# Rayleigh-Brillouin light scattering spectroscopy of air; experiment, predictive model and dimensionless scaling

Spontaneous Rayleigh-Brillouin (RB) scattering experiments have been performed in air for pressures in the range 0.25–3 bar and temperatures in the range 273–333 K. The functional behaviour of the RB-spectral profile as a function of experimental parameters, such as the incident wavelength, scattering angle, pressure and temperature is analysed, as well as the dependence on thermodynamic properties of the gas, as the shear viscosity, the thermal conductivity, the internal heat capacity and the bulk viscosity. Measurements are performed in a scattering geometry detecting at a scattering angle $\theta =55.7\circ $ and an incident wavelength of ${\lambda}_{i}=532.22\mathrm{nm}$, at which the Brillouin features become more pronounced than in a right angles geometry and for ultraviolet light. For pressure conditions of 1–3 bar the RB-spectra, measured at high signal-to-noise ratio, are compared to Tenti-S6 model calculations and values for the bulk viscosity of air are extracted. Values of ${\eta}_{b}$ are found to exhibit a linear dependence on temperature over the measurement interval in the range $1.0--2.0\times 10-5\mathrm{Pa}\cdot s$. A temperature dependent value is deduced from a collection of experiments to yield: ${\eta}_{b}=(0.86\times 10-5\mathrm{Pa}\cdot s)+1.29\times 10-7\cdot (T-250)$. These results are implemented in model calculations that were verified for the low pressure conditions (*p*<1 bar) relevant for the Earth's atmosphere. As a result we demonstrate that the RB-scattering spectral profiles for air under sub-atmospheric conditions can be generated via the Tenti-S6 model, for given gas-phase and detection conditions (*p*, *T*, ${\lambda}_{i}$, and *θ*), and for values for the gas transport coefficients. Spectral profiles for coherent RB-scattering in air are also computed, based on the Tenti-S6 formalism, and the predictions are compared with profiles of spontaneous RB-scattering. Finally data on RB-scattering in air, obtained under a variety of pressure, temperature, wavelength and scattering angles, are analysed in terms of universal scaling, involving the dimensionless uniformity parameter *y* and the dimensionless frequency *x*. Such scaling behaviour is shown to be well behaved for a wide parameter space and implies that RB-scattering spectra can be generated for a wide range of atmospheric applications of RB-scattering. The verification of this dimensionless scaling also shows that air can be treated as an ideal gas in the atmospheric regime, where $y\le 1$.