Expansion and shear effects on cross-scale energy transfer rate: the SEAT model

The energy spectrum of magnetic field fluctuations in fast and alfvénic slow solar winds generally presents a spectral break at low frequencies that separates two distinct regions. In the high-frequency side of the break, the spectrum follows a power-law in frequency with exponents that vary about -3/2 and -5/3. In the lower-frequency side of the spectral break, corresponding to the largest physical scales, the spectrum is less steep and presents a power law as the inverse of the frequency. In the same range of scales, plasma fluctuations in the heliosphere are affected by deformations of the flow due to the expansion of the solar wind and velocity shear caused by wind stream interaction. We investigate the impact of these large-scale deformations of the plasma flow on turbulence properties, with our main focus being the rate at which energy of the fluctuations is transferred from large to small scales. In our study, the energy transfer rate is estimated from a Karman-Howarth-Monin (KHM) equation, a scale-dependent energy budget equation that allows to quantify the contributions of different terms to the energy transfer. We have derived a KHM equation that accounts for the combined contribution of expansion and shear in two particular cases: when the planes affected by Shear and Expansion are Aligned or Transverse (SEAT) to each other. We will present the plasma SEAT equations that model the large-scale deformation of the plasma flow, the KHM equations derived from it and preliminary numerical results from 3D single-fluid simulations that will show how both large-scale deformation of the flow intervene in the cross-scale energy transfer and affect turbulence properties.