Evaluation of Vortex Criteria by Virtue of the Quadruple Decomposition of Velocity Gradient Tensor
arxiv(2024)
摘要
Based on the analysis of the velocity gradient tensor, we investigate in this
paper the physical interpretation and limitations of four vortex criteria:
ω, Q, and λ_ci, and reveal the actual physical
meaning of vortex patterns which are usually illustrated by level sets of
various vortex criteria. A quadruple decomposition based on the normality of
the velocity gradient tensor is proposed for the first time, which resolves the
motion of a fluid element into dilation, axial stretch along the normal frame,
in-plane distortion, and simple shear, in order to clarify the kinematical
interpretation of various vortex criteria. The mean rotation characterized by
the vorticity ω always consists of simple shear; the Q-criterion can
reflect the strength of net rotation within the invariant plane relative to the
axial stretch of a fluid element, and it is a sufficient but unnecessary
condition for the existence of net rotation; the -criterion can
exactly identify the existence of net rotation, but it is not the strength of
net rotation; in the case that net rotation exists, λ_ci characterize
its absolute strength. net rotation is the total effect of the normal rotation
within the invariant plane and the simple shear, where the former is the most
basic rotation. The newly introduced quadruple decomposition can improve our
understanding of vortices in fluids and their motions.
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