Robert Kerr, (NCAR), The Role of Two Length Scales in the Singular Collapse of Euler and Ideal MHD

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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