Generating Kolmogorov spectra and structure functions with a Rosenhead profile trefoil vortex knot
Abstract
Motivated by recent experimental observations by Matsuzawa et al. (2026) of colliding several vortex rings within a water tank, this paper extends a compact trefoil vortex simulation to later times and generates a persistent ==energy spectrum that obeys Kolmogorov scaling, together with other statistics characteristic of fully developed turbulence, including structure function scaling. This temporal extension uses a larger (4pi)3 periodic domain, with the improved compactness being achieved by the use of an algebraic Rosenhead vorticity profile, from which viscosity(nu)-independent finite energy dissipation is generated and pre-reconnection convergence of nu1/4-dependent higher-order vorticity moments. These properties suggest, perhaps for the first time, how decaying Navier-Stokes simulations can generate fully-developed turbulent flow from an unforced initial state that is far from boundaries, thereby suggesting how further simulations at higher values of Re could be harnessed for experimental comparisons. Moreover, the exponents for the energy decay and the integral scale growth, E(t)~(t+t0)-10/7 and and ell(t)~(t+t0)2/7, follow those based upon preservation of the Loitsyanskii integral. On a related question, an integral scale growth rate ell that is close to the experiment rate of ellX~(t+t0)(0.16or1/7)is only obtained if the Fourier modes at the scale of the periodic domain are not considered.
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BibTeX
@misc{kerr2026generating,
title = {{Generating Kolmogorov spectra and structure functions with a Rosenhead profile trefoil vortex knot}},
author = {Robert M. Kerr},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05408},
eprint = {2610.05408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05408},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generating Kolmogorov spectra and structure functions with a Rosenhead profile trefoil vortex knot
AU - Robert M. Kerr
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05408
UR - https://arxiv.org/abs/2610.05408
AB - Motivated by recent experimental observations by Matsuzawa et al. (2026) of colliding several vortex rings within a water tank, this paper extends a compact trefoil vortex simulation to later times and generates a persistent ==energy spectrum that obeys Kolmogorov scaling, together with other statistics characteristic of fully developed turbulence, including structure function scaling. This temporal extension uses a larger (4pi)3 periodic domain, with the improved compactness being achieved by the use of an algebraic Rosenhead vorticity profile, from which viscosity(nu)-independent finite energy dissipation is generated and pre-reconnection convergence of nu1/4-dependent higher-order vorticity moments. These properties suggest, perhaps for the first time, how decaying Navier-Stokes simulations can generate fully-developed turbulent flow from an unforced initial state that is far from boundaries, thereby suggesting how further simulations at higher values of Re could be harnessed for experimental comparisons. Moreover, the exponents for the energy decay and the integral scale growth, E(t)~(t+t0)-10/7 and and ell(t)~(t+t0)2/7, follow those based upon preservation of the Loitsyanskii integral. On a related question, an integral scale growth rate ell that is close to the experiment rate of ellX~(t+t0)(0.16or1/7)is only obtained if the Fourier modes at the scale of the periodic domain are not considered.
ER -