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    Quantifying the impact of coherent structures on the turbulent kinetic energy decay rate: A Proper Orthogonal Decomposition approach

    Ankit Gautam* and Tim Berk

    • *Contact author: ankit.gautam@usu.edu

    Phys. Rev. Fluids 11, 044906 – Published 6 April, 2026

    DOI: https://doi.org/10.1103/z9ds-1yfc

    Abstract

    The influence of coherent vortices on the decay of turbulent kinetic energy (TKE) is experimentally investigated in a synthetic-jet-driven turbulence box. For the baseline homogeneous case, a power-law decay exponent of m=1.41 is obtained. Six cases with a spatial power gradient in the turbulence forcing create turbulence laden with controlled amounts of coherent vortices, quantified by a Rossby number Ro. In these cases, the TKE decay rate is reduced with a minimum of m=0.66 for the case with the strongest power gradient (lowest Ro). Decay values for Ro<1 cases, where rotation is relatively stronger than turbulent fluctuations, are well below expected values based on prior empirical and theoretical works. To investigate the underlying cause, a triple-decomposition-inspired framework based on Proper Orthogonal Decomposition is developed to separate coherent modes from the stochastic component of the velocity field. The method identifies coherent modes as modes that are found across repeated experiments and exhibit slower temporal decay. By omitting these modes, we reconstruct filtered velocity fields that retain the essential stochastic turbulence. The resulting fields yield stabilized turbulence statistics and decay exponents comparable to the homogeneous reference case. The proposed framework enables identification of modes that bias the overall TKE decay rate, potentially resolving observed discrepancies in decay rates across the literature.

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