The introduction of the chapter "The Spectrum of Turbulence" by Siegfried Grossmann highlights the interest in turbulent flow, particularly its nested vortex structures and intermittent bursts of activity. The text emphasizes the presence of multiple time and spatial scales in turbulent flows, where smaller vortices circulate faster and are advected by larger ones. The energy distribution among eddies of various sizes, the characteristic time scale of these eddies, the typical energy dissipation rate, and spatial correlation over eddy distances are key observables in turbulent flow. These quantities exhibit power law behaviors as a function of eddy size. Historically, the importance of power laws or scaling behavior in hierarchically ordered systems was recognized in the first half of the 20th century. In turbulence, the upper scale is the external length scale where energy is injected, and the lower scale is where viscosity becomes dominant. Power laws in isotropic, homogeneous turbulent flow were proposed independently by several authors, including Kolmogorov and Oboukhoff in 1941, and C.F. von Weizsäcker and W. Heisenberg in 1945. Their work, published in 1948, derived the exponents for the energy spectrum and wave number spectrum, confirming the scaling behavior. The chapter also discusses the scaling theory of turbulent flow, where the energy flow rate and the lack of a preferred scale are key control parameters. Dimensional analysis leads to the scaling relations for the energy distribution and the spectral law. Additionally, the historical context includes a contribution by Lars Onsager, which further supported the understanding of turbulent diffusion and scaling behavior.The introduction of the chapter "The Spectrum of Turbulence" by Siegfried Grossmann highlights the interest in turbulent flow, particularly its nested vortex structures and intermittent bursts of activity. The text emphasizes the presence of multiple time and spatial scales in turbulent flows, where smaller vortices circulate faster and are advected by larger ones. The energy distribution among eddies of various sizes, the characteristic time scale of these eddies, the typical energy dissipation rate, and spatial correlation over eddy distances are key observables in turbulent flow. These quantities exhibit power law behaviors as a function of eddy size. Historically, the importance of power laws or scaling behavior in hierarchically ordered systems was recognized in the first half of the 20th century. In turbulence, the upper scale is the external length scale where energy is injected, and the lower scale is where viscosity becomes dominant. Power laws in isotropic, homogeneous turbulent flow were proposed independently by several authors, including Kolmogorov and Oboukhoff in 1941, and C.F. von Weizsäcker and W. Heisenberg in 1945. Their work, published in 1948, derived the exponents for the energy spectrum and wave number spectrum, confirming the scaling behavior. The chapter also discusses the scaling theory of turbulent flow, where the energy flow rate and the lack of a preferred scale are key control parameters. Dimensional analysis leads to the scaling relations for the energy distribution and the spectral law. Additionally, the historical context includes a contribution by Lars Onsager, which further supported the understanding of turbulent diffusion and scaling behavior.