Seminar talk, 17 March 2021: Difference between revisions
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| title = Nonlocal conservation law in a submerged jet | | title = Nonlocal conservation law in a submerged jet | ||
| abstract = Landau was the first to obtain the exact solution of Navier-Stokes equations for an axisymmetric submerged jet generated by a point momentum source. The Landau jet is the main term of a coordinate expansion of the flow far field in the case when the flow is generated by a finite size source (for example, a tube with flow). The next term of the expansion was calculated by Rumer. This term has an indefinite coefficient. To determine this coefficient we need a conservation law connecting the jet far field with the source. Well-known conservation laws of mass, momentum, and angular momentum fail to calculate the coefficient. In my talk, I will solve this problem for low viscosity. In this case, the flow satisfies the boundary layer equations that possess a nonlocal conservation law closing the problem. The problem for an arbitrary viscosity remains open. | | abstract = Landau was the first to obtain the exact solution of Navier-Stokes equations for an axisymmetric submerged jet generated by a point momentum source. The Landau jet is the main term of a coordinate expansion of the flow far field in the case when the flow is generated by a finite size source (for example, a tube with flow). The next term of the expansion was calculated by Rumer. This term has an indefinite coefficient. To determine this coefficient we need a conservation law connecting the jet far field with the source. Well-known conservation laws of mass, momentum, and angular momentum fail to calculate the coefficient. In my talk, I will solve this problem for low viscosity. In this case, the flow satisfies the boundary layer equations that possess a nonlocal conservation law closing the problem. The problem for an arbitrary viscosity remains open. | ||
| video = https://video.gdeq. | | video = https://video.gdeq.org/GDEq-zoom-seminar-20210317-Vladislav_Zhvick.mp4 | ||
| slides = [[Media:Seminar-20210317-Vladislav_Zhvick.pdf|Seminar-20210317-Vladislav_Zhvick.pdf]] | | slides = [[Media:Seminar-20210317-Vladislav_Zhvick.pdf|Seminar-20210317-Vladislav_Zhvick.pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7978-96-82 | | 79YY-MM-DD = 7978-96-82 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Vladislav Zhvick
Title: Nonlocal conservation law in a submerged jet
Abstract:
Landau was the first to obtain the exact solution of Navier-Stokes equations for an axisymmetric submerged jet generated by a point momentum source. The Landau jet is the main term of a coordinate expansion of the flow far field in the case when the flow is generated by a finite size source (for example, a tube with flow). The next term of the expansion was calculated by Rumer. This term has an indefinite coefficient. To determine this coefficient we need a conservation law connecting the jet far field with the source. Well-known conservation laws of mass, momentum, and angular momentum fail to calculate the coefficient. In my talk, I will solve this problem for low viscosity. In this case, the flow satisfies the boundary layer equations that possess a nonlocal conservation law closing the problem. The problem for an arbitrary viscosity remains open.
Video
Slides: Seminar-20210317-Vladislav_Zhvick.pdf