Decomposing the wavelet spectrum of droplet-laden isotropic turbulence

The classical spectrum of turbulence kinetic energy poses a challenge when used to analyze finite-size droplet-laden flows because the Fourier transform used in its definition does not lend itself to a natural decomposition of the domain into droplet and carrier parts. We recall an alternative definition of the energy spectrum that uses the wavelet transform and apply it to the DNS data of droplet-laden decaying isotropic turbulence of Dodd & Ferrante (J. Fluid Mech. 806 (2016), 356–412). We also compute each term of the wavelet-spectrum evolution equation for two-phase flow. We then introduce a new method for decomposing the spectrum that takes advantage of the wavelet transform's preservation of spatial information, which allows us to isolate the effect of the droplets on the carrier fluid. Lastly, we discuss the results of our decomposition analysis.