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We present a method for studying the evolution of plasma turbulence bytracking dispersion relations in the energy spectrum in thewavenumber-frequency domain. We apply hybrid plasma simulations in a simplifiedtwo-dimensional geometry to demonstrate our method and its applicability toplasma turbulence in the ion kinetic regime. We identify four dispersionrelations: ion-Bernstein waves, oblique whistler waves, obliqueAlfv\'en/ion-cyclotron waves, and a zero-frequency mode. The energy partitionand frequency broadening are evaluated for these modes. The method allows us todetermine the evolution of decaying plasma turbulence in our restrictedgeometry and shows that it cascades along the dispersion relations during theearly phase with an increasing broadening around the dispersion relations.

Spectral evolution of two-dimensional kinetic plasma turbulence in the wavenumber-frequency domain