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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2000
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0005035 |
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| _version_ | 1866914099185582080 |
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| author | Nadiga, Balu T. Shkoller, Steve |
| author_facet | Nadiga, Balu T. Shkoller, Steve |
| contents | For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0005035 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Enhanced inverse-cascade of energy in the averaged Euler equations Nadiga, Balu T. Shkoller, Steve Numerical Analysis For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added. |
| title | Enhanced inverse-cascade of energy in the averaged Euler equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0005035 |