메뉴 건너뛰기




Volumn 48, Issue 1, 1997, Pages 325-364

Some recent advances in the theory of homogeneous isotropic turbulence

Author keywords

Critical point phenomena; Homogeneous turbulence; Isotropic turbulence; Theory and models of chaotic systems; Turbulence simulation and modelling

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; GEOMETRY; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; NUMERICAL ANALYSIS; PROBABILITY; THREE DIMENSIONAL; VELOCITY;

EID: 0030682360     PISSN: 03044289     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02845638     Document Type: Article
Times cited : (20)

References (112)
  • 15
    • 45249125458 scopus 로고
    • To the best of our knowledge, a direct mapping of a deterministic partial differential equation (PDE) with spatiotemporal chaos onto a stochastic PDE has been carried out only for the Kuramoto-Sivashinsky (KS) equation. This mapping uses a numerical coarse-graining procedure and shows, both in one and two spatial dimensions, that the KS equation is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation, i.e., the long-distance and long-time behaviours of their correlations functions are the same. (See: S Zaleski, Physica D34, 427 (1989); F Hayot, C Jayaprakash and Ch Josserand, Phys. Rev. E47, 911 (1993); C Jayaprakash, F Hayot and R Pandit, Phys. Rev. Lett. 71, 15 (1993).) The case of the deterministically forced Navier-Stokes equation is considerably more subtle; however, in the absence of a direct mapping, it has been conjectured that the appropriate PDA is the NS equation with an additive, Gaussian white noise whose variance has a power-law dependence on the wave-vector [16,17,18]
    • (1989) Physica , vol.D34 , pp. 427
    • Zaleski, S.1
  • 16
    • 0000158288 scopus 로고
    • To the best of our knowledge, a direct mapping of a deterministic partial differential equation (PDE) with spatiotemporal chaos onto a stochastic PDE has been carried out only for the Kuramoto-Sivashinsky (KS) equation. This mapping uses a numerical coarse-graining procedure and shows, both in one and two spatial dimensions, that the KS equation is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation, i.e., the long-distance and long-time behaviours of their correlations functions are the same. (See: S Zaleski, Physica D34, 427 (1989); F Hayot, C Jayaprakash and Ch Josserand, Phys. Rev. E47, 911 (1993); C Jayaprakash, F Hayot and R Pandit, Phys. Rev. Lett. 71, 15 (1993).) The case of the deterministically forced Navier-Stokes equation is considerably more subtle; however, in the absence of a direct mapping, it has been conjectured that the appropriate PDA is the NS equation with an additive, Gaussian white noise whose variance has a power-law dependence on the wave-vector [16,17,18]
    • (1993) Phys. Rev. , vol.E47 , pp. 911
    • Hayot, F.1    Jayaprakash, C.2    Josserand, Ch.3
  • 17
    • 45249125458 scopus 로고
    • To the best of our knowledge, a direct mapping of a deterministic partial differential equation (PDE) with spatiotemporal chaos onto a stochastic PDE has been carried out only for the Kuramoto-Sivashinsky (KS) equation. This mapping uses a numerical coarse-graining procedure and shows, both in one and two spatial dimensions, that the KS equation is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation, i.e., the long-distance and long-time behaviours of their correlations functions are the same. (See: S Zaleski, Physica D34, 427 (1989); F Hayot, C Jayaprakash and Ch Josserand, Phys. Rev. E47, 911 (1993); C Jayaprakash, F Hayot and R Pandit, Phys. Rev. Lett. 71, 15 (1993).) The case of the deterministically forced Navier-Stokes equation is considerably more subtle; however, in the absence of a direct mapping, it has been conjectured that the appropriate PDA is the NS equation with an additive, Gaussian white noise whose variance has a power-law dependence on the wave-vector [16,17,18]
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 15
    • Jayaprakash, C.1    Hayot, F.2    Pandit, R.3
  • 20
    • 30344463973 scopus 로고
    • V Yakhot and S A Orszag, J. Sci. Comput. 1, 3 (1986); Phys. Rev. Lett. 57, 1722 (1986)
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 1722
  • 21
    • 0039786407 scopus 로고
    • J K Bhattacharjee, J. Phys. A21, L 551 (1988); Phys. Rev. A40, 6374 (1989); Phys. Fluids A3, 879 (1991)
    • (1988) J. Phys. , vol.A21
    • Bhattacharjee, J.K.1
  • 22
    • 6244247788 scopus 로고
    • J K Bhattacharjee, J. Phys. A21, L 551 (1988); Phys. Rev. A40, 6374 (1989); Phys. Fluids A3, 879 (1991)
    • (1989) Phys. Rev. , vol.A40 , pp. 6374
  • 23
    • 0039786407 scopus 로고
    • J K Bhattacharjee, J. Phys. A21, L 551 (1988); Phys. Rev. A40, 6374 (1989); Phys. Fluids A3, 879 (1991)
    • (1991) Phys. Fluids , vol.A3 , pp. 879
  • 27
    • 15744401041 scopus 로고
    • P Bak, C Tang and K Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A38, 364 (1988)
    • (1988) Phys. Rev. , vol.A38 , pp. 364
  • 70
    • 10844232588 scopus 로고    scopus 로고
    • D Lohse and A Müller-Groeling, Phys. Rev. Lett. 74, 1747 (1995); Phys. Rev. E54, (1996)
    • (1996) Phys. Rev. , vol.E54
  • 82
    • 6244276442 scopus 로고
    • edited by A V Johansson and P H Alfredsson Springer, Berlin
    • M Meneguzzi and A Vincent, in Advances in turbulence 3 edited by A V Johansson and P H Alfredsson (Springer, Berlin, 1991) pp. 211-220; A Vincent and M Meneguzzi, J. Fluid Mech. 258, (1994)
    • (1991) Advances in Turbulence 3 , pp. 211-220
    • Meneguzzi, M.1    Vincent, A.2
  • 83
    • 6244231444 scopus 로고
    • M Meneguzzi and A Vincent, in Advances in turbulence 3 edited by A V Johansson and P H Alfredsson (Springer, Berlin, 1991) pp. 211-220; A Vincent and M Meneguzzi, J. Fluid Mech. 258, (1994)
    • (1994) J. Fluid Mech. , vol.258
    • Vincent, A.1    Meneguzzi, M.2
  • 95
    • 6244239733 scopus 로고    scopus 로고
    • Ph.D. thesis, Indian Institute of Science, Bangalore unpublished
    • Sujan K Dhar, Ph.D. thesis, Indian Institute of Science, Bangalore (1996) unpublished
    • (1996)
    • Dhar, S.K.1
  • 98
    • 85033287896 scopus 로고    scopus 로고
    • note
    • -α. If the invariant of order α is conserved, then all lower-order invariants are also conserved. The choice α = 1, i.e., δ = 1/2 for λ = 2 thus conserves both the GOY-model energy and belicity in the inviscid, unforced limit; α = 2, i.e., δ = 5/4 also conserves the GOY-model enstrophy in this limit also, which is of relevance in models for two-dimensional turbulence


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.