We present a generalisation of the Kármán–Howarth–Monin (K–H–M) equation to include variable-density (VD) effects. The derived equation (i) reduces to the original K–H–M equation when density is a constant and (ii) leads to a VD analogue of the 4/5-law with the same value of constant (=4/5) appearing as the prefactor of the dissipation rate.
Multiphase flows are ubiquitous in nature and engineering scenarios; examples include volcanic eruption, cloud formation, land reclamation and subsea oil well blowout. In these flows, one or more heterogeneous materials is/are transported by a …