Abstract
In particle-laden turbulence, the Fourier Lagrangian spectrum of each phase
is regularly computed, and analytically derived response functions relate the
Lagrangian spectrum of the fluid- and the particle phase. However, due to the
periodic nature of the Fourier basis, the analysis is restricted to
statistically stationary flows. In the present work, utilizing the bases of
time-focalized proper orthogonal decomposition (POD), this analysis is extended
to temporally non-stationary turbulence. Studying two-way coupled
particle-laden decaying homogeneous isotropic turbulence for various Stokes
numbers, it is demonstrated that the temporal POD modes extracted from the
dispersed phase may be used for the expansion of both fluid- and particle
velocities. The POD Lagrangian spectrum of each phase may thus be computed from
the same set of modal building blocks, allowing the evaluation of response
functions in a POD frame of reference. Based on empirical evaluations, a model
for response functions in non-stationary flows is proposed. The related
energies of the two phases is well approximated by simple analytical
expressions dependent on the particle Stokes number. It is found that the
analytical expressions closely resemble those derived through Fourier analysis
of statistically stationary flows. These results suggest the existence of an
inherent spectral symmetry underlying the dynamical systems consisting of
particle-laden turbulence, a symmetry which spans across
stationary/non-stationary particle-laden flow states.
Original language | English |
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Article number | 053333 |
Journal | Physics of Fluids |
Volume | 35 |
Number of pages | 12 |
ISSN | 1070-6631 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- Fluid Dynamics (physics.flu-dyn)
- FOS: Physical sciences