An investigation of the structure-conditioned turbulence kinetic energy budget.*

An attempt is made to identify links between the turbulence kinetic energy (TKE) balance in homogeneous isotropic turbulence (HIT) and the underlying local flow topology. This is achieved through conditioning terms of the TKE budget on invariants of the velocity gradient tensor (Q_A, R_A), the strain-rate tensor (Q_S, R_S) and the rotation-rate tensor (Q_Ω). These conditional quantities reveal preferences of the particular TKE budget’s terms to be low or high depending on the specific areas of the Q_A-R_A, Q_S-R_S and Q_S-Q_Ω diagrams. In order to present the evolution of the TKE balance during the mean temporal development of structures, terms of the former are calculated along the conditional mean trajectories evaluated in Q_A-R_A, Q_S-R_S and Q_S-Q_Ω spaces.

The data used to produce the statistics was gathered in a centre region of a von Karman mixing tank, which forms the suitable experimental approximation of HIT. The dataset consisted of nearly 200 000 independent samples of a cubic box of (40η)³ ensuring satisfactory convergence. The DNS data from the John Hopkins University turbulence database is used for comparison.