Transition Wavenumber Research Articles

Synthesis, characterization, electrochemical and solvatochromic investigations of novel monomeric and polymeric vanadyl Schiff-base complexes

This article describes the synthesis and characterization of oxovanadium(IV) complexes containing tetradentate Schiff-base ligands derived from condensation of ethylenediamine, meso-1,2-diphenyl-1,2-ethylenediamine, 1,2-orthophenylenediamine and 1,2-cyclohexanediamine with 5-bromo-3-nitro-2-hydroxybenzaldehyde. The novel VOL1:[VO(5-Br-3-NO2salen)], VOL2:[VO(5-Br-3-NO2saloph)] and VOL3:[VO(5-Br-3-NO2salchxn)] complexes were obtained in orange polymeric form with (V=O) stretching bands at 878, 884 and 884 cm−1, respectively, but the VOL4 complex was obtained as a green monomer with (V=O) stretching band at 978 cm−1. The redox process in acetonitrile was reversible for VOL4 and E° was determined to be approximately 950 mV but for VOL1–3 this process was irreversible or quasi-reversible. The VOL4 complex is considerably soluble in a wide variety of solvents and shows solvatochromic behavior. The 2 B 2 →2 E(I) transition wavenumber shows a linear correlation to the D.N. of the solvent.

Local and nonlocal advection of a passive scalar

Passive and active scalar mixing is examined in a simple one-parameter family of two-dimensional flows based on quasi-geostrophic dynamics, in which the active scalar, the quasi-geostrophic potential vorticity, is confined to a single horizontal surface (so-called surface quasi-geostrophic dynamics) and in which a passive scalar field is also advected by the (horizontal, two-dimensional) velocity field at a finite distance from the surface. At large distances from the surface the flow is determined by the largest horizontal scales, the flow is spectrally nonlocal, and a chaotic advection-type regime dominates. At small distances, z, scaling arguments suggest a transition wavenumber kc∼1∕2z, where the slope of the passive scalar spectrum changes from k−5∕3, determined by local dynamics, to k−1, determined by nonlocal dynamics, analogous to the transition to a k−1 slope in the Batchelor regime in three-dimensional turbulence. Direct numerical simulations reproduce the qualitative aspects of this transition. Other characteristics of the simulated scalar fields, such as the relative dominance of coherent or filamentary structures, are also shown to depend strongly on the degree of locality.

A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause

The horizontal spectra of atmospheric wind and temperature at the tropopause have a steep -3 slope at synoptic scales, but transition to -5/3 at wavelengths of the order of 500-1,000 km [Nastrom, G. D. & Gage, K. S. (1985) J. Atmos. Sci. 42, 950-960]. Here we demonstrate that a model that assumes zero potential vorticity and constant stratification N over a finite-depth H in the troposphere exhibits the same type of spectra. In this model, temperature perturbations generated at the planetary scale excite a direct cascade of energy with a slope of -3 at large scales, -5/3 at small scales, and a transition near horizontal wavenumber k(t) = f/NH, where f is the Coriolis parameter. Ballpark atmospheric estimates for N, f, and H give a transition wavenumber near that observed, and numerical simulations of the previously undescribed model verify the expected behavior. Despite its simplicity, the model is consistent with a number of perplexing features in the observations and demonstrates that a complete theory for mesoscale dynamics must take temperature advection at boundaries into account.

Multi‐frequency scatterometer measurements on water surfaces agitated by artificial and natural rain

Images of rain events over the ocean acquired by a multi‐frequency/multi‐polarization Synthetic Aperture Radar (SAR) show different radar contrasts at different frequencies and polarizations. In order to better understand these effects, field and laboratory experiments were performed at different rain rates and wind speeds with scatterometers working at different radar frequencies, polarizations, and incidence angles. Our results show that the dominant scattering mechanism on a rain‐roughened water surface, observed at VV polarization, at all incidence angles is Bragg scattering from ring waves. At HH polarization the radar backscatter is caused by both ring waves and non‐propagating splash products, with the dominating effect depending on incidence angle. The reduction and enhancement of the surface roughness by ring waves and sub‐surface phenomena, respectively, result in a transition wavenumber between reduction of the radar backscattering and its enhancement of about 100 rad m−1. We assume that this transition wavenumber depends on the drop‐size distribution of the rain. Taking into consideration the different dependencies of the radar backscatter at different frequencies and polarizations on rain rate, we suggest a method to estimate rain rates by calculating the ratio of the radar cross‐sections at L band, VV polarization and at C band, HV polarization. Provided an availability of SAR data at the respective frequency–polarization combinations, this method allows for investigating the nature of small‐scale (convective) rain events over the ocean.

Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.

Scaling laws of density fluctuations at high-k on Tore Supra

Anomalous transport in tokamaks is generally attributed to turbulent fluctuations. Since a large variety of modes are potentially unstable, a wide range of short-scale fluctuations should be measured, with wavenumbers from kρi ∼ 0.1 to kρi ≫ 1. In the Tore Supra tokamak, a light scattering experiment has made possible fluctuation measurements in the medium- and high-k domains where a transition in the k-spectrum is observed: the fluctuation level decreases much faster than usual observations, typically with a power law S(k) ≡ k−6. A scan of the ion Larmor radius shows that the transition wavenumber scales with ρi around kρi ∼ 1.5. This transition indicates that a characteristic length scale should be involved to describe the fluctuation nonlinear dynamics in this range. The resulting very low level of fluctuations at high-k does not support a strong effect of turbulence driven by the electron temperature gradient. For this gyroradius scan, the characteristics of turbulence also exhibit a good matching with predictions from gyro-Bohm scaling: the typical scale length of turbulence scales with the ion Larmor radius, the typical timescales with a/cs; the turbulence level also scales with ρi, according to the mixing length rule.

Stability of a sheared particle suspension

A stability analysis is carried out for a gas–particle suspension in which the energy dissipation occurs due to the viscous drag force exerted on the particles. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions τc is small compared to the viscous relaxation time τv, so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional “diffusion” stress. For a suspension driven by fluid velocity fluctuations, it is found that perturbations are always stable. For a suspension driven by mean shear, the viscous relaxation time is large compared to the collision time for Ḡτv≫1, where Ḡ is the mean strain rate. The rate of diffusion of energy is small compared to the rate of dissipation for k*≪(Ḡτv)−1, where k* is the wave number scaled by the mean free path. In this regime, it is found that density perturbations are unstable in all three directions in the limit of low volume fraction, but become stable when the volume fraction is increased beyond a critical value. For k*≫(Ḡτv)−1, the rate of diffusion of energy is large compared to the rate of dissipation, and it is found that perturbations are always stable. The transition between these two regimes is obtained numerically in the dilute limit, and the neutral stability curves for the density perturbations are obtained. It is found that in the gradient-vorticity plane, the transition wave number is proportional to (Ḡτv)−1 in the limit (Ḡτv)≫1.

Spectral roughness of glaciated bedrock geomorphic surfaces: Implications for glacier sliding

A microroughness meter (MRM) was used to measure the high‐frequency roughness of a number of geomorphic surfaces in the forefield of Glacier de Tsanfleuron, Switzerland. Resulting spectral power densities are added to low‐frequency spectra, measured by electro‐optical distance meter (EDM), to generate composite roughness spectra that include almost 5 orders of magnitude of roughness in the frequency domain. These are used to define two roughness indices: a general index of bed roughness is defined as the integral of the raw, spectral power densities, and a sliding‐related index of bed roughness is defined as the integral of the spectral power densities weighted to account for the optimum dependence of glacier sliding speed on hummock wavelength. Results indicate that MRM‐measured geomorphic components vary in roughness by 3 orders of magnitude, principally depending on the surface microenvironment measured and profile orientation relative to the direction of former ice flow. Both MRM‐ and EDM‐measured roughnesses are lower parallel to the direction of former ice flow than perpendicular to it. Composite roughness spectra consequently indicate that the glacier bed is smoothed in the direction of former ice flow at all horizontal scales from 1 mm to 40 m, typically resulting in an order of magnitude decrease in sliding‐related roughness relative to that measured perpendicular to ice flow. Comparison of data from two survey sites located adjacent to, and ∼1.2 km from, the current glacier margin indicates that postglacial subaerial weathering homogenizes bedrock roughness, in particular reducing high‐frequency, flow‐orthogonal roughness. Accounting for the effect of 28% ice‐bedrock separation over one of the profiles reduces net, sliding‐dependent roughness by between 27% and 43%, depending on the transition wave number used.

The normal field instability in ferrofluids: hexagon–square transition mechanism and wavenumber selection

When a ferrofluid layer is subjected to a uniform and vertically oriented magnetic field, an interfacial instability occurs, above a critical value of the magnetic field, giving rise to a hexagonal array of peaks. On increasing the magnetic field, a smooth morphological transition from the hexagonal array to a square array was observed above a second threshold. The hexagon–square transition phenomenology, in addition to the role of penta–hepta defects initially present in the hexagonal pattern, was investigated. Furthermore, the pattern and wavenumber selection was studied by two different procedures: first by imposing jumps in field intensity and second by varying the magnetic field in a quasi-static way. The results obtained were very different for the two procedures. They indicated that the square pattern was a metastable state induced by the compression of the hexagonal pattern on increasing the control parameter. This hypothesis was confirmed by performing an additional experiment where the pattern was isotropically compressed. In this experiment, the transition was induced at a constant magnetic field lower than the transition onset value. However, the theoretical values for stability domains of hexagons and squares proposed in the literature were found to not agree with the experimental values.

Optical nutation under Raman excitation

Optical nutation under Raman excitation accompanied by considerable (up to inverted) population changes was observed. The Raman-active 6P1/2–6P3/2 transition of thallium atoms was excited by picosecond pulses of a dye and an Nd : YAG laser. Transition polarization and upper level population were probed by delayed pulses at a fixed time by means of coherent Raman scattering and third harmonic generation schemes, respectively. Optical nutation manifested itself in corresponding changes of anti-Stokes and third harmonic signal energies as functions of the product of the pump pulses energies. As a result of the a.c. Stark shift, the nutation picture strongly depended on the sign of wavenumber detuning from the transition wavenumber. Copyright © 2000 John Wiley & Sons, Ltd.

Direct correlation method for OH, NH and CH local modes: vibrational overtone spectroscopy of biphenyl, anthracene, isobutanol, 2-chloroethanol and ethylenediamine at the third overtone region

The vibrational overtone spectra of gaseous biphenyl, anthracene, isobutanol, 2-chloroethanol and ethylenediamine at the Δv=4 vibrational overtone region have been recorded and assigned using the local mode model. For the spectral assignments, linear correlations were determined between the ab initio bond lengths (calculated in this work) and the overtone transition energies (taken from the literature) of aromatic and nonaromatic hydrocarbons, alcohols and amines. The bond lengths were obtained from ab initio geometry optimizations using both the 3-21G * and the 6-31G ** basis sets. The bond length–overtone transition wavenumber correlations for the OH, NH and aromatic, methyl and methylenic CH oscillators are presented for the Δv=4 region for both basis sets. The bond lengths (CH for biphenyl and anthracene, OH for isobutanol and 2-chloroethanol and NH for ethylenediamine) were also determined. These bond lengths were used to predict the transition wavenumbers for Δv=4 transitions which could then be compared to the experimental values. These predictions which accounted for the possibility of various conformations agreed well with the experiment.

Optical nutation under Raman excitation

Optical nutation under Raman excitation accompanied by considerable (up to inverted) population changes was observed. The Raman-active 6P1/2 -6P3/2 transition of thallium atoms was excited by picosecond pulses of a dye and an Nd : YAG laser. Transition polarization and upper level population were probed by delayed pulses at a fixed time by means of coherent Raman scattering and third harmonic generation schemes, respectively. Optical nutation manifested itself in corresponding changes of anti-Stokes and third harmonic signal energies as functions of the product of the pump pulses energies. As a result of the a.c. Stark shift, the nutation picture strongly depended on the sign of wavenumber detuning from the transition wavenumber. Copyright 2000 John Wiley & Sons, Ltd. cross-sections in comparison with those of rotational or rotation-vibrational transitions. For the relatively high transition wavenumbers, typical for atoms, the Doppler dephasing time T 2 can be as low as1 ns. The coher- ence of excitation is secured, provided that pump pulses shorter than T1, T2 and T 2 are applied. By varying the energy of the pump pulses, the system can be transfered into different states, including a state with inverted popu- lation. This scheme was discussed in Ref. 5, where it was proposed to monitor the transition polarization by measur- ing the energy of the coherent Raman scattering signal as function of the product of the pump pulses energies with the probe pulse delayed at a fixed time relative to the pump pulses. At the same time, the third harmonic (TH) is much more effectively generated in thallium, when the upper level 6P3=2 of the Raman-active transition is populated. 6 This effect can be used to monitor the population of the excited level. The application of picosecond pulses ensures, as a rule, the fulfillment of the coherent excitation conditions in gases. Since the Raman cross-sections are small, it is necessary to use powerful picosecond pulses to obtain suf- ficient population changes. This makes the manifestation of the a.c. Stark effect real. In the present work, the optical nutation at a Raman- active transition was observed at resonant Raman excita- tion by picosecond pulses. Optical nutation was accompa- nied by considerable population changes. The a.c. Stark shift manifested itself in an 'asymmetry' of the nutation picture relative to the sign of the wavenumber detuning .!1 !2/ !R.

Measurements of the Effects of Gravity Waves in the Middle Atmosphere Using Parametric Models of Density Fluctuations. Part II: Energy Dissipation and Eddy Diffusion

Part I of this series demonstrated the advantages of parametric models in estimating the gravity wave spectrum from density fluctuation measurements using a large power-aperture-product Rayleigh-scatter lidar. The spectra calculated using the parametric models are now used to estimate energy dissipation due to gravity waves. Energy dissipation for an individual wave in the spectrum is also estimated using Prony’s method, which allows the frequency, amplitude, damping, and phase of individual waves to be estimated. These two independent estimates of energy dissipation highlight the variability of the energy dissipation on short timescales due to gravity waves and turbulence. A combination of the information obtained from the parametric models of the spatial and temporal spectra with the theoretical work of M. E. McIntyre is used to estimate profiles of the eddy diffusion coefficient. This estimate attempts to include the degree of saturation of the vertical wavenumber spectrum, which determines the constant used in the calculation of the eddy diffusion coefficient. The height profile of the eddy diffusion coefficient thus obtained in the upper stratosphere and mesosphere is in good agreement with previous estimates. The degree of saturation of the vertical wavenumber spectrum is shown to increase proportionally to the Hines parameter, a measure of the transition wavenumber from a linear to a nonlinear tail spectrum. It is speculated that this fact can be interpreted as a change in the atmosphere from an “amplifier” state where the tail spectrum is highly nonlinear, but weak when the spectral “gain” is high, to a state of saturation where the high wavenumber tail spectrum is more linear, but has lower gain and more energy available to dissipate at smaller spatial scales.

Eddy stirring and phytoplankton patchiness in the subarctic North Atlantic in late summer

The spatial structure of phytoplankton distributions in the mesoscale eddy field of the North Atlantic (vicinity of 20°W, 59°N) was examined with a series of high resolution, towed transects. Data were obtained after the fall transition in August 1991 as part of the Marine Light-Mixed Layers (MLML) program. Measurements of chlorophyll fluorescence (CF) and the beam attenuation coefficient anomaly ( Δc 490) show that chlorophyll and particles are confined to the surface mixed layer and seasonal pycnocline. Two water masses account for the potential temperature–salinity ( θ– S) structure in the region: North Atlantic Central Water from the sub-tropical gyre and Sub-Arctic Intermediate Water from the sub-polar gyre. These water masses carry distinct particle distributions based on measurements of CF and Δc 490. Spatial distributions of CF and S in the mixed layer are spatially coherent for horizontal wavenumbers k less than a transition wavenumber k t≈0.15 cycles km -1 (transition wavelength λ t= k -1 t≈7 km). The horizontal distribution of θ in the mixed layer is uncorrelated with S. Autospectra of θ, S, CF, and Δc 490 vary approximately as k -2 for k less than k t. For k⩾ k t, CF and Δc 490 decrease approximately as k -3, while S spectra continue as k -2. These observations are consistent with physical control of phytoplankton distributions for k< k t by eddy advection. They are consistent with control by non-conservative biological processes for k⩾ k t. This contradicts some theoretical models of chlorophyll spectra, which predict physical control of phytoplankton distributions above k t and biological control below. The contradiction may arise because the scales of variance sources assumed in the models are not consistent with observed scales in the MLML region.

The CN Mode of HCN: A Comparative Study of the Variation of the Transition Dipole and Herman–Wallis Constants for Seven Isotopomers and the Influence of Vibration–Rotation Interaction

The electric dipole transition moments and vibration-rotation constants of the CN stretching bands of H12C14N and six other isotopomers are reported. Hot-band measurements show the vibrational dependence of the constants. Infrared absorption spectra were measured with a Fourier transform interferometer and a multipass absorption cell with a path length of up to 240 m. The transition wavenumber measurements were used to derive vibration–rotation constants, and the intensities of individual lines were used to determine the transition dipoles and Herman–Wallis factors. The unusually small transition dipole coupled with the large dipole moment of HCN (2.98 D) results in very large values for the first Herman–Wallis factorA1and distorts the shape of the intensity envelope of the band. These measurements show how changes in the masses of the heavy atoms in the molecule have a systematic effect on the transition dipole and on the intensity pattern of the CN stretching band.

Low‐wavenumber spectral characteristics of velocity and temperature in the atmospheric surface layer

The structure of atmospheric surface layer turbulence at low wavenumbers was analyzed using 56 Hz triaxial velocity and temperature measurements above a uniform dry lake bed. A key feature of this experiment was the small roughness length of the surface that resulted in a small roughness Reynolds number. Under near‐neutral atmospheric stability conditions, a −1 power law was observed in both measured velocity and temperature spectra which is consistent with previously proposed dimensional analysis for rough and smooth turbulent boundary layer flows. The wavenumber at which the −1 power law terminates and the −5/3 power law commences was derived as a function of the Kolmogorov and von Karman constants. Good agreement between the predicted and the measured transition wavenumber from −1 to −5/3 was noted for fully rough‐flow conditions. However, this was not the case for other roughness conditions. The similarity theory constants for the neutral case were determined and they compared favorably with other laboratory and field studies. For unstable atmospheric conditions, directional dimensional analysis was used to predict the slopes of the power spectra of temperature and velocity. It was demonstrated that for moderately unstable conditions, the temperature and vertical velocity power spectra exhibited a −1 power law, but the longitudinal velocity exhibited a −2 power law. The agreement between predicted and measured power laws was within experimental errors. Some differences between the constants determined from this experiment and other experiments are also discussed.

Capillary–gravity and capillary waves generated in a wind wave tank: observations and theories

Short water surface waves generated by wind in a water tunnel have been measured by an optical technique that provides a synoptic picture of the water surface gradient over an area of water surface (Zhang &amp; Cox 1994). These images of the surface gradient can be integrated to recover the shape of the water surface and find the two-dimensional wavenumber spectrum. Waveforms and two-dimensional structures of short wind waves have many interesting features: short and steep waves featuring sharp troughs and flat crests are very commonly seen and most of the short waves are far less steep than the limiting wave forms; waveforms that resemble capillary–gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989); capillaries are mainly found as parasitics on the downwind faces of gravity waves, and the longest wavelengths of those parasitic capillaries found are less than 1 cm; the phenomenon of capillary blockage (Phillips 1981) on dispersive freely travelling short waves is also observed. The spectra of short waves generated by low winds show a characteristic dip at the transition wavenumber between the gravity and capillary regimes, and the dip becomes filled in as the wind increases. The spectral cut-off at high wavenumbers shows a power law behaviour with an exponent of about minus four. The wavenumber of the transition from the dip to the cut-off is not sensitive to the change of wind speed. The minus fourth power law of the extreme capillary wind wave spectrum can be explained through a model of energy balances. The concept of an equilibrium spectrum is still useful. It is shown that the dip in the spectrum of capillary–gravity waves is a result of blockage of both capillary–gravity wind waves and parasitic capillary waves.

Fourier Transform Spectra of Overtone Bands of HCN from 4800 to 9600 cm −1: Some New Transitions of Bending Combination Modes

The transition moments and vibration-rotation constants of 18 previously unobserved combination and/or hot bands of H 12C 14N are reported. Overtone absorption spectra were measured with a Fourier transform interferometer and a multipass absorption cell with a pathlength of up to 352 m. The transition wavenumber measurements were used to derive vibration-rotation constants, and the integrated line intensities were used to derive an estimate of the transition moments. The new transitions are 01 13-01 10, 11 12-00 00, 12 02-000, 32 00-02 00, 32 20-02 20, 03 12-01 10, 03 12-00 00, 13 11-01 10, 13 11-00 00, 13 31-02 20, 23 30-03 30, 23 10-03 10, 23 10-00 00, 03 12-02 00, 03 32-02 20, 14 01-02 00, 14 21-02 20, and 04 02-00 00.

Vertical wave number spectra of velocity and shear at small internal wave scales

We analyze spectra from five sets of hourly vertical profiles of upper‐ocean horizontal velocity collected with the Cartesian Diver velocity recorder. Each set consists of 11 to 27 profiles over depth ranges of 25–220 m to 25–340 m. The vertical wave number (m) power spectra of velocity and shear have no reproducible power law form in the band [0.02–0.1] cpm. Shear spectra tend to rise then fall with increasing wave number, with the transition wave number mc varying within the above band. For shear spectra, steepness at m near 0.1 cpm ranges from m−1/2 to m−2. The data sets fall into two categories. For one group, inverse Richardson functions Ri−1(mc) have values near 2. Despite variability of velocity variance, these sets have Ri−1(0.1 cpm) ≈ 3, suggesting that shear is near saturation. Low variability of Ri−1(0.l), despite high kinetic energy variability for this group, suggests that energy at high wave number (and thus shear) is suppressed. This suggests that instability mechanisms attenuate spectra at high wave number, with attenuation becoming more broadband and influencing progressively lower vertical wave numbers (in addition to consistently influenced high wave numbers) at higher energy. For the other group, Ri−1(0.1) ≈ 1, shear spectra are less steep, and shear is concentrated at high wave number, suggesting less attenuation at the small‐scale end of our measurement band. For both groups, predicted wave numbers of spectral steepening, estimated from the data using two techniques, are related approximately inversely with horizontal kinetic energy in the band [0.005–0.01] cpm, quantifying the shear spectral roll‐off.

Energy and entropy evolution of interacting internal gravity waves and turbulence

Abstract The energy and entropy evolutions of two-dimensional interacting internal gravity waves and turbulence in the (x, z) plane are studied in inviscid, viscous decay and forced-dissipative numerical simulation experiments using a spectral model. In each case the entropy evolution is compared with that predicted by the eddy-damped quasinormal Markovian (EDQNM) closure formulated by Carnevale and Frederiksen (1983) for two-dimensional internal waves. Although there is no spectral gap between the internal waves and the turbulence in the experiments, we define a transition wavenumber k 1 such that for wave-numbers k ≪ k 1 wave motion predominates and for wavenumbers k≫k 1 turbulence is dominant. In both experiments in which wave motion is generated from turbulence and in which turbulence is generated from wave instability, it is found that the entropy production and energy transfers are inhibited for increased, Brunt-Vaisala frequencies or transition wavenumbers. In experiments in which a single wave (k ...