九州大学応用力学研究所 Reports No.151（Sep. 2016）
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(2) CONTENTS. Unique phenomena associated with tungsten and plasma particles in fusion reactor By Kazuhito OHSAWA……………………………………………………...……………….......... 1. New Wind Speed Vertical Extrapolation Method by using Power Law in Offshore Wind Observation: Part1 By Takanori UCHIDA........................................................................................................... 4 New Wind Speed Vertical Extrapolation Method by using Power Law in Offshore Wind Observation: Part2 ̿1XPHULFDOLQYHVWLJDWLRQRIWKHRIIVKRUHZLQGHQHUJ\LQWKH+LELNLQDGDUHJLRQɆ By Takanori UCHIDA…………………………………………….………………….........……...12 Large-eddy simulation of airflow over complex terrain aiming at optimal placement method examination of wind turbines ̿,QWKHFDVHRIWKHNXVKLNLQRUHLPHLZLQGIDUPɆ By Yasushi KAWASHIMA and Takanori UCHIDA.............................................................24.
(3) Reports of Research Institute for Applied Mechanics, Kyushu University No.151 (1 – 3) September 2016. Unique phenomena associated with tungsten and plasma particles in fusion reactor KazuhitoOHSAWA∗1 E-mailof correspondingauthor:ohsawa@riam.kyushu-u.ac.jp (Received July 29,2016). Abstract Unique phenomena are expected associated with interaction between tungsten (W) materials and plasma particles in fusion reactors. In the present paper, we introduce some important and interesting studies of the characteristic behaviors of the plasma particles in the W materials. In particular, abnormal stable configurations of multiple hydrogen (H) atoms trapped in a W vacancy are found in terms of firstprinciplecalculations.WecalculatebindingenergiesofthemultipleHatomstoaWvacancy.Besides,zeropoint energy (ZPE) corrections are estimated according to the abnormal H configurations. We estimate bindingenergydifferencedependingontheHisotopesforthefirsttime. Keywords:tungsten,hydrogenisotope,fusionreactor,first-principlecalculation. 1.. Introduction. In the fusion reactor, divertor armor tiles are exposed to extremely intense plasma particle irradiation. In order to protect the divertor armor tiles, its surface is planning to be covered with tungsten (W) or W alloy. So, study of interaction between W and plasma particle started. W is one of promising plasma facing materials because of its high melting point, low hydrogen (H) solubility, and low sputtering erosion. Besides, it has high thermal conductivity and low induced radioactivity. By the way, some unique phenomena are observed associated with the interaction between W and plasma particles. (1) Negative formation energy for di-vacancy in W . Di-vacancy in metals is usually more stable than mono-vacancy because the inner surface of the divacancy is smaller than the total inner surface of the two mono-vacancies. However, it has reported that divacancy in W lattice is unstable 1) . (2) Helium (He) cluster migrations more quickly than a single He atom. He clusters are nucleated in a molecular dynamics simulations and diffusion constants are estimated 2) . He clusters smoothly migrate in the W lattice. (3) Fibreform tungsten covering surface by He irradiation. An characteristic surface morphology has been reported on the W specimens irradiated by He 3) . (4) Abnormal and stable H configurations in a W vacancy has been reported 4, 5, 6) . We will focus on the fourth topics in the present paper. *1 Research Institute for Applied Mechanics, Kyushu University. Typical interstitial sites of bcc metals are tetrahedral interstitial site (T-site) and octahedral interstitial site (O-site). According to the previous works, T-site is more favorable for an H atom than O-site in perfect bcc metals. On the other hand, an H atom trapped in a vacancy is located close to an O-site. If multiple H atoms would be trapped in the vacancy, it was reported that each H atom was also located close to an O-site. As a result, a maximum of 6 H atoms can be accommodated in a vacancy because there are 6 O-sites next to a vacancy in bcc lattice, which is standard model for multiple H atom configuration in a vacancy 7) . However, stable configurations of multiple H atoms trapped in a W vacancy are abnormal and a maximum of 12 H atoms can be accommodated. A large amount of H atoms and H isotopes are retained in irradiation zone of W materials. The hydrogen solubility of W and W alloys is very low but lattice defects of vacancy types are nucleated in the irradiation zone. Then, two types of hydrogen isotopes coexist in fusion reactors because D-T fusion reaction takes place. It is expected that the binding energies of lighter H isotopes to a vacancy are larger than those of heavier ones due to the difference of zero-point energy (ZPE) corrections. The coexistence effects of H isotopes will be important subject associated with fusion reactors. In particular, tritium (T) retention in the W materials is a serious problem for the safety of fusion reactors because T is a radioisotope whose physical half-life is 12 years. We estimate the binding energies of multiple H isotopes trapped in a W vacancy..
(4) 2. 2.. Ohsawa : Unique phenomena associated with tungsten and plasma particles in fusion reactor. Simulation method. (a) W. In the present simulation, we do not assume that H atoms in a W vacancy are located close to the Osites. Instead, initial H positions for ionic relaxation are randomly generated to find unexpected and the most stable configuration. We performed first-principles calculations based on DFT using Vienna ab-initio simulation package (VASP) 8, 9) with PBE potential 10) . Plane wave cut-off energy is 350 eV. Electronic and ionic relaxations are iterated until a break condition (0.003 eV/˚ Afor every atom) is satisfied. When H atoms trapped in a W vacancy are assumed to be classical particles without ZPE corrections, the binding energies for the classical H atoms are estimated to be. O-site. stable 4H O-site (c) W H. (e) W. planar 4H (d). O-site. metal. H. symmetric 6H. stable 6H close to T-site. H. stable12H. Fig. 1 Schematic view of stable H configuration in vacancy in W and BCC metals. -2. (2). where ZI (1 H) is the total ZPE for an interstitial 1 H atom located at a T-site in perfect W lattice, which is estimated to be 0.259 (eV). ZV (1 Hk ) is the total ZPE for k1 H atoms trapped in a W vacancy. The ZPE corrections are calculated by harmonic approximation assuming that the force acting on a 1 H is proportional to the displacement from the equilibrium position 11) .. 3.. H. H. Results. Figure 1 shows typical abnormal but stable configurations of H atoms in a W vacancy. Stable configuration of 4 H atoms is tetrahedral structure, Fig. 1 (a), but planar one, Fig. 1 (b). Stable configuration of 6 H atoms is more complicated, as shown in Fig. 1 (c). Symmetric 6 H structure Fig. 1 (d) is unstable in the case of H atoms trapped in a W vacancy. But the symmetric structure of 6 H atoms is usually stable for other bcc transition metals. A maximum of 12 H atoms can be accommodated in a W vacancy and the H atoms are located close to T-sites, as shown in Fig. 1 (e). Figure 2 shows the total binding energies of single and multiple H atoms (classical H atoms without ZPE. 㼎㼕㼚㼐㼕㼚㼓㻌㼑㼚㼑㼞㼓㼥㻌㼛㼒㻌㻴㻌㼠㼛㻌㼢㼍㼏㼍㼚㼏㼥㻌(eV). {kZI (1 H) − ZV (1 Hk )} √ , a. (b) metal. (a). ek = E[Wn−1 V]−E[Wn−1 V(Hk )]+k(E[Wn HI ]−E[Wn ]), (1) where E is cohesive energies of supercells; Wn−1 V is a supercell composed of (n − 1)W and a vacancy; Wn−1 V(Hk ) is a supercell containing a vacancy trapping k classical H atoms; Wn HI is that composed of nW and an interstitial H atom in W; and Wn is a supercell of perfect W lattice. Positive sign of ek means an attractive interaction between H and W vacancy. H isotopes are represented by a H (1 H = H,2 H = D,3 H = T). The superscript indicates mass number. If the same type of H isotopes a H are trapped in a W vacancy, the binding energies including ZPE corrections are eak = ek +. O-site. 0. energy lebel of H at T-site. Nb. 2. Ta. V Cr. 4. Fe. W. 6. Mo. H2 Formation. 8 0. 2. 4. 6. 8. 10. 12. 14. 16. 㻺㼡㼙㼎㼑㼞㻌㼛㼒㻌㻴㻌㼍㼠㼛㼙㼟㻌㼠㼞㼍㼜㼜㼑㼐㻌㼕㼚㻌㼢㼍㼏㼍㼚㼏㼥(k). Fig. 2 Total binding energies of single and multiple hydrogen atoms trapped in vacancy in bcc transition metals.. correction) to a vacancy in bcc transition metals. A vacancy in W and Mo can accommodate 12 H atoms. However, 6 H atoms are trapped in a vacancy in other bcc metals, which is good agreement with the standard model 7) ..
(5) Reports of Research Institute for Applied Mechanics, Kyushu University No.151 September 2016. k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. e1k (H) 1.381 2.731 3.800 4.816 5.727 6.408 6.623 6.913 7.129 7.294 7.334 7.725 6.890 7.465 6.466. e2k (D) 1.334 2.639 3.710 4.709 5.604 6.276 6.499 6.794 7.002 7.173 7.202 7.587 6.736 7.361 6.325. e3k (T) 1.314 2.598 3.670 4.662 5.550 6.218 6.444 6.741 6.946 7.120 7.144 7.525 6.667 7.315 6.263. ek 1.223 2.415 3.492 4.450 5.309 5.957 6.200 6.506 6.697 6.881 6.885 7.252 6.363 7.110 5.986. ZV (1 Hk ) 0.101 0.201 0.468 0.669 0.876 1.102 1.390 1.664 1.898 2.176 2.399 2.634 2.838 3.270 3.403. 1.0. 㻱㼚㼑㼞㼓㼥㻌㻌㼘㼑㼢㼑㼘㻌㼛㼒㻌㻴㻌㼍㼠㼛㼙㻌㻔㼑㼂㻕㻌㻌. Table 1 Total binding energies of classical H atom ek and H isotopes, e1k , e2k , and e3k to a W monovacancy (eV). ZV (1 Hk ) is the total ZPE of k 1 H trapped in the W vacancy.. 3. H at interstitial site (T-site). 0.8 0.6 0.4 0.2 0.0. 1.182eV 0.971eV 0.575eV. -0.2 -0.4 -0.6. Mo. W. H2 molecule (in vacuum) 㻌. Fe. H in vacancy. -0.8 -1.0. Fig. 3 Energy level of H atom at interstitial site and vacancy in W, Mo and Fe.. References 1) Ventelon L., Willaime F., Fu C.-C., Heran M. and I. Ginoux: J. Nucl. Mater., 425 (2012) 16-21.. Table 1 exhibits the total binding energies for H isotopes (H, D, T) and classical H atoms without ZPE corrections to a W vacancy calculated in Eq. (2). As our expectation, the binding energies for the lighter H isotopes are larger than those for heavier ones.. 4.. Discussion. W and W alloys are promising plasma facing materials in fusion reactors due to their very low H solubility. However, it has been reported that large amounts of H isotopes are retained in W specimen of irradiated zone 12) . Figure 3 shows energy landscape of H atom in BCC transition metals, W, Mo, and Fe. Energy levels of H at interstitial site in W and Mo are very high, which is good agreement with the low H solubility of these metals. However, the difference between energy levels for an H at interstitial site and vacancy is very large. Therefore, vacancy type lattice defects introduced by irradiation are expected to be strong H trapping sites. The binding energies of H isotopes depend on the types of H isotopes, according to Table 1. The amount of T retention in the plasma facing materials is serious problem for safety operation of actual fusion reactors. The results of the present work indicate that the binding energies of T to a W vacancy are smaller than those of H and D. Therefore, T retention is expected to be reduced by coexistence of other H isotopes in the W materials. We are planning to estimate the amounts of H isotopes trapped in a W vacancy in the coexistence circumstance on the basis of a thermodynamic model in the future 6) .. 2) Zhou Y.L., Wang J., Hou Q. and Deng A.H.: J. Nucl. Mater., 446 (2014) 49-55. 3) Kajita S., Sakaguchi W., Ohno N. Yoshida N. and Saeki T. Nucl. Fusion 49 (2009) 095005. 4) Ohsawa K., Goto J., Yamakami M., Yamaguchi M. and Yagi M.: Phys. Rev. B82 (2010) 184117. 5) Ohsawa K., Eguchi K., Watanabe H., Yamaguchi M. and Yagi M.: Phys. Rev. B85 (2012) 094102. 6) Ohsawa K., Nakamori F., Eguchi K., Hatano Y. and Yamagichi M.: J. Nucl. Mater 458 (2015) 187-197. 7) Tateyama Y. and Ohno T.: Phys. Rev. B67 (2003) 174105. 8) Kresse G. and Hafner J.: Phys. Rev. B47 (1993) 558. 9) Kresse G. and Furthmuller J.: Phys. Rev. B54 (1996) 11169. 10) Perdew J. P., Burke K. and Ernzerhof M.: Phys. Rev. Lett. 77 (1996) 3865. 11) Matsumoto R., Inoue Y., Taketomi S. and Miyazaki N.: Scr. Mater. 60 (2009) 555. 12) Alimov V. Kh., Roth J., Gausey R. A., Komarov D. A., Linsmeier Ch., Wilter A., Kost F. and Lindig A.: J. Nucl. Mater. 375 (2009) 192..
(6) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻔㻠㻙㻝㻝㻕㻌㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌. ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛 㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾1 㻌 ෆ⏣㻌 Ꮥ⣖㻖㻌 㻔㻞㻜㻝㻢ᖺ㻣᭶㻞㻥᪥ཷ⌮㻕㻌. 㻌 New Wind Speed Vertical Extrapolation Method by using Power Law in Offshore Wind Observation: Part1 Takanori UCHIDA E-mail of corresponding author: takanori@riam.kyushu-u.ac.jp. Abstract. Offshore wind energy development promises to be a significant domestic renewable energy source. There are two approaches to estimating the increase in wind speed with height: the power law method and the logarithmic method. Logarithmic extrapolation is derived mathematically from a theoretical understanding of how the wind moves across the surface of the earth. In contrast, the power law equation is derived empirically from actual measurements. For an assessment of offshore wind energy resources by using the weather GPV (MSM-S and LFM-S) wind speed data at 10m above the sea surface, a new wind speed vertical extrapolation method based on a power law was proposed in the present study. Key words : Offshore wind energy, Weather GPV data, Vertical extrapolation method, Power law. 㻌 㻝䠊⥴ゝ㻌 ㏆ᖺ䠈㝣ୖ㢼ຊⓎ㟁㻔䜸䞁䝅䝵䜰㢼ຊⓎ㟁㻕䛻ຍ䛘䛶䠈 ὒୖ㢼ຊⓎ㟁㻔䜸䝣䝅䝵䜰㢼ຊⓎ㟁㻕䛜ὀ┠䛥䜜䛶䛝䛶 䛚䜚䠈Ḣᕞ䜢୰ᚰ䛻つᶍ䛺ὒୖ䜴䜲䞁䝗䝣䜯䞊䝮䛜 ᘓタ䛥䜜䛶䛔䜛䠊୍᪉᪥ᮏ䛷䛿䠈㝣ୖ㢼ຊⓎ㟁䛾䜏 䛺䜙䛪ὒୖ㢼ຊⓎ㟁䛾ศ㔝䛷䜒Ḣᕞ䛻䛝䛟ᚋ䜜䜢䛸 䛳䛶䛔䜛䠊㻌 䛧䛛䛧᪥ᮏ䛿䠈㡿ᾏ䛚䜘䜃ⓗ⤒῭Ỉᇦ䜢ྜ䜟 䛫䛯㠃✚䛜ୡ⏺➨㻢䠄⣙㻠㻠㻣㼙㻞䠅䛾ᾏὒᅜ䛷䛒䜚䠈 ὒୖ㢼ຊⓎ㟁䛾䝫䝔䞁䝅䝱䝹䛻䛿ᜨ䜎䜜䛶䛔䜛䠊䜶䝛 䝹䜼䞊ᇶᮏィ⏬㻞㻜㻝㻠䛷䛿䠈䛂୰㛗ᮇⓗ䛻䛿䠈㝣ୖ㢼 ຊ䛾ᑟධྍ⬟䛺㐺ᆅ䛜㝈ᐃⓗ䛺ᡃ䛜ᅜ䛻䛚䛔䛶䠈ὒ ୖ㢼ຊⓎ㟁䛾ᑟධᣑ䛿ྍḞ䛷䛒䜛䛃䛸᭩䛛䜜䛶 䛔䜛䠊ᚋ䠈䛥䜙䛺䜛Ⓨᒎ䛜ᮇᚅ䛥䜜䛶䛔䜛䠊㻌 ୍⯡♫ᅋἲே᪥ᮏ㢼ຊⓎ㟁༠㻔㻶㼃㻼㻭㻕䛻䜘䜜䜀䠈 ᪥ᮏ䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁䛾⣼✚ᑟධ┠ᶆ䛿䠈㻞㻜㻟㻜 ᖺ䛻㻥㻢㻜㼗㼃䠈㻞㻜㻡㻜ᖺ䛻䛿㻟㻘㻣㻜㻜㼗㼃䛸䛺䛳䛶䛚䜚䠈 つᶍ䛻ᑟධ䛥䜜䜛䛸䛾ヨ⟬䛜䜎䛸䜑䜙䜜䛶䛔䜛䠊㻌 ὒୖ㢼ຊⓎ㟁ᴗ䜢᳨ウ䛩䜛㝿䠈䛭䛾ᴗ䛻䛚䛡 䜛᥇⟬ᛶ䜔ᴗ䝸䝇䜽䛺䛹䜢ヲ⣽䛻๓ホ౯䛩䜛ᚲせ㻌 㻌 㻖㻌 ᕞᏛᛂ⏝ຊᏛ◊✲ᡤ㻌. 㻌. 䛜䛒䜛䠊≉䛻䠈㢼ἣㄪᰝ䛾⤖ᯝ䜢⏝䛔䛶㢼㌴䛾タィ 䜔᭱㐺䛺タ⨨ィ⏬䛜సᡂ䛥䜜䜛䛯䜑䠈ṇ☜䛺㢼ἣᢕ ᥱ䛿᭱㔜せ᳨ウ㡯┠䛷䛒䜛䠊㻌 ୍⯡䛻䠈ὒୖ㢼ἣㄪᰝ䛷䛿䠈ほ 㧗ᗘ䛸㢼㌴䝝䝤 㧗䛾㛫䛾㧗ᗘ⿵ṇ䛜ᚲせ䛸䛺䜛䠊ᩘ್㢼ἣ䝅䝭䝳䝺䞊 䝅䝵 䞁䜢⏝䛔䛺䛔ሙྜ䛻䛿䠈⤒㦂๎䛺䜉䛝๎䠄㼍㼚㻌 㼑㼙㼜㼕㼞㼕㼏㼍㼘㻌 㼜㼛㼣㼑㼞㻌 㼘㼍㼣㻕䛻ᇶ䛵䛔䛶䠈㢼㏿䛾㧗ᗘ⿵ṇ䛜 ⾜䜟䜜䜛䛾䛜୍⯡ⓗ䛷䛒䜛䠊㻌 ᡃ䚻䛾䜾䝹䞊䝥䛷䛿䠈Ẽ㇟ᗇ䛜ᥦ౪䛩䜛✀䚻䛾Ẽ ㇟㻳㼞㼕㼐㻌 㻼㼛㼕㼚㼠㻌 㼂㼍㼘㼡㼑㻔㻳㻼㼂㻕䝕䞊䝍䜢䠈㢼ຊⓎ㟁ศ㔝䜈 㐺⏝䛩䜛䛯䜑䛾◊✲㛤Ⓨ䜢㐍䜑䛶䛝䛯䠊≉䛻䠈ᾏ㠃䛛 䜙䛾㧗ᗘ䛜㻝㻜㼙䛻ᅛᐃ䛥䜜䛶䛔䜛䝯䝋ᩘ್ணሗ䝰䝕䝹 㻹㼑㼟㼛㻌 㻿㼏㼍㼘㼑㻌 㻹㼛㼐㼑㼘㻔㻹㻿㻹㻙㻿䠈Ỉᖹゎീᗘ㻡㼗㼙㻕䛸䠈ᒁᆅ ᩘ್ணሗ䝰䝕䝹㻸㼛㼏㼍㼘㻌 㻲㼛㼞㼑㼏㼍㼟㼠㻌 㻹㼛㼐㼑㼘㻔㻸㻲㻹㻙㻿䠈Ỉᖹ ゎീᗘ㻞㼗㼙㻕䛾⏝䛸䛭䛾ண ⢭ᗘ䛾᳨ド䜢⾜䛳䛶䛝 䛯㻝㻙㻣㻕䠊㻌 ᮏሗ䛷䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ୖグ䛾ᆅ ୖ㧗㻝㻜㼙⨨䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘䜃 㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗䛥 㻤㻜㼙䡚㻥㻜㼙䛻㧗ᗘ⿵ṇ䛩䜛ሙྜ䛾ၥ㢟Ⅼ䜢ᣦ䛩䜛 䛸䛸䜒䛻䠈᪂䛯䛺㧗ᗘ⿵ṇᡭἲ䛾ᥦ䜢⾜䛖䠊㻌 㻌.
(7) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻡. 㻌. 㻌. 㻞䠊ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖㻌. 㻟䠊ゎᯒ⤖ᯝ䛚䜘䜃⪃ᐹ㻌. 㻺㻱㻰㻻㻔ᅜ❧◊✲㛤Ⓨἲே᪂䜶䝛䝹䜼䞊䞉⏘ᴗᢏ⾡ ⥲ྜ㛤Ⓨᶵᵓ㻕䛷䛿䠈༓ⴥ┴㖯ᏊἈ䛚䜘䜃⚟ᒸ┴ ᕞᕷἈ䛾㻞ᆅⅬ䜢ᑐ㇟䛻䛧䠈ᅜෆ䛷ึ䜑䛶䛾Ἀྜ 䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁䛾ᐇ⌧䛻ྥ䛡䛶䠈㢼ྥ䛸㢼㏿ 䜢ほ 䛩䜛ὒୖ㢼ἣほ 䝍䝽䞊䛸ᐇ㝿䛻ὒୖ䛻䛚䛔 䛶Ⓨ㟁䜢⾜䛖ὒୖ㢼㌴䜢ᐇᾏᇦ䛻タ⨨䛩䜛䝥䝻䝆䜵䜽 䝖䜢㻞㻜㻜㻥ᖺᗘ䜘䜚ᐇ䛧䛶䛔䜛䠊㖯ᏊἈ䛷䛿㻞㻜㻝㻟ᖺ㻟 ᭶䛛䜙䠈ᕞᕷἈ䛷䛿㻞㻜㻝㻟ᖺ㻢᭶䛛䜙䛭䜜䛮䜜㐠 ㌿䜢㛤ጞ䛧䠈ᐇド◊✲䛜⾜䜟䜜䛶䛔䜛㻔ᅗ㻝䡚ᅗ㻟䠈 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻕䠊㻌 㻞㻜㻝㻢ᖺ㻟᭶㻞㻟᪥䛻䛿䠈ୖグ䛾༓ⴥ┴㖯ᏊἈ䛸⚟ᒸ ┴ᕞᕷἈ䛺䛹䛷ྲྀ䜚⤌䜣䛷䛝䛯╔ᗋᘧὒୖ㢼ຊ Ⓨ㟁䛾ᐇド◊✲䛾ᡂᯝ䛾୍㒊䛸䛧䛶䠈㢼ἣ䠈ᾏ㇟䛚 䜘 䜃 㢼 ㌴ 䛾 Ⓨ 㟁 ほ 䝕 䞊 䝍 䛜 බ ⾲ 䛥 䜜 䛯 㻔㼔㼠㼠㼜㻦㻛㻛㻌 㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼚㼑㼣㼟㻛㼜㼞㼑㼟㼟㻛㻭㻭㻡㼋㻝㻜㻜㻡㻟㻥㻚㼔㼠㼙㼘㻕䠊ᮏ◊ ✲䛷䛿䠈䛣䜜䜙䛾ὒୖ㢼ἣ䝕䞊䝍䜢⏝䛔䛯䠊㻌 㻌 㻌 㻌 㻌. 㻌 ᮏ◊✲䛾┠ⓗ䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ᆅୖ 㧗㻝㻜㼙⨨䛷ᢳฟ䛧䛯Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘䜃 㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗䛥 㻤㻜㼙䡚㻥㻜㼙䛻䛚䛡䜛㢼㏿್䜢㧗⢭ᗘ䛻᥎ᐃ㻔㧗ᗘ⿵ ṇ㻕䛩䜛ᡭἲ䜢☜❧䛩䜛䛣䛸䛷䛒䜛䠊ᅗ㻠䛻䛿䠈ᮏ◊✲ 䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗㻝㻜㼙㻕䛾ྲྀ ᚓ⨨䛸ὒୖ㢼ἣほ ᆅⅬ䛸䛾⨨㛵ಀ䜢♧䛩䠊Ẽ ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗㻝㻜㼙㻕䛾ヲ⣽䛻䛴䛔䛶 䛿ᩥ⊩㻝㻙㻣㻕䜢ཧ↷䛧䛶㡬䛝䛯䛔䠊㻌 ᅗ㻠㻔㼍㻕䛻♧䛩䜘䛖䛻䠈༓ⴥ┴㖯ᏊἈ䛾䝕䞊䝍ゎᯒ䛷 䛿㻼㼛㼕㼚㼠㻝䛚䜘䜃㻼㼛㼕㼚㼠㻟䛷ྲྀᚓ䛥䜜䛯Ẽ㇟㻳㻼㼂䝕䞊䝍 㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗㻝㻜㼙㻕䜢⥺ᙧⓗ䛻ෆᤄ䛧䛯㢼㏿್䜢 ほ ᆅⅬ䛾㢼㏿್䛸ぢ䛺䛧䛶⏝䛔䛯䠊୍᪉䠈ᅗ㻠㻔㼎㻕䛻 ♧䛩䜘䛖䛻䠈⚟ᒸ┴ᕞᕷἈ 䛾䝕䞊 䝍ゎᯒ䛷䛿 㻼㼛㼕㼚㼠㻟䛷ྲྀᚓ䛥䜜䛯Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗 㻝㻜㼙㻕䜢ほ ᆅⅬ䛾㢼㏿್䛸ぢ䛺䛧䛶⏝䛔䛯䠊㻌. 㻌. ᅗ㻝㻌 ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻌 㻌.
(8) 㻢㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻝㻌. 㻌. 㻌 㻔㼍㻕༓ⴥ┴㖯ᏊἈ㻌 㻌. 㻌. 㻌 㻌 㻔㼎㻕⚟ᒸ┴ᕞἈ㻌 㻌 ᅗ㻞㻌 ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖䛾ヲ⣽㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻌. 㻌.
(9) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻣. 㻌. 㻌. 㻔㼍㻕༓ⴥ┴㖯ᏊἈ㻌 㻌. 㻌. 㻔㼎㻕⚟ᒸ┴ᕞἈ㻌 㻌 ᅗ㻟㻌 ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖䛾┿㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼜㼔㼛㼠㼛㼓㼍㼘㼘㼑㼞㼥㻚㼔㼠㼙㼘㻌.
(10) 㻤㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻝㻌. 㻌. 㻔㼍㻕༓ⴥ┴㖯ᏊἈ㻌 㻌. 㻌. 㻌. 㻔㼎㻕⚟ᒸ┴ᕞἈ㻌 㻌 㻌 ᅗ㻠㻌 Ẽ㇟㻳㻼㼂䝕䞊䝍䛾ྲྀᚓ⨨䛸ὒୖ㢼ἣほ ᆅⅬ䛸䛾⨨㛵ಀ.
(11) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻥. 㻌. ᐇ 䝕䞊䝍㻌 㐣ᑠホ౯㻌. 7.50 7.31 7.18 6.98 6.92 6.53. ᕞᕷἈ䛾㻌. 㻳㻼㼂 䝕䞊䝍㻌. 5.67 㐣ホ౯㻌. 㻌 㻌 㻔㼍㻕༓ⴥ┴㖯ᏊἈ㻌 㻌. 䛆㉥⥺䛇㻌 㧗ᗘ㻤㻜㼙䛾ᐇ 䝕䞊䝍䛛䜙㻌 㻺㻩㻥㻚㻡䛷㧗ᗘ㻝㻜㼙䜎䛷㻌 ⾲♧䛧䛯⤖ᯝ㻌 䊻㧗ᗘ㻝㻜㼙䛾㢼㏿㻔㻳㻼㼂㻕㻌 㻌 㻌 㻌 䛻ᑐ䛧䛶㐣ホ౯㻌 㻌 䛆㟷⥺䛇㻌 㧗ᗘ㻝㻜㼙䛾㻳㻼㼂䝕䞊䝍䛛䜙㻌 㻺㻩㻥㻚㻡䛷㧗ᗘ㻤㻜㼙䜎䛷㻌 ⾲♧䛧䛯⤖ᯝ㻌 䊻㧗ᗘ㻤㻜㼙䛾ᐇ ್䛻㻌 㻌 㻌 ᑐ䛧䛶㐣ᑠホ౯㻌. ᐇ 䝕䞊䝍㻌 㐣ᑠホ౯㻌. 7.10 6.97 6.72 6.59 6.40 6.34. 5.16 㻳㻼㼂 䝕䞊䝍㻌. 㐣ホ౯㻌. 㻌 㻌 㻔㼎㻕⚟ᒸ┴ᕞἈ㻌. 䛆⥳⥺䛇䠖᪂䛧䛔㧗ᗘ⿵ṇ㻌 㻌 䛂䝇䝔䝑䝥㻝䛃㻌 㧗ᗘ㻝㻜㼙䛾㻳㻼㼂䝕䞊䝍䛸㻌 㧗ᗘ㻟㻜㼙䛾ᐇ 䝕䞊䝍䛛䜙㻌 㻔㻝㻕ᘧ䛻䜘䜚䠈㻺 㻺㻩㻡㻚㻟䜢ᑟฟ㻌 㻌 䛂䝇䝔䝑䝥㻞䛃㻌 㧗ᗘ㻟㻜㼙䛾ᐇ 䝕䞊䝍䛸㻌 㧗ᗘ㻤㻜㼙䛾ᐇ 䝕䞊䝍㻌 䛛䜙㻔㻝㻕ᘧ䛻䜘䜚䠈㻌 㻺㻩㻤㻚㻣䜢ᑟฟ㻌 㻌 䊼㻌 㻌 䖃㧗ᗘ㻝㻜㼙䡚㧗ᗘ㻟㻜㼙㻌 㻌 䊻㻺 㻺㻩㻡㻚㻟䛾䜉䛝๎㻌 㻌 䖃㧗ᗘ㻟㻜㼙䡚㧗ᗘ㻤㻜㼙㻌 㻌 䊻㻺 㻺㻩㻤㻚㻣䛾䜉䛝๎㻌 㻌. 㻞ẁ㝵䛷㧗ᗘ⿵ṇ䜢ᐇ㻌. 㻌. ᅗ㻡㻌 ᐇ 䝕䞊䝍䠄㯮䠅䠈ᮏ◊✲䛷ᥦ䛩䜛᪂䛧䛔㧗ᗘ⿵ṇ᪉ἲ䛻䜘䜛⤖ᯝ䠄ᅗ୰䛻⥳Ⰽ䛷⾲♧䠅㻌 䝕䞊䝍ゎᯒᮇ㛫㻌 䠖㻌 㻞㻜㻝㻟ᖺ㻝᭶㻝᪥䡚㻝㻞᭶㻟㻝᪥䛾㻝ᖺ㛫㻌.
(12) 㻝㻜㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻝㻌. 㻌. 㻌. 㻌. 㻔㼍㻕༓ⴥ┴㖯ᏊἈ㻌. 㻔㼍㻕༓ⴥ┴㖯ᏊἈ䠈ᅗ㻠㻔㼍㻕䛾㻼㼛㼕㼚㼠㻝㻌 㻌. 㻌. 㻌. 㻌. 㻔㼎㻕⚟ᒸ┴ᕞἈ㻌 㻌 ᅗ㻢㻌 ᐇド䝃䜲䝖䛾ほ 䝕䞊䝍䛛䜙ホ౯䛧䛯㢼㓄ᅗ䠈 䝕䞊䝍ゎᯒᮇ㛫䠖㻞㻜㻝㻟ᖺ㻝᭶㻝᪥䡚㻝㻞᭶㻟㻝᪥䛾㻝ᖺ㛫㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼜㼡㼎㼘㼕㼏㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻌. 㻌 ᅗ㻡䛻䛿䠈ᐇ 䝕䞊䝍㻔㯮㻕䛚䜘䜃ᮏ◊✲䛷ᥦ䛩 䜛᪂䛧䛔㧗ᗘ⿵ṇ᪉ἲ䛻䜘䜛⤖ᯝ㻔⥳Ⰽ䛾ᐇ⥺㻕䛺䛹䜢 ♧䛩䠊ᅗ୰䛾㯤Ⰽ䛾ᅄゅ䝅䞁䝪䝹䛷⾲♧䛧䛶䛔䜛䛾 䛿䠈᪤䛻㏙䜉䛯ほ ᆅⅬ䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍 㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗㻝㻜㼙㻕䛾㢼㏿್䛷䛒䜛䠊᭱ึ䛻ᅗ୰䛾 ㉥Ⰽ䛾ᐇ⥺䛻ὀ┠䛧䛶㡬䛝䛯䛔䠊䛣䜜䛿ᐇ 䝕䞊䝍 䛛䜙ᚓ䜙䜜䛯㻺್䛻ᇶ䛵䛝䠈㧗ᗘ㻝㻜㼙䛛䜙㧗ᗘ㻤㻜㼙䜎䛷 䛾⠊ᅖ䜢⾲♧䛧䛯⤖ᯝ䛷䛒䜛䠊㻺್䛾⟬ฟ䛻㛵䛧䛶䠈 㖯ᏊἈ䛾ሙྜ䛻䛿ὒୖほ 䝍䝽䞊䛻䛚䛡䜛㻞㻜㻝㻟ᖺ㻢 ᭶䡚㻝㻞᭶䛾ᖹᆒ㢼㏿䛾㖄┤䝕䞊䝍䛻ᇶ䛵䛝䠈㧗ᗘ 㻞㻜㼙䛸㧗ᗘ㻥㻜㼙䛾ᖹᆒ㢼㏿䛛䜙䜉䛝๎㻔ᘧ㻔㻝㻕㻕䜢⏝䛔 䛶ồ䜑䛶䛚䜚䠈䛭䛾್䛿㻥㻚㻤䛸ሗ࿌䛥䜜䛶䛔䜛䠊㻌 㻌 1. U h2
(13). § h ·N U h1
(14) ¨ 2 ¸ 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻔㻝㻕㻌 © h1 ¹. 㻔㼎㻕⚟ᒸ┴ᕞἈ䠈ᅗ㻠㻔㼎㻕䛾㻼㼛㼕㼚㼠㻟㻌 㻌 ᅗ㻣㻌 ᐇド䝃䜲䝖䛾Ẽ㇟㻳㻼㼂䝕䞊䝍䛛䜙ホ౯䛧䛯㻌 㢼㓄ᅗ䠈䝕䞊䝍ゎᯒᮇ㛫䠖㻞㻜㻝㻟ᖺ㻝᭶㻝᪥䡚㻝㻞᭶㻟㻝᪥ 䛾㻝ᖺ㛫㻌 㻌 ୍᪉䠈ᕞᕷἈ䛾ሙྜ䛻䛿ὒୖほ 䝍䝽䞊䛻䛚 䛡䜛㻞㻜㻝㻟ᖺ㻝᭶䡚㻝㻞᭶䛾ᖹᆒ㢼㏿䛾㖄┤䝕䞊䝍䛻ᇶ 䛵䛝䠈㧗ᗘ㻞㻜䡉䛸㧗ᗘ㻤㻜㼙䛾ᖹᆒ㢼㏿䛛䜙ồ䜑䛶䛚䜚䠈 䛭䛾್䛿㻥㻚㻡䛸ሗ࿌䛥䜜䛶䛔䜛䠊୧䜿䞊䝇䛸䜒䛻ᆅୖ㧗 㻝㻜㼙⨨䛾Ẽ㇟㻳㻼㼂䝕䞊䝍䛻ᑐ䛧䛶㐣ホ౯䛧䛶䛔 䜛䛾䛜ศ䛛䜛䠊㻌 ḟ䛻ᅗ୰䛾㟷⥺䛻ὀ┠䛧䛶㡬䛝䛯䛔䠊䛣䜜䛿Ẽ㇟ 㻳㻼㼂䝕䞊䝍㻔ᆅୖ㧗㻝㻜㼙㻕䜢ᇶ‽䛻䛧䠈ඛ䛻♧䛧䛯㻺್ 䜢⏝䛔䛶㧗ᗘ㻤㻜㼙䜎䛷䛾⠊ᅖ䜢⾲♧䛧䛯⤖ᯝ䛷䛒䜛䠊 䛣䛾ሙྜ䛻䛿䠈୧䜿䞊䝇䛸䜒䛻ᆅୖ㧗㻤㻜㼙⨨䛾ᐇ 䝕䞊䝍䛻ᑐ䛧䛶㐣ᑠホ౯䛩䜛⤖ᯝ䛸䛺䜛䠊㻌 䛭䛣䛷䠈ୖグ䛾ၥ㢟Ⅼ䜢ゎỴ䛩䜛䛯䜑䛻䠈ᮏ◊✲䛷 䛿㻞ẁ㝵䛾㧗ᗘ⿵ṇ᪉ἲ䜢ᥦ䛩䜛䠊䛣䛾᪉ἲ䛾⪃䛘 ᪉䛿ᅗ㻡䛻䛚䛔䛶䠈ᕞᕷἈ䛾ሙྜ䜢䛻♧䛧䛶䛔 䜛䠊䛣䛾᪉ἲ䛻䜘䜚ᚓ䜙䜜䛯㢼㏿䛾㖄┤ศᕸ䜢ᅗ㻡䛻 ⥳⥺䛷♧䛩䠊ᮏᡭἲ䜢㐺⏝䛩䜛䛣䛸䛷䠈ᆅୖ㧗㻝㻜㼙 ⨨䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘䜃㻸㻲㻹㻙㻿㻕䛾 㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗䛥㻤㻜㼙䡚㻥㻜㼙㻌.
(15) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻝㻝. 㻌 䜈䛾㧗ᗘ⿵ṇ䛜ྍ⬟䛻䛺䜛䠊㻌 ᅗ㻢䛚䜘䜃ᅗ㻣䛻䛿䠈ᐇ 䝕䞊䝍䛚䜘䜃Ẽ㇟㻳㻼㼂䝕 䞊䝍㻔ᆅୖ㧗㻝㻜㼙㻕䛛䜙ゎᯒ䛥䜜䛯㢼㓄ᅗ㻔䝕䞊䝍ゎᯒ ᮇ㛫䠖㻞㻜㻝㻟ᖺ㻝᭶㻝᪥䡚㻝㻞᭶㻟㻝᪥䛾㻝ᖺ㛫㻕䜢♧䛩䠊༓ ⴥ┴㖯ᏊἈ䛸⚟ᒸ┴ᕞᕷἈ䛾୧䜿䞊䝇䛸䜒䛻ᐃ ᛶⓗ䛺ഴྥ䛿㠀ᖖ䛻㢮ఝ䛧䛶䛔䜛䛣䛸䛜♧䛥䜜䛯䠊㻌. 㻌 㻠䠊⤖ゝ㻌 ᮏ◊✲䛾┠ⓗ䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ᆅ ୖ㧗㻝㻜㼙⨨䛷ᢳฟ䛧䛯Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘 䜃㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤 㧗䛥㻤㻜㼙䡚㻥㻜㼙䛻䛚䛡䜛㢼㏿್䜢㧗⢭ᗘ䛻᥎ᐃ㻔㧗ᗘ ⿵ṇ㻕䛩䜛ᡭἲ䜢☜❧䛩䜛䛣䛸䛷䛒䜛䠊㻌 ᮏ◊✲䛷䛿䠈༓ⴥ┴㖯ᏊἈ䛚䜘䜃⚟ᒸ┴ᕞ ᕷἈ䛾ᐇ 䝕䞊䝍䜢⏝䛔䛶䠈ୖグ䛾ᆅୖ㧗㻝㻜㼙⨨ 䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘䜃㻸㻲㻹㻙㻿㻕䛾㢼 ㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗䛥㻤㻜㼙䡚㻥㻜㼙䛻 㧗ᗘ⿵ṇ䛩䜛ሙྜ䛾ၥ㢟Ⅼ䜢ᣦ䛩䜛䛸䛸䜒䛻䠈᪂䛯 䛺㧗ᗘ⿵ṇᡭἲ䛾ᥦ䜢⾜䛳䛯䠊㻌 㻌. 㻌. ཧ㻌 ⪃㻌 ᩥ㻌 ⊩㻌 㻝㻕. 㻞㻕. 㻟㻕. 㻠㻕. 㻡㻕. 㻢㻕. ㅰ㻌 ㎡㻌 ᮏ◊✲䛷ᥖ㍕䛧䛯ᅗ㠃䜔ᐇ 䝕䞊䝍䛿䠈㻺㻱㻰㻻䛾 䝩 䞊 䝮 䝨 䞊 䝆 㻔㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㻌 㼔㼠㼙㼘㻕䛛䜙ᘬ⏝䛥䛫䛶㡬䛝䜎䛧䛯䠊䛣䛣䛻グ䛧䛶㛵ಀ⪅ 䛻ឤㅰ䛾ព䜢⾲䛧䜎䛩䠊㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌. 㻣㻕. 㻌 㻌. ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈Ⲩᒇ㻌 ு䠈Ẽ㇟㻳㻼㼂䝕 䞊䝍䛾㢼ຊⓎ㟁ศ㔝䜈䛾ά⏝䛻㛵䛩䜛᳨ウ䠈 ᕞ Ꮫ ᛂ ⏝ ຊ Ꮫ ◊ ✲ ᡤ ᡤ ሗ 䠈 ➨ 㻝㻠㻠 ྕ 䠈 㼜㼜㻚㻟㻟㻙㻠㻜䠈㻞㻜㻝㻟㻌 ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈ἢᓊ㒊䛻䛚䛡䜛Ẽ㇟ 㻳㻼㼂䝕䞊䝍䜢⏝䛔䛯⡆᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉㮵 ඣᓥ┴ෆ䛾㢼ຊⓎ㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛ ᛂ⏝ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻣ྕ䠈㼜㼜㻚㻝㻡㻙㻞㻥䠈㻞㻜㻝㻠㻌 ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈ᒣ㛫㒊䛻䛚䛡䜛Ẽ㇟ 㻳㻼㼂䝕䞊䝍䜢⏝䛔䛯⡆᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉㜿 ⸽㌴ᖐ㢼ຊⓎ㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛᛂ⏝ ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻣ྕ䠈㼜㼜㻚㻟㻝㻙㻠㻟䠈㻞㻜㻝㻠㻌 ෆ⏣㻌 Ꮥ⣖䠈⚟ᒸᕷෆ䛻䛚䛡䜛㝣ୖ䛸ὒୖ䛾㢼 ἣ≉ᛶ䠈ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻤 ྕ䠈㼜㼜㻚㻡㻝㻙㻡㻤䠈㻞㻜㻝㻡㻌 ෆ⏣㻌 Ꮥ⣖䠈⚟ᒸᕷෆ䛻䛚䛡䜛Ꮨ䛾㢼ἣ≉ᛶ䠈 ᕞ Ꮫ ᛂ ⏝ ຊ Ꮫ ◊ ✲ ᡤ ᡤ ሗ 䠈 ➨ 㻝㻠㻤 ྕ 䠈 㼜㼜㻚㻠㻟㻙㻠㻥䠈㻞㻜㻝㻡㻌 ᕝᓥ㻌 Ὀྐ䠈ෆ⏣㻌 Ꮥ⣖䠈」㞧ᆅᙧ䛻䛚䛡䜛Ẽ㇟ ᗇᒁᆅᩘ್ணሗ䝰䝕䝹䝕䞊䝍㻔㻸㻲㻹㻕䜢⏝䛔䛯⡆ ᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉୵ᮌ㔝䜜䛔䜑䛔㢼ຊⓎ 㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤ ሗ䠈➨㻝㻠㻥ྕ䠈㼜㼜㻚㻡㻝㻙㻢㻟䠈㻞㻜㻝㻡㻌 ෆ ⏣ 㻌 Ꮥ ⣖ 䠈⚟ᒸ ᕷ༤ ከ‴䜢ᑐ ㇟ 䛻䛧䛯 Ẽ㇟ 㻳㻼㼂䝕䞊䝍䛻䜘䜛ὒୖ㢼ἣゎᯒ䠈ᕞᏛᛂ⏝ ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻥ྕ䠈㼜㼜㻚㻢㻠㻙㻣㻝䠈㻞㻜㻝㻡㻌.
(16) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻔㻝㻞㻙㻞㻟㻕㻌㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌. ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛 㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾2 䇷⚟ᒸ┴ᕞᕷ㡪ℿὒୖ㢼ຊⓎ㟁䛾᳨ウ䇷 㻌 ෆ⏣㻌 Ꮥ⣖㻖㻌 㻔㻞㻜㻝㻢ᖺ㻣᭶㻞㻥᪥ཷ⌮㻕㻌. 㻌 New Wind Speed Vertical Extrapolation Method by using Power Law in Offshore Wind Observation: Part2 ̿Numerical investigation of the offshore wind energy in the Hibikinada region̿ Takanori UCHIDA E-mail of corresponding author: takanori@riam.kyushu-u.ac.jp. Abstract. Offshore wind energy development promises to be a significant domestic renewable energy source. There are two approaches to estimating the increase in wind speed with height: the power law method and the logarithmic method. Logarithmic extrapolation is derived mathematically from a theoretical understanding of how the wind moves across the surface of the earth. In contrast, the power law equation is derived empirically from actual measurements. For an assessment of offshore wind energy resources by using the weather GPV (MSM-S and LFM-S) wind speed data at 10m above the sea surface, a new wind speed vertical extrapolation method based on a power law was proposed in the present study. In addition, the numerical investigation of the offshore wind energy in the Hibikinada region was performed. Key words : Offshore wind energy, Weather GPV data, Vertical extrapolation method, Power law. 㻌 㻝䠊⥴ゝ㻌 ㏆ᖺ䠈㝣ୖ㢼ຊⓎ㟁㻔䜸䞁䝅䝵䜰㢼ຊⓎ㟁㻕䛻ຍ䛘䛶䠈 ὒୖ㢼ຊⓎ㟁㻔䜸䝣䝅䝵䜰㢼ຊⓎ㟁㻕䛜ὀ┠䛥䜜䛶䛝䛶 䛚䜚䠈Ḣᕞ䜢୰ᚰ䛻つᶍ䛺ὒୖ䜴䜲䞁䝗䝣䜯䞊䝮䛜 ᘓタ䛥䜜䛶䛔䜛䠊୍᪉᪥ᮏ䛷䛿䠈㝣ୖ㢼ຊⓎ㟁䛾䜏 䛺䜙䛪ὒୖ㢼ຊⓎ㟁䛾ศ㔝䛷䜒Ḣᕞ䛻䛝䛟ᚋ䜜䜢䛸 䛳䛶䛔䜛䠊㻌 䛧䛛䛧᪥ᮏ䛿䠈㡿ᾏ䛚䜘䜃ⓗ⤒῭Ỉᇦ䜢ྜ䜟 䛫䛯㠃✚䛜ୡ⏺➨㻢䠄⣙㻠㻠㻣㼙㻞䠅䛾ᾏὒᅜ䛷䛒䜚䠈 ὒୖ㢼ຊⓎ㟁䛾䝫䝔䞁䝅䝱䝹䛻䛿ᜨ䜎䜜䛶䛔䜛䠊䜶䝛 䝹䜼䞊ᇶᮏィ⏬㻞㻜㻝㻠䛷䛿䠈䛂୰㛗ᮇⓗ䛻䛿䠈㝣ୖ㢼 ຊ䛾ᑟධྍ⬟䛺㐺ᆅ䛜㝈ᐃⓗ䛺ᡃ䛜ᅜ䛻䛚䛔䛶䠈ὒ ୖ㢼ຊⓎ㟁䛾ᑟධᣑ䛿ྍḞ䛷䛒䜛䛃䛸᭩䛛䜜䛶 䛔䜛䠊ᚋ䠈䛥䜙䛺䜛Ⓨᒎ䛜ᮇᚅ䛥䜜䛶䛔䜛䠊㻌 ୍⯡♫ᅋἲே᪥ᮏ㢼ຊⓎ㟁༠㻔㻶㼃㻼㻭㻕䛻䜘䜜䜀䠈 ᪥ᮏ䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁䛾⣼✚ᑟධ┠ᶆ䛿䠈㻞㻜㻟㻜 ᖺ䛻㻥㻢㻜㼗㼃䠈㻞㻜㻡㻜ᖺ䛻䛿㻟㻘㻣㻜㻜㼗㼃䛸䛺䛳䛶䛚䜚䠈 㻖㻌 ᕞᏛᛂ⏝ຊᏛ◊✲ᡤ㻌. 㻌. つᶍ䛻ᑟධ䛥䜜䜛䛸䛾ヨ⟬䛜䜎䛸䜑䜙䜜䛶䛔䜛䠊㻌 ὒୖ㢼ຊⓎ㟁ᴗ䜢᳨ウ䛩䜛㝿䠈䛭䛾ᴗ䛻䛚䛡 䜛᥇⟬ᛶ䜔ᴗ䝸䝇䜽䛺䛹䜢ヲ⣽䛻๓ホ౯䛩䜛ᚲせ 䛜䛒䜛䠊≉䛻䠈㢼ἣㄪᰝ䛾⤖ᯝ䜢⏝䛔䛶㢼㌴䛾タィ 䜔᭱㐺䛺タ⨨ィ⏬䛜సᡂ䛥䜜䜛䛯䜑䠈ṇ☜䛺㢼ἣᢕ ᥱ䛿᭱㔜せ᳨ウ㡯┠䛷䛒䜛䠊㻌 ୍⯡䛻䠈ὒୖ㢼ἣㄪᰝ䛷䛿䠈ほ 㧗ᗘ䛸㢼㌴䝝䝤 㧗䛾㛫䛾㧗ᗘ⿵ṇ䛜ᚲせ䛸䛺䜛䠊ᩘ್㢼ἣ䝅䝭䝳䝺䞊 䝅䝵 䞁䜢⏝䛔䛺䛔ሙྜ䛻䛿䠈⤒㦂๎䛺䜉䛝๎䠄㼍㼚㻌 㼑㼙㼜㼕㼞㼕㼏㼍㼘㻌 㼜㼛㼣㼑㼞㻌 㼘㼍㼣㻕䛻ᇶ䛵䛔䛶䠈㢼㏿䛾㧗ᗘ⿵ṇ䛜 ⾜䜟䜜䜛䛾䛜୍⯡ⓗ䛷䛒䜛䠊㻌 ᡃ䚻䛾䜾䝹䞊䝥䛷䛿䠈Ẽ㇟ᗇ䛜ᥦ౪䛩䜛✀䚻䛾Ẽ ㇟㻳㼞㼕㼐㻌 㻼㼛㼕㼚㼠㻌 㼂㼍㼘㼡㼑㻔㻳㻼㼂㻕䝕䞊䝍䜢䠈㢼ຊⓎ㟁ศ㔝䜈 㐺⏝䛩䜛䛯䜑䛾◊✲㛤Ⓨ䜢㐍䜑䛶䛝䛯䠊≉䛻䠈ᾏ㠃䛛 䜙䛾㧗ᗘ䛜㻝㻜㼙䛻ᅛᐃ䛥䜜䛶䛔䜛䝯䝋ᩘ್ணሗ䝰䝕䝹 㻹㼑㼟㼛㻌 㻿㼏㼍㼘㼑㻌 㻹㼛㼐㼑㼘㻔㻹㻿㻹㻙㻿䠈Ỉᖹゎീᗘ㻡㼗㼙㻕䛸䠈ᒁᆅ ᩘ್ணሗ䝰䝕䝹㻸㼛㼏㼍㼘㻌 㻲㼛㼞㼑㼏㼍㼟㼠㻌 㻹㼛㼐㼑㼘㻔㻸㻲㻹㻙㻿䠈Ỉᖹ ゎീᗘ㻞㼗㼙㻕䛾⏝䛸䛭䛾ண ⢭ᗘ䛾᳨ド䜢⾜䛳䛶䛝.
(17) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻝㻟. 䛯㻝㻙㻣㻕䠊㻌 ᮏሗ䛷䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ୖグ䛾ᆅ ୖ㧗㻝㻜㼙⨨䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘䜃 㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗䛥 㻤㻜㼙䡚㻥㻜㼙䛻㧗ᗘ⿵ṇ䛩䜛ሙྜ䛾ၥ㢟Ⅼ䜢ᣦ䛩䜛 䛸䛸䜒䛻䠈᪂䛯䛺㧗ᗘ⿵ṇᡭἲ䛾ᥦ䜢⾜䛖䠊䛥䜙䛻䠈 ⚟ᒸ┴ᕞᕷ䛾㡪ℿὒୖ㢼ຊⓎ㟁ᑟධ䛾᳨ウ䜒 ⾜䛳䛯䠊㻌 㻌. 㻞䠊ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖㻌 㻺㻱㻰㻻㻔ᅜ❧◊✲㛤Ⓨἲே᪂䜶䝛䝹䜼䞊䞉⏘ᴗᢏ⾡ ⥲ྜ㛤Ⓨᶵᵓ㻕䛷䛿䠈༓ⴥ┴㖯ᏊἈ䛚䜘䜃⚟ᒸ┴ ᕞᕷἈ䛾㻞ᆅⅬ䜢ᑐ㇟䛻䛧䠈ᅜෆ䛷ึ䜑䛶䛾Ἀྜ 䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁䛾ᐇ⌧䛻ྥ䛡䛶䠈㢼ྥ䛸㢼㏿ 䜢ほ 䛩䜛ὒୖ㢼ἣほ 䝍䝽䞊䛸ᐇ㝿䛻ὒୖ䛻䛚䛔 䛶Ⓨ㟁䜢⾜䛖ὒୖ㢼㌴䜢ᐇᾏᇦ䛻タ⨨䛩䜛䝥䝻䝆䜵䜽 䝖䜢㻞㻜㻜㻥ᖺᗘ䜘䜚ᐇ䛧䛶䛔䜛䠊㖯ᏊἈ䛷䛿㻞㻜㻝㻟ᖺ㻟 ᭶䛛䜙䠈ᕞᕷἈ䛷䛿㻞㻜㻝㻟ᖺ㻢᭶䛛䜙䛭䜜䛮䜜㐠 ㌿䜢㛤ጞ䛧䠈ᐇド◊✲䛜⾜䜟䜜䛶䛔䜛㻔㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㻌 㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻕䠊ᮏ◊✲䛷䛿䠈⚟ᒸ┴ 㻌. ᕞᕷἈ䛾ὒୖ㢼ἣ䝕䞊䝍䜢ᑐ㇟䛻ㄪᰝ䜢⾜䛖䛸 䛸䜒䛻䠈ὒୖ㢼ຊⓎ㟁䛾⤒῭ⓗヨ⟬䜢ᐇ䛧䛯㻔ᅗ㻝䛸 ᅗ㻞䜢ཧ↷㻕㻌㻤㻘㻌㻥㻕䠊㻌 㻌. 㻟䠊ゎᯒ⤖ᯝ䛚䜘䜃⪃ᐹ㻌 ᮏ◊✲䛾┠ⓗ䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ᆅ ୖ㧗㻝㻜㼙⨨䛷ᢳฟ䛧䛯Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䛚䜘 䜃㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤 㧗䛥㻤㻜㼙䡚㻥㻜㼙䛻䛚䛡䜛㢼㏿್䜢㧗⢭ᗘ䛻᥎ᐃ㻔㧗ᗘ ⿵ṇ㻕䛩䜛ᡭἲ䜢☜❧䛩䜛䛣䛸䛷䛒䜛䠊㻌 ᅗ㻟䛻䛿䠈ᮏ◊✲䛻䛚䛡䜛Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈 ᆅୖ㧗㻝㻜㼙㻕䛾ྲྀᚓ⨨䛸ὒୖ㢼ἣほ ᆅⅬ䛸䛾⨨ 㛵ಀ䜢♧䛩䠊Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗㻝㻜㼙㻕䛾 ヲ⣽䛻䛴䛔䛶䛿ᩥ⊩㻝㻙㻣㻕 䜢ཧ↷䛧䛶㡬䛝䛯䛔䠊ྠᅗ䛻 ♧䛩䜘䛖䛻䠈⚟ᒸ┴ᕞᕷἈ䛾䝕䞊䝍ゎᯒ䛷䛿䠈 㻼㼛㼕㼚㼠㻟䛷ྲྀᚓ䛥䜜䛯Ẽ㇟㻳㻼㼂䝕䞊䝍㻔㻹㻿㻹㻙㻿䠈ᆅୖ㧗 㻝㻜㼙㻕䜢ほ ᆅⅬ䛾㢼㏿್䛸ぢ䛺䛧䛶⏝䛔䛯䠊ホ౯ᮇ 㛫䛿㻞㻜㻝㻞ᖺ㻝㻜᭶㻝᪥䡚㻞㻜㻝㻟ᖺ㻤᭶㻟㻝᪥䜎䛷䛾㻝㻝䞄᭶ 䛷䛒䜛䠊㻌. 㻌 㻌 ᅗ㻝㻌 ᮏ◊✲䛷ᑐ㇟䛸䛧䛯ᐇド◊✲䝃䜲䝖䛾ヲ⣽㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㼔㼠㼙㼘㻌.
(18) 㻝㻠㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻞㻌. 㻌. 㻌. 㻌 ᅗ㻞㻌 ᐇド◊✲䝃䜲䝖䛾┿㻌 㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼜㼔㼛㼠㼛㼓㼍㼘㼘㼑㼞㼥㻚㼔㼠㼙㼘㻌 㻌. 㻌. 㻌 ᅗ㻟㻌 Ẽ㇟㻳㻼㼂䝕䞊䝍䛾ྲྀᚓ⨨䛸ὒୖ㢼ἣほ ᆅⅬ䛸䛾⨨㛵ಀ㻌.
(19) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻝㻡. 㻌 㻌 㻌. 㻌. 㻌 㻌 㻌. 㻌 㻌 ᅗ㻠㻌 㝣䛛䜙䛾㢼䜢ᑐ㇟䛸䛧䛯ሙྜ㻌 䝕䞊䝍ゎᯒᮇ㛫㻌 䠖㻌 㻞㻜㻝㻞ᖺ㻝㻜᭶㻝᪥䡚㻞㻜㻝㻟ᖺ㻤᭶㻟㻝᪥䜎䛷䛾㻝㻝䞄᭶㻌 㻌.
(20) 㻝㻢㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻞㻌. 㻌. 㻌 ᅗ㻡㻌 ᾏ䛛䜙䛾㢼䜢ᑐ㇟䛸䛧䛯ሙྜ㻌 䝕䞊䝍ゎᯒᮇ㛫㻌 䠖㻌 㻞㻜㻝㻞ᖺ㻝㻜᭶㻝᪥䡚㻞㻜㻝㻟ᖺ㻤᭶㻟㻝᪥䜎䛷䛾㻝㻝䞄᭶㻌 㻌 㻌. 㻌. ᅗ㻢㻌 䝕䞊䝍䛾㢼䜢ᑐ㇟䛸䛧䛯ሙྜ㻌 䝕䞊䝍ゎᯒᮇ㛫㻌 䠖㻌 㻞㻜㻝㻞ᖺ㻝㻜᭶㻝᪥䡚㻞㻜㻝㻟ᖺ㻤᭶㻟㻝᪥䜎䛷䛾㻝㻝䞄᭶㻌.
(21) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻝㻣. 㻔㼍㻕㢼㏿䠖᭷ḟඖ㻌. 㻌. 㻔㼎㻕㢼㏿䠖↓ḟඖ㻌. 㻌. ᅗ㻣㻌 ᮏ◊✲䛷ᥦ䛩䜛᪂䛧䛔㧗ᗘ⿵ṇ᪉ἲ䛻䜘䜚㻌 ホ౯䛥䜜䛯㢼㏿䛾㖄┤ศᕸ䛾ẚ㍑㻌 㻌 䝕䞊䝍ゎᯒᮇ㛫㻌 䠖㻌 㻞㻜㻝㻞ᖺ㻝㻜᭶㻝᪥䡚㻞㻜㻝㻟ᖺ㻤᭶㻟㻝᪥䜎䛷䛾㻝㻝䞄᭶㻌 㻌.
(22) 㻝㻤㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻞㻌. 㻌 㻌. 㻌. ᅗ㻤㻌 㢼㌴䛾䝟䝽䞊䜹䞊䝤㻌 㻌 㻌. 㻌. ᅗ㻥㻌 㻞㻜㻝㻟ᖺ䛾㢼㓄ᅗ㻌.
(23) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻝㻥. 㻌 㻌. 㻌 ᅗ㻝㻜㻌 㻞㻜㻝㻠ᖺ䛾㢼㓄ᅗ㻌 㻌 㻌. 㻌. ᅗ㻝㻝㻌 㻞㻜㻝㻡ᖺ䛾㢼㓄ᅗ㻌.
(24) 㻞㻜㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻞㻌. 㻌 㻌 㻌. 㻌 㻌. 㻌 㻌 ᅗ㻝㻞㻌 㻞㻜㻝㻟ᖺ䛾㢼ἣ䛸⤒῭ᛶ䛾ヨ⟬⤖ᯝ㻌.
(25) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻞㻝. 㻌 㻌 㻌. 㻌. 㻌. 㻌 ᅗ㻝㻟㻌 㻞㻜㻝㻠ᖺ䛾㢼ἣ䛸⤒῭ᛶ䛾ヨ⟬⤖ᯝ㻌. 㻌.
(26) 㻞㻞㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 ෆ⏣䠖ὒୖ㢼ἣㄪᰝ䛻䛚䛡䜛㢼㏿䛾㧗ᗘ⿵ṇ䛻㛵䛩䜛᪂䛧䛔ᥦ㻌 䛭䛾㻞㻌. 㻌 㻌 㻌. 㻌. 㻌. 㻌 㻌 ᅗ㻝㻠㻌 㻞㻜㻝㻡ᖺ䛾㢼ἣ䛸⤒῭ᛶ䛾ヨ⟬⤖ᯝ㻌.
(27) ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ㻌 ➨㻝㻡㻝ྕ㻌 㻞㻜㻝㻢ᖺ㻥᭶㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻞㻟. 㻌 ᅗ㻠䡚ᅗ㻣䛻䛿䠈ᮏ◊✲䛷ᥦ䛩䜛㻞ẁ㝵䛾㧗ᗘ⿵ ṇ᪉ἲ䛻䜘䜚ᚓ䜙䜜䛯⤖ᯝ䜢♧䛩䠊䛣䛣䛷䠈㻞ẁ㝵䛾㧗 ᗘ⿵ṇ᪉ἲ䛿ୗグ䛻♧䛩㏻䜚䛷䛒䜛䠊䜎䛯䠈ᅗ㻠䛻䛿 ᾏ䛛䜙䛾㢼䠈㝣䛛䜙䛾㢼䛸䛧䛶ᐃ⩏䛧䛯㢼ྥ䜒♧䛩䠊㻌 㻌 㻌 䛂䝇䝔䝑䝥㻝䛃㻌 㧗ᗘ㻝㻜㼙䛾㻳㻼㼂䝕䞊䝍䛸㻌 㧗ᗘ㻟㻝㻚㻢㼙䛾ᐇ 䝕䞊䝍䛛䜙㻌 㻔㻝㻕ᘧ䛻䜘䜚䠈㻺್䜢ᑟฟ㻌 㻌 䛂䝇䝔䝑䝥㻞䛃㻌 㧗ᗘ㻟㻝㻚㻢㼙䛾ᐇ 䝕䞊䝍䛸㻌 㧗ᗘ㻤㻝㻚㻢㼙䛾ᐇ 䝕䞊䝍䛛䜙㻌 㻔㻝㻕ᘧ䛻䜘䜚䠈㻺್䜢ᑟฟ㻌 㻌 䜉䛝๎. 㧗䛔䛣䛸䛜ᨵ䜑䛶♧䛥䜜䛯䠊ᚋ䠈䛥䜙䛺䜛ㄪᰝ䞉◊ ✲䜢ᐇ䛧䛶䛔䛟ணᐃ䛷䛒䜛䠊㻌 㻌. ཧ㻌 ⪃㻌 ᩥ㻌 ⊩㻌 㻝㻕. 㻞㻕. 㻟㻕. 1. U h2
(28). § h ·N U h1
(29) ¨ 2 ¸ 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻔㻝㻕㻌 © h1 ¹. 㻌 ᮏ◊✲䛷ᥦ䛩䜛㻞ẁ㝵䛾㧗ᗘ⿵ṇ᪉ἲ㻌 㻌 ᅗ㻤䡚ᅗ㻝㻠䛻䛿䠈ᅗ㻟䛻♧䛩㻼㼛㼕㼚㼠㻟䛷ᢳฟ䛧䛯㻞㻜㻝㻟㻘㻌 㻞㻜㻝㻠㻘㻌 㻞㻜㻝㻡ᖺ䛾㻟ᖺ㛫䛾Ẽ㇟㻳㻼㼂䝕䞊䝍㻔ᆅୖ㧗㻝㻜㼙㻕 䛻ᑐ䛧䛶䠈ᮏ◊✲䛷ᥦ䛩䜛㻞ẁ㝵䛾㧗ᗘ⿵ṇ᪉ἲ 䜢㐺⏝䛧䠈ᆅୖ㧗㻤㻜㼙䛻㧗ᗘ⿵ṇ䛧䛯䝕䞊䝍䛻ᇶ䛵䛔 䛶ゎᯒ䛧䛯⤖ᯝ䜢♧䛩䠊ᚓ䜙䜜䛯䛣䜜䜙䛾⤖ᯝ䛛䜙䠈 ⚟ᒸ┴ᕞᕷ䛾㡪ℿᆅ༊䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁 ᑟධ䛾ྍ⬟ᛶ䛿䠈㠀ᖖ䛻㧗䛔䛣䛸䛜ᨵ䜑䛶♧䛥䜜䛯䠊㻌 㻌. ㅰ㻌 ㎡㻌 ᮏ◊✲䛷ᥖ㍕䛧䛯ᅗ㠃䜔ᐇ 䝕䞊䝍䛿䠈㻺㻱㻰㻻䛾 䝩 䞊 䝮 䝨 䞊 䝆 㻔㼔㼠㼠㼜㻦㻛㻛㼣㼣㼣㻚㼚㼑㼐㼛㻚㼓㼛㻚㼖㼜㻛㼒㼡㼡㼟㼔㼍㻛㼕㼚㼐㼑㼤㻚㻌 㼔㼠㼙㼘㻕䛛䜙ᘬ⏝䛥䛫䛶㡬䛝䜎䛧䛯䠊䛣䛣䛻グ䛧䛶㛵ಀ⪅ 䛻ឤㅰ䛾ព䜢⾲䛧䜎䛩䠊㻌. 㻌 㻠䠊⤖ゝ㻌 ᮏሗ䛷䛿䠈⤒㦂๎䛺䜉䛝๎䜢㐺⏝䛧䠈ᆅୖ㧗㻝㻜㼙 ⨨ 䛻 䛚 䛡 䜛 Ẽ ㇟ 㻳㻼㼂 䝕 䞊 䝍 㻔㻹㻿㻹㻙㻿 䛚 䜘 䜃 㻸㻲㻹㻙㻿㻕䛾㢼㏿್䛛䜙䠈୍⯡ⓗ䛺ὒୖ㢼㌴䛾䝝䝤㧗 䛥㻤㻜㼙䡚㻥㻜㼙䛻㧗ᗘ⿵ṇ䛩䜛ሙྜ䛾ၥ㢟Ⅼ䜢ᣦ䛩 䜛䛸䛸䜒䛻䠈᪂䛯䛺㧗ᗘ⿵ṇᡭἲ䛾ᥦ䜢⾜䛳䛯䠊䛥 䜙䛻䠈⚟ᒸ┴ᕞᕷ䛾㡪ℿὒୖ㢼ຊⓎ㟁ᑟධ䛾 ᳨ウ䜒⾜䛳䛯䠊䛭䛾⤖ᯝ䠈⚟ᒸ┴ᕞᕷ䛾㡪ℿᆅ ༊䛻䛚䛡䜛ὒୖ㢼ຊⓎ㟁ᑟධ䛾ྍ⬟ᛶ䛿䠈㠀ᖖ䛻. 㻠㻕. 㻡㻕. 㻢㻕. 㻣㻕. 㻤㻕. 㻥㻕. 㻌 㻌㻌. ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈Ⲩᒇ㻌 ு䠈Ẽ㇟㻳㻼㼂䝕 䞊䝍䛾㢼ຊⓎ㟁ศ㔝䜈䛾ά⏝䛻㛵䛩䜛᳨ウ䠈 ᕞ Ꮫ ᛂ ⏝ ຊ Ꮫ ◊ ✲ ᡤ ᡤ ሗ 䠈 ➨ 㻝㻠㻠 ྕ 䠈 㼜㼜㻚㻟㻟㻙㻠㻜䠈㻞㻜㻝㻟㻌 ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈ἢᓊ㒊䛻䛚䛡䜛Ẽ㇟ 㻳㻼㼂䝕䞊䝍䜢⏝䛔䛯⡆᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉㮵 ඣᓥ┴ෆ䛾㢼ຊⓎ㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛ ᛂ⏝ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻣ྕ䠈㼜㼜㻚㻝㻡㻙㻞㻥䠈㻞㻜㻝㻠㻌 ෆ⏣㻌 Ꮥ⣖䠈ᕝᓥ㻌 Ὀྐ䠈ᒣ㛫㒊䛻䛚䛡䜛Ẽ㇟ 㻳㻼㼂䝕䞊䝍䜢⏝䛔䛯⡆᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉㜿 ⸽㌴ᖐ㢼ຊⓎ㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛᛂ⏝ ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻣ྕ䠈㼜㼜㻚㻟㻝㻙㻠㻟䠈㻞㻜㻝㻠㻌 ෆ⏣㻌 Ꮥ⣖䠈⚟ᒸᕷෆ䛻䛚䛡䜛㝣ୖ䛸ὒୖ䛾㢼 ἣ≉ᛶ䠈ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻤 ྕ䠈㼜㼜㻚㻡㻝㻙㻡㻤䠈㻞㻜㻝㻡㻌 ෆ⏣㻌 Ꮥ⣖䠈⚟ᒸᕷෆ䛻䛚䛡䜛Ꮨ䛾㢼ἣ≉ᛶ䠈 ᕞ Ꮫ ᛂ ⏝ ຊ Ꮫ ◊ ✲ ᡤ ᡤ ሗ 䠈 ➨ 㻝㻠㻤 ྕ 䠈 㼜㼜㻚㻠㻟㻙㻠㻥䠈㻞㻜㻝㻡㻌 ᕝᓥ㻌 Ὀྐ䠈ෆ⏣㻌 Ꮥ⣖䠈」㞧ᆅᙧ䛻䛚䛡䜛Ẽ㇟ ᗇᒁᆅᩘ್ணሗ䝰䝕䝹䝕䞊䝍㻔㻸㻲㻹㻕䜢⏝䛔䛯⡆ ᫆㢼ἣ᥎ᐃἲ䛾ヨ䜏䠉୵ᮌ㔝䜜䛔䜑䛔㢼ຊⓎ 㟁ᡤ䜢䛸䛧䛶䠉䠈ᕞᏛᛂ⏝ຊᏛ◊✲ᡤᡤ ሗ䠈➨㻝㻠㻥ྕ䠈㼜㼜㻚㻡㻝㻙㻢㻟䠈㻞㻜㻝㻡㻌 ෆ ⏣ 㻌 Ꮥ ⣖ 䠈⚟ᒸ ᕷ༤ ከ‴䜢ᑐ ㇟ 䛻䛧䛯 Ẽ㇟ 㻳㻼㼂䝕䞊䝍䛻䜘䜛ὒୖ㢼ἣゎᯒ䠈ᕞᏛᛂ⏝ ຊᏛ◊✲ᡤᡤሗ䠈➨㻝㻠㻥ྕ䠈㼜㼜㻚㻢㻠㻙㻣㻝䠈㻞㻜㻝㻡㻌 ྜྷᮧ㻌 㻌 ㇏䠈ᕞᕷἈὒୖ㢼ຊⓎ㟁䝅䝇䝔䝮ᐇ ド◊✲➼䛾≧ἣ䠈➨㻟㻡㢼ຊ䜶䝛䝹䜼䞊⏝䝅䞁 䝫䝆䜴䝮ㅮ₇ㄽᩥ㞟䠈㼜㼜㻚㻠㻣㻤㻙㻠㻤㻝䠈㻞㻜㻝㻟㻌 㟷ᮌ㻌 ຌ䠈ྜྷᮧ㻌 㻌 ㇏䠈ᕞᕷἈὒୖ㢼ἣほ 䝅䝇䝔䝮ᐇド◊✲䛻䜘䜛ὒୖ㢼ἣ≉ᛶゎᯒ䠈➨ 㻟㻡㢼ຊ䜶䝛䝹䜼䞊⏝䝅䞁䝫䝆䜴䝮ㅮ₇ㄽᩥ㞟䠈 㼜㼜㻚㻠㻤㻞㻙㻠㻤㻡䠈㻞㻜㻝㻟㻌.
(30) ěŵƹîÒȮȻîĭċſſȖ ƺ Ņ
(31) ǯĩ. ŋóÙĕÄİāÒwÚŪ_bŋóáĬĽġöŗj µŨwŞīf_bx}iqtĉğŋÅĆĞ JÉŝşuSpSŋŬľįüwŭf_dJ Caj >ÏĖAiqtŋÅĶĊōďD ƤǞ ƷŘ ǩǘ ļĂ ǯĩ ǬŲȲ Large-eddy simulation of airflow over complex terrain aiming at optimal placement method examination of wind turbines. In the case of the kushikinoreimei wind farm Yasushi KAWASHIMA and Takanori UCHIDA E-mail of corresponding author: y-kawashima@wjec.co.jp Abstract. Recently to become, in wind farm, which was built on the complex terrain, the operation rate is less than the initial expectations, ie, power generation output and significantly bad windmill, failure of windmill inside and outside (for example, failure of the yaw motor and Yogia, windmill blades cracks, etc.) of the problem of is actualized. The main cause is a change in the windmill most recent slight terrain relief becomes origin, I considered to be a disorder of the wind (terrain turbulence) generated from there. In response to this situation, in our group, precise numerical wind diagnosis by real terrain version RIAM-COMPACT® software (the wind risk assessment) was performed, has conducted studies safe windmill operating method 1). In this paper, Kyudenko Corporation under the cooperation of the New Energy Co., Ltd., as the target of the 10 Unit kushikinorei wind farm (operation started in November 2012), for the purpose of windmill optimal placement study that takes into account the wind turbine structural strength conditions, since it was carried out numerical wind conditions diagnosis, to report on the results. Key words : Large-Eddy Simulation, Wind energy, Complex terrain, optimal placement method. <ýÕ ŎęrqAŕöȇqpsȋœǁģƆrīơbh ȈȻǷǙſrYVmAÛǣȵ[ǠžsȫƧÕâA dq iAǷǙŹȻ[ljc]¾VȈŭ~AȈŭǩæsĶ ƅJȼXuA²G®GG~²GsĶƅAȈŭ¨¶G ¡s³qpKsȦƻ[İŐÖcmVB`sŮhIJ ÊtAȈŭnjęsėZqǁģąȉsȒÖ[ąĴoqA g`ZǷƚdȈsȰJǁģȰȷKnUoŀX B `sȭqdžAǬțʼnǩsȴƆȈŭsƇņAǔǁĊ |mAŊķbrŕöȇqpsȋœǁģrȈŭīơ[ Ə|`o[ȫƧbh|AȈŭţĶ~Ķƅǎ ijddzǂȂØŰȘsêȶ[ǿȯnUB `sWqƊđŲ^AßFsĭċµG©ntAý ơȈŭƳƄrŪǁģǹ! # § . rƛȝqƕǀȈđƎƿJ¹¡´ȂØKŪ ŞcAÁƥqȈŭÏǖȗȘsĬǢŪŞcmV Bț ȖntAěǙĽƍ£µGɄsĎȻsÕAĞȤȧ V|VȈȻǷǙſȐƘ ǯ. ĩÏǖäŚsȈ ŭ ŅÿƳƄocmAȈŭĿƫĐǜƉĪŀȸch ƕǀȈđȣZsȈŭŎǔdzǂŰȘsĬǢȥǓoc mAȈŭ¨¶G¡ɂz~ȈđGĦƭcAĦƭG ZȈŭĿƫĐǜwŎ}ÐĒȬXhȈĻǧǐc hsngsáƝĨÚrkVmȖňdByhAȈđȣZ sȈŭŎǔdzǂŰȘsêȶsh|AǧǐbhȈĻ ƳƄrƕǀȈđƎƿŪŞchsnAgsĨÚrk Vm}ȖňdB. ƜǬțĆźäǷɄLěŵƹîŁĝÍLJĽîƣľūàƐǵřÝǑŐƟMCěŵƹîÒȮȻîĭċſ.
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