍᖁŝᯕ۵
bᮥ⊂ᱶ⦹ᩡ݅. Figure 4ᨱᕽFroudeᙹ᮹ᄡ⪵ᨱෙ↽ݡ❭⨆
b᮹⧕ᕾ⧕᪡FLOW-3D ᙹ⊹ᝅ⨹᮹đŝෝእƱ⦹ᩡŁ, ᮁᔍ⦽
đŝa ӹ᪵݅.
ᅙᱩᨱᕽ⧎ᵝ❭᮹↽ݡ❭⨆bᮥᩩ⊂⦹۵ߑᯩᨕᕽFLOW-3D a ᱶ⪶⯩ᰍ⩥⧉ᮥ⪶ᯙ⦹ᩡ݅. ᱽ4ᰆᨱᕽ۵ᵲeᙹᝍᨱᕽ⧎ᵝ❭
᮹❭⨆ᮥᩩ⊂⦹۵ᯕು⧕ෝFLOW-3D᮹ᙹ⊹⧕᪡እƱ⦹ᩍ
ᯕು⧕᮹ ᱶ⪶ᖒᮥ á᷾⦹Łᯱ ⦽݅.
4. ᄡᙹᝍᨱᕽᯕು⧕á᷾
4.1 ࣡ਕছාச൞൞෴ਐଭଲߨැ
ᅙᩑǍ᮹⧎ᵝ❭❭⩶ᮥᄡᙹᝍᨱᱢᬊ⦹໕, ᖁᗮŝᙹᝍ᮹
ᄡ⪵ᨱᙹಕ⦹۵ၵ݆Ğᔍaݍḡ۵äᮥ⪶ᯙ⦹ᩡŁ⧕ᕾ
ᮥᙹ⧪⦽݉໕ࠥ۵Figure 5᪡z݅. ᩍʑᕽ, ƆƁ۵⧎ᱢᵲᝍᖁᨱᕽ ᮹ ᙹᝍ, ƆƂ۵ ʫᮡ Ŕᨱᕽ᮹ ᙹᝍ, ƆƑ۵ ᧶ᮡ Ŕᨱᕽ᮹ ᙹᝍ, ÎîƑ۵ ၵ݆Ğᔍෝ ᮹ၙ⦽݅.
Figure 6ᮡᄡᙹᝍᨱᕽ⧎ᵝ❭⩶ᔢ᮹ᯕು⧕ෝᅕᩍᵝŁᯩ݅.
® á ÕƋî, áà ÎÎÏᯕŁ⧎ᱢᵲᝍᖁᨱᕽ᮹ᙹᝍᮡƆƁá Î×Ƌ
ᯕ݅. ၵ݆Ğᔍ᮹ᄡ⪵ෝᵝ໕⧎ᵝ❭᮹ᱥ❭᧲ᔢᯕᄡ⪵⦹۵äᮥ
ᅝᙹaᯩᮝ໑, ၵ݆ĞᔍaÎîÓÎᅕ݅᪥อ⦽Ğᔍᨱᕽᙹಕ⦹ᩡ
݅. ᯕ۵ၵ݆Ğᔍaɪ⧁Ğᬑᨱ۵⧕ᩢᩎᨱaʭᬭḡအಽ⧕a
ᙹಕ⦹ḡᦫ۵äᮝಽ❱݉ࡽ݅. ၵ݆Ğᔍaɪ⧁ᙹಾ᳦❭᪡⬂❭
᮹᳭·ᬑእݡ⋎ᯕⓍíၽᔾ⦹ᩡ݅. ᷪ, ⧎ᱢᵲᝍᖁ᮹ᮡ⧎ᱢ ᵲᝍᖁᨱᕽມᨕḩᙹಾᙹᝍᯕ᧶ᦥᲙᕽǕᱩಽᯙ⦹ᩍ❭ᅪᖁᯕ
⧕ᦩᖁ(ᷪ, ⧎ᱢᵲᝍᖁ)ŝӹ⧕ḡŁ, ⧎ᱢᵲᝍᖁ᮹᪅ෙᮡ⧎
ᱢᵲᝍᖁᨱᕽມᨕḩᙹಾᙹᝍᯕʫᨕᲙᕽᩎǕᱩಽᯙ⦹ᩍ❭ᅪ ᖁᯕ⧕ᦩᖁŝḢbᮥᯕᨩ݅. ⧎ᵝ❭۵ᖁၶᯕ⧎⧪⧁ভ⧎ᱢᵲ ᝍᖁ᮹bb᮹ᬱᱱᮝಽᇡ░ľႊ⨆ᮝಽᱥ❭⦹۵ḥ⧪❭aǑ❭
᮹⩶┽ಽᱥ❭⦹Ł᳦❭᪡⬂❭᮹ᯥ᮹᮹ᱱᨱ۵ᕽಽ݅ෙᵝʑ᪡
ႊ⨆ᮥaḥḥ⧪❭ॅ᮹᳑⧊ᮝಽᯕᨕᲙᯩʑভྙᨱǕᱩᨱ
᮹⦽ ⬉ŝෝ ᱶ⪶⯩ ᩩ⊂⦹ʑa ᨕಖ݅.
4.2 FLOW-3D ౿ැଲߨැण֗
ᅙᩑǍᨱᕽ۵FLOW-3Dෝᔍᬊ⦹ᩍᙹ⊹ᝅ⨹ᮥᙹ⧪⦹ᩡ݅.
ᖁၶ᮹ᱽᬱᮡTable 1ŝz݅. ᩍʑᕽ, ᖁၶ᮹⮹ᙹ۵⧎ᵝ❭᮹
Table 1. Ship dimensions
dimensions magnitude (unit: m) length (L) 8.53 width (B) 2.74 draft (D) 1.00
(a) (b)
Fig. 7. Comparison of ship wave patterns on varying water dept (U = 6m /s, hc = 10m) : dot = FLOW-3D, solid line = present theory, (a) slope
= 1/100, (b) slope = 1/61
❭⩶ŝ۵ྕš⦹Ł❭Ł᮹ᄡ⪵ᨱอᩢ⨆ᮥᵝʑভྙᨱᯥ᮹ಽ
ᖅᱶ⦹ᩡ݅. ᄡᙹᝍᨱᕽ᮹⧎ᵝ❭᮹❭⩶ᮥᰍ⩥⦽FLOW-3D᮹
ᙹ⊹⧕᪡ᯕು⧕ෝእƱ⦹ᩡ݅. ⧎ᵝ❭ෝᰍ⩥⦹ʑ᭥⦹ᩍᖁᗮᮥ
®á Óîì ÕîಽࢱŁ, ⧎ᱢᵲᝍᖁᨱᕽ᮹ᙹᝍᮥƆƁá Î×Ƌಽࢱᨩ݅. ၵ݆ĞᔍෝÎîƑ áÎîÎ××,ÎîÓÎಽݍญ⦹໕ᕽၵ
݆Ğᔍᨱ ෙ ⧎ᵝ❭᮹ ❭⩶᮹ ᄡ⪵ࠥ ⧉̹ እƱ⦹ᩡ݅.
Ɩì Ɨ⇶ႊ⨆᮹ĥᔑᩢᩎᮥÎîƑ á0, ÎîÎ×× ᯙĞᬑ800m
200mಽࢱᨩŁ, ÎîƑ á1/61ᯙĞᬑ800m244mಽࢱᨩ݅. Ƙ⇶
ႊ⨆᮹ĥᔑᩢᩎᮡ⠪Ɂ⧕ᙹ໕ᨱᕽ↽ݡᙹᝍƆƂʭḡਉᨕḥᙹḢ
Ñญᯕ݅. ↽ݡᙹᝍƆƂᮡ ၵ݆ ĞᔍÎîƑ᪡ ⧎ᱢᵲᝍᖁᨱᕽ᮹
ᙹᝍƆƁᨱ݅íࡽ݅. ĊᯱeĊᮥĢƗ á1m, ĢƘ á0.5mಽ
⦹ᩡ݅. ੱ⦽ ᖁၶᯕ ⇽ၽ⦽ ḡᱱ ɝᯙƖ á0~300m Ǎeᨱ
ĢƖ=1m᮹ᖒʕĊᯱෝ៝Ł, Ɩ á300~800m Ǎeᨱ⧎ᵝ❭᮹
❭⩶ᮥᱶ⪶⯩⊂ᱶ⦹ʑ᭥⦹ᩍĢƖ=0.5m᮹᳑ၡ⦽Ċᯱෝ៝݅.
FLOW-3Dಽᙹ⊹ᝅ⨹ᮥ⦽⬥⧎ᱢᵲᝍᖁ᮹Ḣbႊ⨆᮹᳭⢽
(ᷪ,Ɨ⇶᳭⢽)ෝ⧎ᱢᵲᝍᖁႊ⨆(ᷪ, Ɩ⇶ႊ⨆)ᮝಽᙹ໕ᄡ᭥
a↽ݡaࡹ۵ḡᱱᮥᦹ݅. ᯕᱱᮥᯕᮡᖁᯕ⧎ᵝ❭᮹❭ᅪᖁᯕ
݅. ᯕ❭ᅪᖁᮥᯕᮝ໕⧎ᵝ❭᮹⩶┽ᷪ, ᳦❭᪡⬂❭ෝᯕí
ࡽ݅.
Figure 7ᮡᖁᗮᯕ®á Óî,⧎ᱢᵲᝍᖁ᮹ᙹᝍᯕƆƁá Î×ƋᯙĞᬑ⧎ᵝ❭᮹ᙹ⊹⧕᪡ᯕು⧕ෝእƱ⦽əฝᯕ݅. ᯕ
᳑ÕᨱᕽFroudeᙹaƐá ×íÓÎಽᕽᔢඹᯕŁ, ❭⨆bľ á ×Ţᯙ (ᷪ, ❭ᰆᯕaᰆʕ) ⬂❭᮹ĞᬑᔢݡᙹᝍᯕƉƆ á ×íÕÓņಽᵲeᙹ ᝍᯕḡอᝍ⧕ᨱaʾ݅. ᙹ⊹⧕ෝᅕ໕᳦❭۵ᅕᯕḡᦫ۵ߑ
⬂❭۵ᇥ⯩ᅕᩡ݅. ᯕ۵ᝍ⧕ᨱᕽऽ్ӹ۵⩥ᔢᯕʑࠥ⦹݅.
ੱ⦽, ၵ݆ĞᔍaᯩᮭᨱࠥᇩǍ⦹Ł⧎ᱢᵲᝍᖁᮥʑᵡᮝಽ⦽
⧎ᵝ❭᮹ ᳭·ᬑ እݡ⋎ᖒᯕ Ⓧí ӹ┡ӹḡ ᦫᦹ݅.
Figure 8ᮡᖁᗮᯕ®á Õî,⧎ᱢᵲᝍᖁ᮹ᙹᝍᯕƆƁá Î×ƋᯙĞᬑ⧎ᵝ❭᮹ᙹ⊹⧕᪡ᯕು⧕ෝእƱ⦽əฝᯕ݅. ᯕ
᳑ÕᨱᕽFroudeᙹ۵Ɛá ×íÕÎಽᕽᔢඹᯕḡอFigure 7ᨱእ⧕
ᔍඹᨱaʾŁ, ❭⨆bľ á ×Ţᯙ(ᷪ, ❭ᰆᯕaᰆʕ) ⬂❭᮹Ğᬑ
ᔢݡᙹᝍᯕƉƆ á ×íÑÏņಽᵲeᙹᝍᯕḡอFigure 7ᨱእ⧕⧕
ᨱaʾ݅. ᙹ⊹⧕ෝᅕ໕⬂❭۵ᅕᯕḡᦫ۵ߑ᳦❭۵ᇥ⯩
ᅕᩡ݅. ᯕ۵⧕ᨱᕽऽ్ӹ۵⩥ᔢᯕʑࠥ⦹݅. ੱ⦽, ⧎ᱢᵲᝍ ᖁᮥʑᵡᮝಽ᳦❭᮹ ᳭·ᬑእݡ⋎⩥ᔢᯕ ૽ಘ⦹íӹ┡ԍ݅.
ᷪ, ⧎ᱢᵲᝍᖁ᮹(ᷪ, ᙹᝍᯕ᧶ᮡ)ᨱᯩ۵❭ᅪᖁᮡǕᱩ
⩥ᔢᮝಽ⧕ᦩᖁŝӹ⧕ḡŁ, ᪅ෙ(ᷪ, ᙹᝍᯕʫᮡ)ᨱᯩ۵
❭ᅪᖁᮡᩎǕᱩ⩥ᔢᮝಽ⧕ᦩᖁŝḢbᮥᯕᨩ݅. ᯕ్⦽እݡ
⋎ ⩥ᔢᮡ ၵ݆Ğᔍa ɪ⧁ᙹಾ ᝍ⦹í ၽᔾ⦹ᩡ݅.
ᖁၶ᮹अᨱ⧎ᵝ❭᮹❭⩶ᯕᩍ్}ӹ┡ԍŁ, अಽiᙹಾ
❭⩶᮹Ⓧʑa᷾a⦹ᩡ݅. ᯕ۵⧎ᵝ❭ၽᔾᯕ⬥eᯕĞŝ⧁ᙹ
ಾ⧎ᵝ❭aມญ⟝Კaʑভྙᯕ݅. Figure 7ŝFigure 8ᮡ
᳦❭᪡⬂❭aอӹ۵ḡᱱᯕ⧎ᱢᵲᝍᖁᨱᕽbb40m, 100m ԕಽਉᨕḥ⧎ᵝ❭᮹Ğᬑᨱᙹ⊹⧕᪡⧕ᕾ⧕ෝእƱ⦽əฝᯕ
݅. ᯕভ⧎ᵝ❭Ⓧʑෝđᱶ⦹۵ᔢᙹ۵bb áà Î××, á à ÎÎÏᨱaʭᭁ݅. ᅙᩑǍᨱᕽᱽᦩ⦽⧎ᵝ❭❭⩶᮹ᯕು⧕a
ᙹ⊹⧕᪡ ᱶᖒᱢᮝಽ ᮁᔍ⦹í ӹ᪵݅.
ᯕჩᨱ۵⧎ᵝ❭᮹❭⩶ᮥᱶపᱢᮝಽእƱ⦹ᩡ݅. ᖁᗮᯕ®á ÓƋîᯙĞᬑᙹᝍᯕᔢݡᱢᮝಽʫᨕᕽš⊂ᯕᬊᯕ⦽⬂❭᮹
(a) (b)
Fig. 8. Comparison of ship wave patterns on varying water dept (U = 8m /s, hc = 10m) : dot = FLOW-3D, solid line = present theory, (a) slope
= 1/100, (b) slope = 1/61
Table 2. RMSE (%) of transverse wave crest positions for U = 6m /sec ship speed
(m/sec)
ƆƁ(m) / Ɛ 10 / 0.61 11 / 0.58
bottom slope 0 1/100 1/61 0 1/100 1/61
6
-102 -100 -100 -100 -99 -99
left range of
ćƗƋſƖ
Ɨ (0.01,1) (0.01,1) (0.02,1) (0.01,1) (0.01,1) (0.02,1)
right range of
ćƗƋſƖ
Ɨ (0.01,1) (0.01,1) (0.02,1) (0.01,1) (0.01,1) (0.02,1)
RMSE (%) 0.16 0.17 0.14 0.14 0.14 0.15
᭥⊹ᨱݡ⦽ᯕು⧕᪡ᙹ⊹⧕ෝእƱ⦹ᩡŁ, ᖁᗮᯕ®á ÕƋî
ᯙ Ğᬑᙹᝍᯕ ᔢݡᱢᮝಽ ᧶ᦥᕽš⊂ᯕ ᬊᯕ⦽ ᳦❭ᨱݡ⧕
እƱ⦹ᩡ݅. ၵ݆Ğᔍ۵ÎîƑ á ×ì ÎîÎ××ì ÎîÓÎ,⧎ᱢᵲᝍᖁ᮹ᙹ ᝍᮡƆƁá Î×ì ÎÎƋಽࢱᨕⅾ12aḡ(ᷪ, 232aḡ) Ğᬑᨱ
እƱ⦹ᩡ݅.
⬂❭۵ ⧎ᱢᵲᝍᖁ(ᷪ, Ɩ⇶)ŝ ӹ⦹í ᱥ❭⦹အಽ ⬂❭᮹
᭥⊹ෝእƱ⦹ʑ᭥⦹ᩍƗ⇶ᮥƖ⇶᮹᳭⢽ෝእƱ⦹ᩡ݅.
᳦❭۵⧎ᱢᵲᝍᖁ᮹ჶᖁ(ᷪ,Ɨ⇶)ŝӹ⦹íᱥ❭⦹အಽ᳦❭᮹
᭥⊹ෝእƱ⦹ʑ᭥⦹ᩍƖ⇶ᮥƗ⇶᮹᳭⢽ෝእƱ⦹ᩡ݅.
Figure 1ᨱ ⬂❭ ၰ ᳦❭᮹ ᱥ❭ ႊ⨆ᮥ ᅝ ᙹ ᯩ݅.
Table 2, 3ᨱ⧎ᵝ❭᮹᭥⊹ᨱݡ⦽᪅₉ෝRMSE (ᷪ, root- mean-squared error)ಽ ݅ᮭŝ zᯕ ⢽⩥⦹ᩡ݅.
RMSE (%) = Ē
ē
Ĕ
ĕ ĕ ö
ć ćÎ
ā á Î
Þ
ćmmà {ß
ÏZ Î×× ƒƐſƌƑƔƃƐƑƃ ƕſƔƃ
ö
ććƌÎāƉ á ÎƌÞ
ćƗƗƋſƖà Ɨß
ƉÏZ Î×× ƂƇƔƃƐƅ Ƈƌƅ ƕſƔƃ (20)ᩍʑᕽ, ᦥ௹℉ᯱ᪡۵zᮡbbFLOW-3D ᙹ⊹⧕᮹᳭⢽, ᅙᩑǍ᮹ᯕು⧕᮹᳭⢽ෝ᮹ၙ⦹Ł, ƌᮡ᪅₉ĥᔑᱢᬊࡹ۵
FLOW-3D ᙹ⊹⧕᮹ⅾ}ᙹෝ᮹ၙ⦽݅. ༉ुĞᬑᨱ⧎ᵝ❭᮹
᭥⊹ᨱ ݡ⦽ ᪅₉ෝ ݡ॒⦹í እƱ⦹ʑ ᭥⦹ᩍ ⧎ᵝ❭᮹ ᯕ࠺
Ñญෝ b Ğᬑ᮹ ↽ݡ ᯕ࠺ Ñญ(ᷪ, ⬂❭᮹ ĞᬑƗmᯕŁ,
Table 3. RMSE (%) of diverging wave crest positions for U = 8m /sec ship speed
(m/sec)
ƆƁ(m) / Ɛ 10 / 0.81 11 / 0.77
bottom slope 0 1/100 1/61 0 1/100 1/61
8
-116 -112 -112 -112 -110 -114
left range of ćƗƋſƖ
Ɨ (0.24,1) (0.17,1) (0.11,1) (0.27,1) (0.23,1) (0.19,1)
right range of
ćƗƋſƖ
Ɨ (0.24,1) (0.19,1) (0.27,1) (0.27,1) (0.24,1) (0.24,1)
RMSE (%) 1.35 2.29 1.79 3.49 2.86 1.78
᳦❭᮹ ĞᬑƖm)ಽ ӹ٥ᨩ݅.
༉ु❭⨆bᨱᕽ⧎ᵝ❭᮹᭥⊹š⊂ᯕa܆⦹ḡᦫᦹ݅. ᕽ, b Ğᬑᨱš⊂⦽ ჵ᭥ෝ ⧎ᱢᵲᝍᖁ᮹ჶᖁ ႊ⨆ᮝಽ ⦽↽ݡ
ᯕ࠺Ñญ(ᷪ, Ɨm)ಽ ӹ٥ᨕ ӹ┡ԕᨩ݅. ® á Óî᮹Ğᬑ
(ᷪ, Table 2᮹ Ğᬑ) ᵲeᙹᝍᨱᕽ ᝍ⧕ᨱ aʭᬕ ⧎ᵝ❭ᯕʑ
ভྙᨱᄡᙹᝍᨱᕽ᳭ࠥ·ᬑእݡ⋎ᖒᯕⓍḡᦫᦥ⧎ᵝ❭᮹ᱢᬊჵ
᭥ࠥ ᳭·ᬑ ݡ⋎ᮝಽ ⪶ᯙࡹᨩ݅. ၹ໕® á Õî᮹ Ğᬑ(ᷪ, Table 3᮹Ğᬑ) ᵲeᙹᝍᨱᕽ⧕ᨱaʭᬕ⧎ᵝ❭ᯕʑ ভྙᨱ
ᄡᙹᝍᨱᕽ᳭·ᬑእݡ⋎ᖒᯕӹ┡ӹ⧎ᵝ❭᮹ᱢᬊჵ᭥᳭ࠥ·ᬑ
እݡ⋎ᮝಽ ⪶ᯙࡹᨩ݅.
Łಅ⦽༉ुĞᬑᨱRMSE۵༉ࢱ4% ᯕԕಽ᯲ᦹ݅. ᯕ۵
ᅙ ᩑǍ᮹ ❭⩶ ᯕುᯕ ᯝᱶᙹᝍ ᐱอ ᦥܩ ᄡᙹᝍᨱᕽࠥ
ᱢᬊ a܆⦹݅۵ äᮥ ᮹ၙ⦽݅.
5. đು
ᅙᩑǍᨱᕽ⧎ᵝ❭᮹❭⩶ᷪ, ᳦❭᪡⬂❭᮹᭥⊹ෝᩩ⊂⦹۵
ᯕುᮥ}ၽ⦹ᩡ݅. Kelvin (1887)ᮡᝍ⧕ᨱᕽอᱢᬊa܆⦽
⧎ᵝ❭᮹❭⨆ᨱݡ⦽ᯕುᮥ}ၽ⦹ᩡ۵ߑᅙᩑǍᨱᕽ}ၽ⦽
ᮡ ᝍ⧕ ᐱอ ᦥܩ ᵲeᙹᝍ⧕ʭḡ ᱢᬊᯕ a܆⦹݅. ੱ⦽
ᯝᱶᙹᝍᐱอᦥܩ᪥Ğᔍ᮹ᄡᙹᝍᨱᕽࠥᱢᬊᯕa܆⦹݅.
FLOW-3Dෝᔍᬊ⦹ᩍᝍ⧕ᨱᕽᇡ░ ⧕ʭḡ⧎ᵝ❭ෝᰍ⩥
⦹ᩍ↽ݡ❭⨆bᮥ⊂ᱶ⦹ᩍHavelock (1908)᮹ᯕುŝእƱ⦹
ᩍFLOW-3D᮹⧎ᵝ❭᮹ᰍ⩥ᖒᮥá᷾⦹ᩡ݅. ᅙᩑǍᨱᕽ}ၽ
⦽ᯕುᮥFLOW-3Dᨱ᮹⦽ᙹ⊹⧕᪡እƱ⦹ᩡ݅. ᷪ, ᝍ⧕ᐱอ
ᦥܩᵲeᙹᝍᨱᕽ⧎ᵝ❭᮹❭⩶ᮥᰍ⩥⦹ᩡŁ, ੱ⦽ᯝᱶᙹᝍ
ᐱอᦥܩᄡᙹᝍᨱᕽࠥ⧎ᵝ❭᮹❭⩶ᮥᰍ⩥⦹ᩡ݅. əđŝ
ᙹᝍᯕ᧶ᮥᙹಾ⧎ᵝ❭a᳭·ᬑಽມญ⟝Კӹa۵äᮥ
ᙹᯩᨩ݅. ੱ⦽ᯝᱶĞᔍ᮹ᄡᙹᝍᨱᕽᖁၶᯕ⧕ᦩᖁŝӹ⦹í
ᯕ࠺⦹۵ Ğᬑ ⧕ᦩᖁᨱ aʭᬕ (ᷪ, ᙹᝍᯕ ᧶ᮡ )ᨱᕽ۵
Ǖᱩᯕၽᔾ⦹ᩍ❭ᅪᖁᯕ⧕ᦩᖁŝӹ⧕ḡ۵ Ğ⨆ᯕᯩᨕᕽ
↽ݡ❭⨆bᯕᯝᱶᙹᝍᨱእ⧕ᕽ⍅Ჭ݅. ၹ໕⧕ᦩᖁᨱມᨕḥ
(ᷪ, ᙹᝍᯕʫᮡ)ᨱᕽ۵ᩎǕᱩᯕၽᔾ⦹ᩍ❭ᅪᖁᯕ⧕ᦩᖁ ŝᙹḢᮥᯕ۵Ğ⨆ᯕᯩᨕᕽ↽ݡ❭⨆bᯕᯝᱶᙹᝍᨱእ⧕ᕽ
᯲ᦹ݅. ༉ुĞᬑᨱ⧎ᵝ❭᮹❭⩶᮹᭥⊹ෝᯕುŝᙹ⊹⧕ෝ
ᱶపᱢᮝಽ እƱ⦽ đŝ ᪅₉a 4% ᯕԕಽ ᯲í ӹ᪵݅. ᯕ۵
ᯕುᯕ ᙹ⊹⧕᪡ ɝᔍ⦹í ӹ᪕ᮥ ᷾⦹۵ äᯕ݅.
ᦿᮝಽᅙᩑǍ۵݅᧲⦽Ğᬑᨱݡ⦹ᩍá᷾ᮥ⧁⦥aᯩᮝ໑,
⧕ᨱᕽ(ᷪ, Froudeᙹa 1ᅕ݅ ⓑ Ğᬑ) ⧎ᵝ❭᮹ ᱥ❭᧲ᔢᮥ
ᩩ⊂⧁ ᙹ ᯩ۵ ᯕುᮥ }ၽ⦹ࠥಾ ӹᦥa ⧁ äᯕ݅.
qᔍ᮹ɡ
ᯕםྙᮡ2012֥ࠥᱶᇡ(Ʊᮂŝ⦺ʑᚁᇡ)᮹ᰍᬱᮝಽ⦽ǎᩑ Ǎᰍ݉᮹ ḡᬱᮥ ၼᦥ ᙹ⧪ࡽ ʑⅩᩑǍᔍᨦᯥ(No. 2012R1A1 A2043775).
References
Havelock, T. H. (1908). “The propagation of groups of waves in dispersive media, with application to waves on water produced by a travelling disturbance.” Proc. Royal Society of London, Series A., pp. 398-430.
Kelvin (1887). “On the waves produced by a single impulse in water of any depth.” Proc. Royal Society of London, Vol. 42, pp.
80-83.
Lee, C., Lee, B. W., Kim, Y. J. and Ko, K. O. (2011). “Ship wave crests in intermediate-depth water.” Proc. 6th International Conference on Asian and Pacific Coasts, Hong Kong, pp.
1818-1825.
Taylor, D. W. (1943). The Speed and Power of Ships, U.S. Govt.
Printing Office.
