Wave-field decay rate estimate from the wavenumber-frequency spectra

Observational data for wave or turbulent fields are conveniently analyzed and interpreted in the Fourier domain spanning the frequencies and the wavenumbers. If a wave field has not only oscillatory components (characterized by real parts of frequency) but also temporally decaying components (characterized by imaginary parts of frequency), the energy spectrum shows a frequency broadening around the peak due to the imaginary parts of frequency (or the decay rate). The mechanism of the frequency broadening is the same as that of the Breit-Wigner spectrum in nuclear resonance phenomena. We show that the decay rate can observationally and directly be estimated once multi-point data are available, and apply the method to Cluster four-point magnetometer data in the solar wind on a spatial scale of about 1000 km. The estimated decay rate is larger than the eddy turnover time, indicating that the decay profile of solar wind turbulence is more plasma physical such as excitation of whistler waves and other modes rather than hydrodynamic turbulence behavior.