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Conversions between kinetic and surface energy in periodically forced multiphase turbulence

J. Vahé and F. Thiesset*

  • *Contact author: fabien.thiesset@cnrs.fr
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Phys. Rev. Fluids 11, 074002 – Published 14 July, 2026

DOI: https://doi.org/10.1103/crts-5b7y

Abstract

In multiphase flows, kinetic and interfacial energies coexist, and their mutual conversion can potentially influence the overall energy balance. However, in statistically steady flows, these energy reservoirs remain constant, making such conversions undetectable. For them to be observed, a degree of unsteadiness must be introduced, here provided by the deliberate use of a fluctuating time-periodic input of kinetic energy into the system. The main focus of the present work is on the dynamical cycle connecting energy injection, conversion, and dissipation, which we explore using direct numerical simulations of multiphase homogeneous isotropic turbulence, subjected to periodic forcing. The database includes various Reynolds and Weber numbers and volume fractions in the dense regime. To interpret and replicate the observed dynamics, we reformulate the Ka-Pi-bara model of Bos [J. Turbul. 27, 157 (2026)] (an extension of the k−ε model) in terms of total energy (the sum of kinetic and surface energy), which we further enhance by adding equations for the surface energy and its destruction. This model accurately captures a key feature of turbulence: nonequilibrium effects, seen as the phase lag between kinetic energy and its rate of dissipation, which are also found to operate in multiphase flows. Linearizing the model highlights the various relevant timescales of the system and provides predictions of how different observables are coupled and respond to the energy input.

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Information

Phys. Rev. Fluids 11, 074002– Published 14 July, 2026
  • Received 6 February 2026
  • Accepted 22 June 2026
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