Revisiting the linear forcing of turbulence in two-phase flows

Maintaining realistic turbulence in numerical simulations is a key element for studying complex flows. This is typically achieved by forcing turbulence through the synthetic injection of energy at prescribed wavenumbers. The task gets challenging in two-phase flows, where turbulence is closely coupled with interface dynamics. In this work, we revisit the linear forcing method proposed by Lundgren and extend its application to turbulent emulsions and droplet-laden turbulence. We propose a general linear forcing that incorporates two-phase flow contributions and enables $a$ $p\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i$ control of the turbulent characteristics.