{"title":"湍流和混沌时间相关函数的衰减形式","authors":"H. Mori, M. Okamura","doi":"10.1143/PTP.127.615","DOIUrl":null,"url":null,"abstract":"Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms of the projection operator formalism, and then investigate the decay forms of the time correlation function Uk(t) and its memory function Γk(t )f or a normal mode uk(t) of the system with a wavenumber k .L etτ (u) k and τ (γ) k be the decay times of Uk(t )a ndΓk(t), respectively, with τ (u) k ≥ τ (γ) k . Here, τ (u) k is a macroscopic time scale if k � 1, but a microscopic time scale if k & 1, whereas τ (γ) k is always a microscopic time scale. Changing the length scale k −1 and the time scales τ (u) k , τ (γ) k , we can obtain various aspects of","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"615-629"},"PeriodicalIF":0.0000,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.615","citationCount":"1","resultStr":"{\"title\":\"Decay Forms of the Time Correlation Functions for Turbulence and Chaos\",\"authors\":\"H. Mori, M. Okamura\",\"doi\":\"10.1143/PTP.127.615\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms of the projection operator formalism, and then investigate the decay forms of the time correlation function Uk(t) and its memory function Γk(t )f or a normal mode uk(t) of the system with a wavenumber k .L etτ (u) k and τ (γ) k be the decay times of Uk(t )a ndΓk(t), respectively, with τ (u) k ≥ τ (γ) k . Here, τ (u) k is a macroscopic time scale if k � 1, but a microscopic time scale if k & 1, whereas τ (γ) k is always a microscopic time scale. Changing the length scale k −1 and the time scales τ (u) k , τ (γ) k , we can obtain various aspects of\",\"PeriodicalId\":49658,\"journal\":{\"name\":\"Progress of Theoretical Physics\",\"volume\":\"127 1\",\"pages\":\"615-629\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1143/PTP.127.615\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress of Theoretical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1143/PTP.127.615\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress of Theoretical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1143/PTP.127.615","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Decay Forms of the Time Correlation Functions for Turbulence and Chaos
Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms of the projection operator formalism, and then investigate the decay forms of the time correlation function Uk(t) and its memory function Γk(t )f or a normal mode uk(t) of the system with a wavenumber k .L etτ (u) k and τ (γ) k be the decay times of Uk(t )a ndΓk(t), respectively, with τ (u) k ≥ τ (γ) k . Here, τ (u) k is a macroscopic time scale if k � 1, but a microscopic time scale if k & 1, whereas τ (γ) k is always a microscopic time scale. Changing the length scale k −1 and the time scales τ (u) k , τ (γ) k , we can obtain various aspects of