Schedule Feb 10, 2000
The Role of Two Length Scales in the Singular Collapse of Euler and Ideal MHD
Robert Kerr, (NCAR)
Experimental and numerical evidence is presented for a change in the scaling of structure functions within the inertial subrange at approximately $\lambda$. Kinematic arguments based on pressure are given for why longitudinal and transverse scaling should be the same for $r>\lambda$, but there are no restrictions for $r<\lambda$. It is speculated that this shift in scaling could be related to the anisotropy of small scale structures. First vortex tubes. Then the structure developing around a putative singularity of Euler. It is shown numerical and by mathematical arguements that the collapse of the Euler structure must involve two length scales. One goes as $R\sim(T_c-t)^{1/2}$ and the other as $\rho\sim(T_c-t)$.

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