Motivated by the upcoming Solar Orbiter and Solar Probe Plus missions, qualitative and quantitative predictions are made for the effects of the violation of the Taylor hypothesis on the magnetic energy frequency spectrum measured in the near-Sun environment. The synthetic spacecraft data method is used to predict observational signatures of the violation for critically balanced Alfvenic turbulence or parallel fast/whistler turbulence. The violation of the Taylor hypothesis can occur in the slow flow regime, leading to a shift of the entire spectrum to higher frequencies, or in the dispersive regime, in which the dissipation range spectrum flattens at high frequencies. It is found that Alfvenic turbulence will not significantly violate the Taylor hypothesis, but whistler turbulence will. The flattening of the frequency spectrum is therefore a key observational signature for fast/whistler turbulence.
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