کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896492 | 1044435 | 2010 | 4 صفحه PDF | دانلود رایگان |

The ‘triad interactions’, arising from the spectral resolution of the nonlinear terms in the Navier–Stokes equations, have so far not been substantially modified in the wavelet representation. In this paper, the multiscale interactions are captured by exact expressions evaluated at a single scale of the Mexican hat wavelet coefficients: the larger-scale terms as a volume integral of nearby wavelet coefficients, and the smaller-scale contributions as iterated Laplacians of the coefficient at the point of interest. As a result, the Navier–Stokes equations are expressed exactly at a single scale. This facilitates the evaluation of the dominant Hölder exponent near singularities. From the scaling properties of wavelet coefficients, it is shown that Euler dynamics would generate stronger singularities for any h<1h<1, but that viscous dynamics would not unless h<−1h<−1 (a discontinuous case). We discuss how this conclusion could be affected by boundary conditions.
Journal: Physica D: Nonlinear Phenomena - Volume 239, Issue 14, 15 July 2010, Pages 1232–1235