The flux Richardson number
Estimation of Turbulence Parameters in the Lower Troposphere from ShUREX (2016–2017) UAV Data
Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of highresolution and fastresponse coldwire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate ε and temperature structure function parameter C T 2 from onedimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating ε and C T 2 valid for Kolmogorov turbulence in steady state, the flux Richardson number R f and the mixing efficiency χ m are then estimated. The statistical analysis confirms the variability of R f and χ m around ~ 0.13 − 0.14 and ~ 0.16 − 0.17 , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale L O , the buoyancy Reynolds number R e b , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of N 2 , C T 2 and ε , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined.
more »
« less
 Award ID(s):
 1632829
 NSFPAR ID:
 10208958
 Date Published:
 Journal Name:
 Atmosphere
 Volume:
 10
 Issue:
 7
 ISSN:
 20734433
 Page Range / eLocation ID:
 384
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract R _{f}, also called the mixing efficiency of stratified turbulence, is important in determining geophysical flow phenomena such as ocean circulation and air‐sea transports. MeasuringR _{f}in the field is usually difficult, thus parameterization ofR _{f}based on readily observed properties is essential. Here, estimates ofR _{f}in a strongly turbulent, sediment‐stratified estuarine flow are obtained from measurements of covariance‐derived turbulent buoyancy fluxes (B ) and spectrally fitted values of the dissipation rate of turbulent kinetic energy (ε ). We test scalings forR _{f}in terms of the buoyancy Reynolds number (Re _{b}), the gradient Richardson number (Ri ), and turbulent Froude number (Fr _{t}). Neither theRe _{b}‐based nor theRi ‐based scheme is able to describe the observed variations inR _{f}, but theFr _{t}‐based parameterization works well. These findings support further use of theFr _{t}‐ based parameterization in turbulent oceanic and estuarine environments. 
Measurements of turbulence, as rate of dissipation of turbulent kinetic energy (ε), adjacent to the airwater interface are rare but essential for understanding of gas transfer velocities (k) used to compute fluxes of greenhouse gases. Variability in ε is expected over diel cycles of stratification and mixing. MoninObukhov similarity theory (MOST) predicts an enhancement in ε during heating (buoyancy flux, β+) relative to that for shear (u*w 3/κz where u*w is water friction velocity, κ is von Karman constant, z is depth). To verify and expand predictions, we quantified ε in the upper 0.25 m and below from profiles of temperaturegradient microstructure in combination with time series meteorology and temperature in a tropical reservoir for winds <4 m s−1. Maximum likelihood estimates of nearsurface ε during heating were independent of wind speed and high, ∼5 × 10−6 m2 s−3, up to three orders of magnitude higher than predictions from u*w 3/κz, increased with heating, and were ∼10 times higher than during cooling. k, estimated using nearsurface ε, was ∼10 cm hr−1, validated with k obtained from chamber measurements, and 2–5 times higher than computed from windbased models. The flux Richardson number (Rf) varied from ∼0.4 to ∼0.001 with a median value of 0.04 in the upper 0.25 m, less than the critical value of 0.2. We extend MOST by incorporating the variability in Rf when scaling the influence of β+ relative to u*w 3/κz in estimates of ε, and by extension, k, obtained from time series meteorological and temperature data.more » « less

High Reynolds number wallbounded turbulent flows subject to buoyancy forces are fraught with complex dynamics originating from the interplay between shear generation of turbulence ( $S$ ) and its production or destruction by density gradients ( $B$ ). For horizontal walls, $S$ augments the energy budget of the streamwise fluctuations, while $B$ influences the energy contained in the vertical fluctuations. Yet, return to isotropy remains a tendency of such flows where pressure–strain interaction redistributes turbulent energy among all three velocity components and thus limits, but cannot fully eliminate, the anisotropy of the velocity fluctuations. A reduced model of this energy redistribution in the inertial (logarithmic) sublayer, with no tuneable constants, is introduced and tested against large eddy and direct numerical simulations under both stable ( $B<0$ ) and unstable ( $B>0$ ) conditions. The model links key transitions in turbulence statistics with flux Richardson number (at $Ri_{f}=B/S\approx$ $2$ , $1$ and $0.5$ ) to shifts in the direction of energy redistribution. Furthermore, when coupled to a linear Rottatype closure, an extended version of the model can predict individual variance components, as well as the degree of turbulence anisotropy. The extended model indicates a regime transition under stable conditions when $Ri_{f}$ approaches $Ri_{f,max}\approx +0.21$ . Buoyant destruction $B$ increases with increasing stabilizing density gradients when $Ri_{f}
more » « less 
We experimentally explored the effect of singlesidewall cooling on Rayleigh–Bénard (RB) convection. Canonical RB was also studied to aid insight. The scenarios shared tank dimensions and bottom and top wall temperatures; the single sidewall cooling had the top wall temperature. Turbulence was explored at two canonical Rayleigh numbers, $Ra=1.6\times 10^{10}$ and $Ra=2\times 10^9$ under Prandtl number $Pr=5.4$ . Particle image velocimetry described vertical planes parallel and perpendicular to the sidewall cooling. The two $Ra$ scenarios reveal pronounced changes in the flow structure and largescale circulation (LSC) due to the sidewall cooling. The density gradient induced by the sidewall cooling led to asymmetric descending and ascending flows and irregular LSC. Flow statistics departed from the canonical case, exhibiting lower buoyancy effects, represented by an effective Rayleigh number with effective height dependent on the distance from the lateral cooling. Velocity spectra show two scalings, $\varPhi \propto f^{5/3}$ Kolmogorov (KO41) and $\varPhi \propto f^{11/5}$ Bolgiano (BO59) in the larger $Ra$ ; the latter was not present in the smaller setup. The BO59 scaling with sidewall cooling appears at higher frequencies than its canonical counterpart, suggesting weaker buoyancy effects. The LSC core motions allowed us to identify a characteristic time scale of the order of vortex turnover time associated with distinct vortex modes. The velocity spectra of the vortex core oscillation along its principal axis showed a scaling of $\varPhi _c \propto f^{5/3}$ for the single sidewall cooling, which was dominant closer there. It did not occur in the canonical case, evidencing the modulation of LSC oscillation on the flow.more » « less

Context. Phosphorus (P) is considered to be one of the key elements for life, making it an important element to look for in the abundance analysis of spectra of stellar systems. Yet, only a select number of spectroscopic studies exist to estimate the phosphorus abundances and investigate its trend across a range of metallicities. This is due to the lack of good phosphorus lines in the optical wavelength region and the requirement of careful manual analysis of the blended phosphorus lines in nearinfrared Hband spectra obtained with individual observations and surveys such as the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Aims. Based on a consistent and systematic analysis of highresolution, nearinfrared Immersion GRating INfrared Spectrograph (IGRINS) spectra of 38 K giant stars in the Solar neighborhood, we present and investigate the phosphorus abundance trend in the metallicity range of −1.2 dex < [Fe/H] < 0.4 dex. Furthermore, we compare this trend with the available chemical evolution models to shed some light on the origin and evolution of phosphorus. Methods. We have observed full H  and K band spectra at a spectral resolving power of R = 45 000 with IGRINS mounted on the Gemini South telescope, the Discovery Channel Telescope, and the Harlan J Smith Telescope at McDonald Observatory. Abundances were determined from spectral lines by modeling the synthetic spectrum that best matches the observed spectrum by χ 2 minimization. For this task, we used the Spectroscopy Made Easy (SME) tool in combination with onedimensional (1D) Model Atmospheres in a Radiative and Convective Scheme (MARCS) stellar atmosphere models. The investigated sample of stars have reliable stellar parameters estimated using optical FIberfed Echelle Spectrograph (FIES) spectra obtained in a previous study of a set of stars called Giants in the Local Disk (GILD). In order to determine the phosphorus abundances from the 16482.92 Å phosphorus line, we needed to take special care blending the CO( v = 7−4) line. With the stellar parameters known, we thus determined the C, N, and O abundances from atomic carbon and a range of nonblended molecular lines (CO, CN, and OH) which are plentiful in the Hband region of K giant stars, assuring an appropriate modeling of the blending CO( v = 7−4) line. Results. We present the [P/Fe] versus [Fe/H] trend for K giant stars in the metallicity range of −1.2 dex < [Fe/H] < 0.4 dex and enhanced phosphorus abundances for two metalpoor srich stars. We find that our trend matches well with the compiled literature sample of prominently dwarf stars and the limited number of giant stars. Our trend is found to be higher by ~0.05−0.1 dex compared to the theoretical chemical evolution trend resulting from the core collapse supernova (type II) of massive stars with the phosphorus yields arbitrarily increased by a factor of 2.75. Thus the enhancement factor might need to be ~0.05−0.1 dex higher to match our trend. We also find an empirically determined primary behavior for phosphorus. Furthermore, the phosphorus abundance is found to be elevated by ~0.6−0.9 dex in the two senriched stars compared to the theoretical chemical evolution trend.more » « less