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Register a new userRayleigh-Brillouin light scattering spectroscopy of air; experiment, predictive model and dimensionless scaling
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Spontaneous Rayleigh-Brillouin scattering (RBS) 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 analyzed, 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 $lambda_i=532.22$ 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 $1.0 - 2.0 times 10^{-5}$ Pa$cdot$s. A temperature dependent value is deduced from a collection of experiments to yield: $eta_{rm b} = (0.86 times 10^{-5}) + 1.29 times 10^{-7} cdot (T - 250)$. These results are implemented in model calculations that were verified for the low pressure conditions ($p < 1$ bar) relevant for the Earths 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 $theta$), and for values for the gas transport coefficients.
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Rayleigh-Brillouin scattering spectra of CO$_2$ were measured at pressures ranging from 0.5 to 4~bar, and temperatures from 257 to 355~K using green laser light (wavelength 532~nm, scattering angle of 55.7$^circ$). These spectra were compared to two lineshape models, which take the bulk viscosity as a parameter. One model applies to the kinetic regime, i.e. low pressures, while the second model uses the continuum, hydrodynamic approach and takes the rotational relaxation time as a parameter, which translates into the bulk viscosity. We do not find a significant dependence of the bulk viscosity with pressure or temperature. At pressures where both models apply we find a consistent value of the ratio of bulk viscosity over shear viscosity $eta_b/eta_s = 0.41 pm 0.10$. This value is four orders of magnitude smaller than the common value that is based on the damping of ultrasound, and signifies that in light scattering only relaxation of rotational modes matters, while vibrational modes remain frozen.
High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N$_2$O) gas at an incident wavelength of 403.00 nm, at 90$^circ$ scattering, at room temperature and at gas pressures in the range $0.5-4$ bar. The resulting Rayleigh-Brillouin light scattering spectra are compared to a number of models describing in an approximate manner the collisional dynamics and energy transfer in this gaseous medium of this polyatomic molecular species. The Tenti-S6 model, based on macroscopic gas transport coefficients, reproduces the scattering profiles in the entire pressure range at less than 2% deviation at a similar level as does the alternative kinetic Grads 6-moment model, which is based on the internal collisional relaxation as a decisive parameter. A hydrodynamic model fails to reproduce experimental spectra for the low pressures of 0.5-1 bar, but yields very good agreement ($< 1$%) in the pressure range $2-4$ bar. While these three models have a different physical basis the internal molecular relaxation derived can for all three be described in terms of a bulk viscosity of $eta_b sim (6 pm 2) times 10^{-5}$ Pa$cdot$s. A rough-sphere model, previously shown to be effective to describe light scattering in SF$_6$ gas, is not found to be suitable, likely in view of the non-sphericity and asymmetry of the N-N-O structured linear polyatomic molecule.
It is important to be able to calculate the moist-air entropy of the atmosphere with precision. A potential temperature has already been defined from the third law of thermodynamics for this purpose. However, a doubt remains as to whether this entropy potential temperature can be represented with simple but accurate first- or second-order approximate formulas. These approximations are rigorously defined in this paper using mathematical arguments and numerical adjustments to some datasets. The differentials of these approximations lead to simple but accurate formulations for tendencies, gradients and turbulent fluxes of the moist-air entropy. Several physical consequences based on these approximations are described and can serve to better understand moist-air processes (like turbulence or diabatic forcing) or properties of certain moist-air quantities (like the static energies).
A framework is introduced to compare moist `potential temperatures. The equivalent potential temperature, $theta_e,$ the liquid water potential temperature, $theta_ell,$ and the entropy potential temperature, $theta_s$ are all shown to be potential temperatures in the sense that they measure the temperature moist-air, in some specified state, must have to have the same entropy as the air-parcel that they characterize. They only differ in the choice of reference state composition: $theta_ell$ describes the temperature a condensate-free state, $theta_e$ a vapor-free state, and $theta_s$ a water-free state would require to have the same entropy as the given state. Although in this sense $theta_e,$ $theta_ell,$ and $theta_s$ are all different flavors of the same thing, only $theta_ell$ satisfies the stricter definition of a `potential temperature, as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; only $theta_e$ approximately measures the ability of moist-air to do work; and only $theta_s$ measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature, $theta$ in the limit as the water mass fraction goes to zero. As is well known, $theta$ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various -- but descriptively less rich -- moist counterparts. All, involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist `potential temperatures, $theta_s$ is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a basis for constraining mixing processes.
Recent years witnessed much broader use of Brillouin inelastic light scattering spectroscopy for the investigation of phonons and magnons in novel materials, nanostructures, and devices. Driven by developments in instrumentation and the strong need for accurate knowledge of energies of elemental excitations, the Brillouin - Mandelstam spectroscopy is rapidly becoming an essential technique, complementary to the Raman inelastic light scattering spectroscopy. We provide an overview of recent progress in the Brillouin light scattering technique, focusing on the use of this photonic method for the investigation of confined acoustic phonons, phononic metamaterials, magnon propagation and scattering. The Review emphasizes emerging applications of the Brillouin - Mandelstam spectroscopy for phonon engineered structures and spintronic devices and concludes with a perspective for future directions.
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