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We present results from a numerical forward model to evaluate one-dimensionalreduced power spectral densities (PSD) from arbitrary energy distributions in$\mathbf{k}$-space. In this model, we can separately calculate the diagonalelements of the spectral tensor for incompressible axisymmetric turbulence withvanishing helicity. Given a critically balanced turbulent cascade with$k_\|\sim k_\perp^\alpha$ and $\alpha<1$, we explore the implications on thereduced PSD as a function of frequency. The spectra are obtained under theassumption of Taylor's hypothesis. We further investigate the functionaldependence of the spectral index $\kappa$ on the field-to-flow angle $\theta$between plasma flow and background magnetic field from MHD to electron kineticscales. We show that critically balanced turbulence asymptotically developstoward $\theta$-independent spectra with a slope corresponding to theperpendicular cascade. This occurs at a transition frequency$f_{2D}(L,\alpha,\theta)$, which is analytically estimated and depends on outerscale $L$, critical balance exponent $\alpha$ and field-to-flow angle $\theta$.We discuss anisotropic damping terms acting on the $\mathbf{k}$-spacedistribution of energy and their effects on the PSD. Further, we show that thespectral anisotropies $\kappa(\theta)$ as found by Horbury et al. (2008) andChen et al. (2010) in the solar wind are in accordance with a damped criticallybalanced cascade of kinetic Alfv\'en waves. We also model power spectraobtained by von Papen et al. (2014) in Saturn's plasma sheet and find that thechange of spectral indices inside $9\,R_\mathrm{s}$ can be explained by dampingon electron scales.

Forward Modeling of Reduced Power Spectra From Three-Dimensional k-Space