Individual Wavenumbers Research Articles

Statistics of gravity wave spectra in the troposphere and lower stratosphere over Beijing

We utilize the temperature profiles with a height resolution of 50-m obtained over the Beijing Observatory in the period between January of 2002 and December of 2002 to study vertical wavenumber spectra of normalized temperature fluctuations in the 1.67–8.02 km and 13.57–19.92 km altitude ranges and compare them with linear saturation model. Results indicate that individual vertical wavenumber spectra reveal a considerable variability in both slope and amplitude. The observed variability is not consistent with the predictions of linear saturation model. However, mean vertical wavenumber spectra in the troposphere measured at different seasons and different local times show great similarities with fairly uniform negative slopes of ~3.0 and amplitudes proportional to N 4 , suggesting that the seasonal mean spectra observed in the troposphere completely obey the linear saturation model and are unique at present. In contrast, while the spectral slopes of the mean vertical wavenumber spectra in the lower stratosphere tend to support the explanation of the observed temperature fluctuations by linear saturation model, the spectral amplitudes diverge significantly from linear saturation model, suggesting that the seasonal mean spectra in the lower stratosphere do not obey the linear saturation model and are unique at present. The dominant vertical wavelengths derived from the observed mean vertical wavenumber spectra are estimated to be ~3.2–~2.1 km in the troposphere and lower stratosphere, which is generally consistent with those reported in the literature. Balloon measurements, temperature and temperature spectra, gravity waves and saturation mode, dominant vertical wavelengths.

Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter

We investigate the scale-locality of subgrid-scale (SGS) energy flux and interband energy transfers defined by the sharp spectral filter. We show by rigorous bounds, physical arguments, and numerical simulations that the spectral SGS flux is dominated by local triadic interactions in an extended turbulent inertial range. Interband energy transfers are also shown to be dominated by local triads if the spectral bands have constant width on a logarithmic scale. We disprove in particular an alternative picture of “local transfer by nonlocal triads,” with the advecting wavenumber mode at the energy peak. Although such triads have the largest transfer rates of all individual wavenumber triads, we show rigorously that, due to their restricted number, they make an asymptotically negligible contribution to energy flux and log-banded energy transfers at high wavenumbers in the inertial range. We show that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain an energy cascade to small scales. Furthermore, nonlocal triads are argued to contribute even less to the space-average energy flux than is implied by our rigorous bounds, because of additional cancellations from scale-decorrelation effects. We can thus recover the −4/3 scaling of nonlocal contributions to spectral energy flux predicted by Kraichnan’s abridged Lagrangian-history direct-interaction approximation and test-field model closures. We support our results with numerical data from a 5123 pseudospectral simulation of isotropic turbulence with phase-shift dealiasing. We also discuss a rigorous counterexample of Eyink [Physica D 78, 222 (1994)], which showed that nonlocal wavenumber triads may dominate in the sharp spectral flux (but not in the SGS energy flux for graded filters). We show that this mathematical counterexample fails to satisfy reasonable physical requirements for a turbulent velocity field, which are employed in our proof of scale locality. We conclude that the sharp spectral filter has a firm theoretical basis for use in large-eddy simulation modeling of turbulent flows.

Determination of Glucose and Cellobiose Dissolved in the Ionic Liquid 1-Ethyl-3-Methylimidazolium Acetate Using Fourier Transform Infrared Spectroscopy

The conversion of biogenic carbohydrate feedstock to chemicals or energy equivalents is a promising approach to solve the problem of limited fossil fuel reserves. Some concepts to accomplish these transformations are based on ionic liquids (ILs) due to their ability to dissolve biopolymers, such as cellulose, and even complex biopolymer mixtures, such as wood. However, concerning control of such conversions, a reliable tool for process analytics is required. In this paper we demonstrate the applicability of Fourier transform infrared (FT-IR) spectroscopy to perform quantitative concentration measurements of glucose and cellobiose as two examples of carbohydrates dissolved in the room-temperature ionic liquid [EMIM][OAc] (1-ethyl-3-methylimidazolium acetate). For this purpose, binary mixtures in the range 0-20 wt% have been studied. A previously developed method for the data analysis, which was based on the Beer-Lambert relation, has been universalized by employing empirical correlations between the measured quantity (i.e., extinction) and the carbohydrate concentration. In the entire spectral range under investigation (500-4000 cm(-1)) numerous individual wave-numbers have been identified, allowing quantitative measurements with high accuracy and precision.

Improved detection of large cirrus particles from infrared spectral observations

Spectral observations of cirrus clouds can be analyzed to obtain cloud particle effective radii using measurements at select wavenumbers in the infrared atmospheric window. The suitability of these wavenumbers to determine a range of sizes is constrained by the dependence on particle radius of ice absorption efficiency (Qabs). By using only those wavenumbers at which Qabs varies monotonically with radius, cloud particle radii up to approximately 20 μm can be determined; larger values, however, present problems. At some wavenumbers, the variation in Qabs is not sufficiently large to distinguish between large particle radii. At other wavenumbers, larger particles are more easily distinguished, but Qabs values do not correspond to unique particle radii. Using one set of wavenumbers only to determine whether the particle is large or small, and a second set to actually determine the effective radius of a large cloud particle, the limitations faced at individual wavenumbers can be partially overcome. This is demonstrated using yearlong spectral observations of ice clouds at South Pole station.

Modal inverse methods: An overview

Geoacoustic inversion using modal inverse methods is based on a very simple experimental geometry. Data are acquired from synthetic aperture measurements of a point source acoustic field using a single hydrophone translating through the water column at constant depth. The modal composition of the propagating field is extracted by exploiting the Hankel transform relationship between the acoustic field, measured as a function of range, and the horizontal wavenumber spectrum for horizontally stratified media. Modal content, estimated as discrete values of the horizontal wavenumber, are used as input data for a general linear inverse problem, where small perturbations to a background sound speed profile are related to changes in individual horizontal wavenumbers. An overview of the method is presented with an emphasis placed on the application to range-dependent shallow water environments. Inversion results are presented from a recent workshop on geoacoustic inversion for range-dependent environments, as well as from recent at-sea measurements. [Work supported by ONR.]

Parameterization of the Optical Properties of Sulfate Aerosols in the Infrared

Abstract Parameterizations of absorptance depth for ammonium sulfate [(NH4)2SO4], ammonium bisulfate (NH4HSO4), and sulfuric acid (H2SO4) in the infrared are provided for an eight-band model (covering 340–2500 cm−1) and for 32 individual wavenumbers in order to generate other band schemes. The parameterization is simple in form and in its dependence on relative humidity. It is found that the aerosol surface infrared forcing can cancel about 12%–24% aerosol surface solar forcing in a clear sky condition. Also the existence of clouds could enhance the ratio of aerosol surface infrared forcing to the aerosol surface solar forcing. In contrast to the solar case, a small mode size distribution does not always produce a larger aerosol surface forcing. Also it is found that the aerosol surface forcing is dependent on the aerosol location. Very simple analysis is presented to help understand the related physics on sulfate aerosol infrared radiative forcing.

Chemical waves in inhomogeneous excitable media

Propagating chemical waves are typically studied in homogeneous, excitable reaction mixtures. Chemical waves in an inhomogeneous excitable medium are examined in this paper. Cation exchange beads, loaded with ferroin, are bathed in Belousov-Zhabotinsky reaction mixtures containing no catalyst. Spiral waves are spontaneously initiated above a critical bromate concentration, which is dependent on the size of the ferroin-loaded beads. At high bromate concentrations, irregular patterns are formed due to an overcrowding of spirals. An upper limit in the number of individual waves is exhibited, which is independent on the bead size. Regular and irregular patterns are analyzed by calculating spatial correlation functions from digital images.

Daily spectral energy conversions of the global circulation during 10-27 January 1979

The energetics of the daily wave activity over tropical and middle latitudes are examined for part of the first special observing period of FGGE using a modified version of ECMWF Level III-b analyses. Overall, the results are in good agreement with prior investigations. It is found that the eddy available potential (AE) is increased by sensible heat transport down the temperature gradient (CA) at all wavenumbers and that it is immediately converted to eddy kinetic energy (KE) through warmer air rising and/or colder air sinking (CE). Moreover, it is seen that this energy cycle takes place at each individual wavenumber, n , with the major contributions being due to n = 2–4 and n = 6–7. It is also seen that the wave-to-wave interactions are generally much less important than the remaining terms in the eddy energy budgets. Special attention in this study is devoted to the southern hemisphere energetics. In the southern tropics, it is found that CE dominates over other conversion processes. The contribution from n = 4 accounts for the major portion of this conversion. It appears that latent heating in the south Pacific may be the main cause for the significance of this wavenumber 4 domination. In southern mid-latitudes, all conversion terms are equally important and the major contributions occur at intermediate wavelengths, n = 6–8. The energy cycle consists of a conversion of zonal available potential energy (AZ) to AE to KE to zonal kinetic energy (KZ). DOI: 10.1111/j.1600-0870.1988.tb00329.x

Scale Selection and Energy Spectra of Disturbances in Southern Hemisphere Flows

The growth and nonlinear interaction of initially small-amplitude disturbances, having a complete spectrum of zonal wavenurnbers, with zonally averaged flows characteristic of January and May SouthernHemisphere situations, are studied in a multilevel primitive equation spectral model-incorporating spherical geometry and viscous dissipation. For January, the fastest growing scale has zonal wavenumberm = 9, in close agreement with linear instability theory. However, the contribution from m = 7 subsequently exceeds that of rn = 9 and is largely responsible for the general agreement between model andobserved eddy streamfunctions and fluxes. Although the individual wavenumber contributions, eg,m = 9 and m = 7 undergo vacillation cycles similar to ones found earlier with single zonal wavenumberdisturbances growing on the same zonal flows, the total eddy kinetic energy after the initial growth periodis relatively constant. This appears to be due to the interference between the larger number of waves. ForMay the fastest growing scale has m = 5 and initially grows on the polar jet. As the disturbance maturessecondary growth occurs on the subtropical jet and the disturbance achieves significant amplitude in theupper troposphere in the latitude band between 30 and 60. Unlike previous baroclinic instability results,the nonlinear model and observed eddy fluxes are also in close qualitative agreement. For January a very long-time viscous integration was carried out and the kinetic energy spectra werestudied at various stages. When zonal wavenumber m = 7 reaches its peak (day 23), the spectrum has anapproximate m-s power law. This. however, is not a statistical quasi-steady state and further integrationout to days 45-SO was needed to reach such a state. Then it was found that the spectra satisfy the m-3power law of classical two-dimensional and quasi-geostrophic turbulence theory.

Theoretical Regime Diagrams for Thermally Driven Flows in a Beta-Plane Channel

It is noted that thermally driven flows in rotating laboratory containers with cylindrical geometry can be axially symmetric or wavelike depending on the experimental parameters. In anticipation that rotating fluid experiments might soon be done in spherical shell geometry, Barcilon's model has been extended to a beta-plane channel in order to gain a rough understanding of the effects of rotating spherical geometry. An incompressible fluid version of the Charney (1947) model of baroclinic instability, modified to include Ekman pumping at rigid horizontal boundaries is used. With this model, stability boundaries are mapped out for individual zonal wavenumbers in the parameter space used by Barcilon.

Line intensities of methane in the 2700–2862-cm −1 region

Individual strengths and wavenumbers of 2080 methane absorption lines have been measured between 2700 and 2862 cm −1 at an average resolution of 0.023 cm −1 using a grating spectrometer. The results include all lines with strengths greater than 3 × 10 −5 cm −2 atm −1 observable at 296 K with a maximum path of 32 m and a pressure of 4 Torr.

A Wavenumber-Frequency Analysis of Large-Scale Tropospheric Motions in the Extratropical Northern Hemisphere

Abstract The geopotential height and temperature at 500 and 300 mb at various northern latitudes are analysed in wavenumber-frequency space, for a summer and a winter season. The power spectra at individual wave-numbers are flattish or peaked at low frequencies, but above a cutoff frequency (which increases with wavenumber from 0.03 to 0.3 cycles per day) they fall off sharply, with a −3 to −4 power law for the geopotential height at mid-latitudes. Temperature spectra are less steep than height spectra, and summer spectra less steep than winter spectra. The quadrature spectra show higher eastward phase speeds in the winter than in the summer. Westward-moving ultralong waves at mid-latitudes are visible in the quadrature spectra of height, but not of temperature. By means of quadrature spectral analysis, separate wavenumber spectra are computed for travelling and stationary waves. The stationary-wave spectra of the temperature fall almost monotonically with wave-number, and at mid-latitudes tend to a −3 po...

The motion generated by a body moving along the axis of a uniformly rotating fluid

Experiments have been made to investigate the motion generated by a body moving along the axis of a uniformly rotating fluid.Part of the investigation concerns the motion generated in a cylinder whose radial dimensions are much greater than those of the body. Measurements have been made of the velocities of particles on the axis of rotation both ahead of and behind the body, and the results indicate that there is a significant axial motion generated by the body over a wide range of Rossby numbers. A measurement of the instantaneous velocity profile ahead of the body, determined as a function of the radius, agrees fairly well with a low Rossby number calculation of the flow due to a circular disk (Morgan 1951). In addition, the forward influence of the body has been measured as a function of the Rossby number and from these results it is suggested that the body has a finite influence far upstream at all Rossby numbers and that the blocking phenomenon first reported by Taylor (1922) probably occurs for all values of the Rossby number (UΩa) less than a critical value which is about 0·7.Experiments have also been made in a long cylindrical tube which acts as a wave guide. At large distances from the body the separate effects of the various modes can be observed and hence it is possible to measure the flow corresponding to an individual wave-number: these measurements show that, as a result of the Doppler effect, the motion a large distance ahead of the body is different from that far behind (see Lighthill 1967). Moreover, the experiments indicate that no disturbances propagate ahead of the body when its velocity exceeds the maximum group velocity in the fluid, but that disturbances trail behind the body when its velocity is far in excess of the maximum group velocity. Measurements of the maximum group velocity are in good agreement with the theoretical value.

ON THE INTERANNUAL VARIABILITY OF THE TROPOSPHERIC ENERGY CYCLE AND THE QUASI-BIENNIAL OSCILLATION

Geostrophic computations in the wave number domain have been made of the “eddy” kinetic energy, the transfer of kinetic energy between the zonal flow and the eddies, and the internal redistribution of kinetic energy among the eddies at 500 mb. An 11-yr record has been inspected for year-to-year variations and the results related to the quasi-biennial oscillation in the lower stratosphere. The individual wave numbers indicate significant year-to-year variations in their energy cycle that must be considered when only short time periods are under study. While no consistent relationship was found between these variations and the quasi-biennial oscillation, our results suggest that a profitable line of inquiry would be to examine the annual variations of the vertical transfer of kinetic energy by the pressure-work term at the interface of the troposphere and stratosphere.

Decay of Isotropic Turbulence in the Direct-Interaction Approximation

The direct-interaction equations for the decay of isotropic turbulence are integrated numerically with initial spectra of several shapes and initial values of Rλ ≲ 40. Results are presented for the evolution of total energy, dissipation, energy transfer, skewness factor, and other integral quantities, together with the associated wavenumber spectra. Similarity and self-preservation features of the evolving spectra are exhibited. The results are compared with grid-turbulence measurements by Stewart and Townsend. Results are also given for the time-correlation of the total velocity at a fixed point in space and for the time-correlation and response functions of individual wavenumber modes.