{"title":"流体圣维南近似中的奇异行为和奇点","authors":"P. Luchini","doi":"10.4081/INCONTRI.2018.386","DOIUrl":null,"url":null,"abstract":"A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.","PeriodicalId":119535,"journal":{"name":"Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"SURPRISING BEHAVIOUR AND SINGULARITY IN THE SAINT VENANT APPROXIMATION FOR A FLUID\",\"authors\":\"P. Luchini\",\"doi\":\"10.4081/INCONTRI.2018.386\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.\",\"PeriodicalId\":119535,\"journal\":{\"name\":\"Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4081/INCONTRI.2018.386\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4081/INCONTRI.2018.386","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SURPRISING BEHAVIOUR AND SINGULARITY IN THE SAINT VENANT APPROXIMATION FOR A FLUID
A research line is reviewed which, over a few years, led to a substantial change of perspective about the simplified models that underlie the description of quasi-onedimensional streams, their instabilities, and their effects upon sandy beds. Even when the flow is assumed to be laminar, the Saint-Venant equation of quasi-onedimensional fluid flow can be formulated in more than one manner; it will be shown that only one of these choices is consistent with the complete three-dimensional Navier- Stokes equations. When the flow is turbulent, an added complication is the presence of a turbulence model, most often of the eddy-viscosity type; it will be shown that such a model can be in strong contrast with a direct numerical simulation of the same phenomenon, even to the point of producing results of opposite sign. In addition, the complete numerical simulation of flow past an undulated bottom exhibits a non-monotonic approach to its long-wave, quasi-onedimensional limit, with a surprising resonance that has no laminar counterpart and must become the subject of future investigations.