Vertical Eddy Diffusion Coefficient Research Articles

Some estimates of transport processes in Long Island Sound

A parametric description of lateral and vertical oscillatory transport in two segments of Long Island Sound is presented. The vertical eddy viscosity and diffusivity coefficients are estimated on the basis of a model for turbulent kinetic energy transfer. Characteristics of horizontal mixing are examined by means of dimensional analysis. The relative importance of the mechanisms controlling mass distribution in the estuary is evaluated by calculating longitudinal dispersion coefficients in a form introduced by Fisher (1972). It is shown that the mass transport in Long Island Sound is governed mainly by two processes: lateral turbulent dispersion and net longitudinal transport caused by the density gradients.

One-dimensional vertical model for ozone and other gases in the atmospheric boundary layer

A vertical eddy diffusion coefficient profile for mass transport in the atmospheric boundary layer is established on the basis of a calculation where the equations of motion and the thermodynamic energy equation are solved. A one-dimensional vertical model for the chemical turnover is then developed. It is assumed that the turbulent mass transport is equal to the product of the vertical mean concentration gradient and the vertical eddy diffusion coefficient for mass transport. About 40 chemical species are calculated in the model, and about 90 chemical reactions are involved. A log-linear grid is introduced, with close spacing near the ground and coarser towards the free troposphere. The diurnal cycle of ozone in an atmospheric boundary layer with strong convective mixing during the day and a shallow layer under the influence of mechanical stress at night, is computed and compares well with observations. It is found that in polluted air, depletion of ozone close to the ground through reaction with NO prevents ozone from reaching the ground and be removed by deposition. The concentration of hydroxyl has a marked gradient with height, with maximum in the layers where nitrogen oxides, hydrocarbons and sulphur dioxide are emitted. Nitrogen dioxide, sulphur dioxide and the hydrocarbons (ethane, n- butane , ethylene, propylene and m- xylene ) accumulate throughout the night in the shallow nocturnal layer.

Vertical Turbulent Diffusion in Air-Driven Water Flows

Turbulence intensities and Reynolds stresses produced in a water channel by an air flow over the surface have been measured. An expression for the vertical eddy diffusion coefficient is derived from these results. The drag necessary for the creation of waves and the development of a boundary layer, including the acceleration of the water mass, have been taken into account and are shown to be significant. A linear shear stress distribution has been measured within the boundary layer, and the Prandtl mixing length theory and Boussinesq hypothesis are shown to provide a good basis for describing the diffusion process.

A simple formula for vertical eddy diffusion coefficients under conditions of nonneutral stability

Vertical turbulent transport of heat and momentum in water bodies is often parameterized as the neutral value of the appropriate (vertical) eddy diffusion coefficient, multiplied by a function of the gradient Richardson number. An analysis of previously published formulae for these stability functions shows that they are not consistent with observed values for the ratio between nonneutral and neutral values of the vertical eddy diffusion coefficients [Ueda et al., 1981] nor with observed values of the turbulent Prandtl number or the flux Richardson number [Linden, 1979]. A new formulation for the stability function in the case of turbulent heat transfer is proposed which is of an inverse quadratic form. It is shown that this representation, together with an appropriate inverse linear form in the case of momentum transfer, is in excellent agreement with recent data.

The variability of mesospheric water vapor

Measurements of the H2O emission line at 22.2 GHz show that the concentration in the mesosphere of water vapor molecules can be highly variable, ranging from nearly constant mixing ratios of 2‐4 ppmv, up to a layer near 65 km altitude with peak values around 12 ppmv. Results above 70 km altitude have been used to deduce a value for the vertical eddy diffusion coefficient of (4.4 ± 0.7)×105 cm²sec−1.

On the vertical structure of the eddy diffusion coefficient in the PBL

An attempt is made to determine the vertical eddy diffusion coefficient K = K( z, R i ) considering the basic structure of the turbulent diffusion process ( R i Richardson number). To achieve this, K is assumed to be an operating function which represents the effects produced by turbulent eddies from all levels on level z. The determining equation for K is derived by a variational method utilizing some basic consequences of the structure of turbulent diffusion. The eddy coefficient K thus derived, accounts approximately for the consideration of vertical stability conditions, e.g. temperature inversions and their time-dependent development, when dealing with the diffusion of air pollutants; besides, it offers a sufficient presentation for the whole PBL, which avoids matching problems.

Winds and waves (10 min‐30 days) in the mesosphere and lower thermosphere at Saskatoon (52°N, 107°W, L = 4.3) during the year, October 1979 to July 1980

Winds from a medium frequency (2.2 MHz) radar, operating as a partial reflection drifts system, have been obtained for four seasons of 1979/1980. Harmonic and spectral analyses have been used to provide monthly profiles of zonal and meridional winds, and the amplitudes and phases of 12 and 24 hour tides, at heights from 70 to 110 km. There are distinctive changes in tidal vertical wavelengths and phases between winter‐ and summer‐like months. Fluctuations of the mean daily wind and the tides during the stratwarm of February 1980 are documented. Oscillation of the wind, for all seasons, with periods from 2 to 30 days, are related to Rossby periods for atmospheric normal modes. Energy densities for oscillations appropriate to waves ranging in scale from gravity, through tidal, to planetary waves are evaluated by month and are compared with turbulence parameters for energy dissipation rates and vertical eddy diffusion coefficients. There are winter maxima and summer secondary maxima in both energy densities and turbulence parameters, which suggest a relationship between certain waves and the creation of turbulence.

Large-Scale Vertical Eddy Diffusion in the Main Pycnocline of the Central North Pacific

Abstract Indirect procedures are used to estimate the latitudinal distribution of the large-scale vertical eddy diffusivity coefficient in the main pycnocline from the interannual change in Tθ, ρθ structure of the water column in the central midlatitude North Pacific from 35–44°N, 150–170°W. Using T, S data from two identical hydrographic surveys, one made in June 1976 and the other in May 1977, the interannual change in potential temperature is recorded on three potential density surfaces (i.e., ρθ = 26.6, 27.0 and 27.2) that lie in the upper, middle and lower part of the main pycnocline, respectively. By relating these interannual changes to the vertical gradients of the average potential temperature on each surface (i.e., through the heat conservation equation), the large-scale vertical eddy diffusivity coefficient and its vertical gradient were determined by least-squares estimate procedures. The vertical eddy diffusivity coefficient K is found to have been positive over the entire region, with magnit...

Eddy diffusion coefficient for the atmosphere of Venus from radio scintillation measurements

Estimates of the vertical mass eddy diffusion coefficient K are necessary to understand the dynamics and photochemistry of a planetary atmosphere. Most previous estimates for the atmosphere of Venus1–10, pertain to the upper atmosphere. In the lower atmosphere (≲80 km), information on small-scale (≲1 km) temperature fluctuations has been provided by radio scintillations observed during radio occultation by the atmosphere11–18. Here we relate the vertical mass eddy diffusion coefficient to these radio scintillation observations so that reliable estimates can be obtained near the tropopause level of 60 km for the first time. Using the recent Pioneer Venus radio occultation measurements16, and assuming that the turbulence is generated by shear instability, we find that K = 4 × 104 cm2 s−1, the energy dissipation rate ɛ = 20 cm2 s−1, and the dissipation rate of temperature fluctuations Nθ = 10−3 K2 s−1. These results indicate that small-scale turbulence probably plays a major part in vertical transport near the tropopause of Venus.

Water vapor budget in the lower stratosphere over Japan.

The water vapor budget in the lower stratosphere over Japan was studied. At Kagoshima and Tateno the observed water vapor mass mixing ratio is explained by a modified Brewer circulation model adding the water vapor source of CH4 oxidation except in spring at Kagoshima. The vertical eddy diffusion coefficient at an altitude of 20.7 km was estimated to be 1.2-1.4×103cm2sec-1 from the vertical profiles of water vapor and the production rate of water vapor by the oxidation of CH4. Seasonal variation of the residence time of water vapor in the lower stratosphere was obtained; minimum in winter-spring (0.3 year) and maximum in fall (0.95 year). Mean vertical velocity of the return Hadley circulation (the descending branch of the Hadley circulation) was estimated to be 0.010-0.035cm sec-1. Water vapor in the lower stratosphere at Sapporo cannot be explained by the same model as Tateno and Kagoshima except in spring. A very low water vapor mixing ratio is observed in spring from Kagoshima through Sapporo and in winter at Sapporo, suggesting some water vapor removal processes. Aerosols in the lower stratosphere make negligible contribution to the water vapor budget except after an extensive volcanic eruption.

Radium-228 in the Japan Sea

The distribution of228Ra in surface and subsurface waters in the Japan Sea was studied. The concentrations of228Ra in surface waters were around 100 dpm/1000l which were much higher than those reported for Pacific surface waters. The concentrations of228Ra decreased with increasing depth to less than 10 dpm/1000l in the Japan Sea Proper Water. Based on the comparison between observed values of228Ra and calculated profile through the near-surface water mass and the underlying main water mass in the Japan Sea, the apparent vertical eddy diffusion coefficient was estimated to be about 2 cm2 s−1.

228Ra and 228Th concentrations in GEOSECS Atlantic surface waters

An average 228Ra flux of 0.6±0.1 dpm cm −2 yr −1 from continental shelf sediments can maintain the estimated total 228Ra inventory of about 5 × 10 17 dpm in Atlantic surface waters. By fitting 228Ra and potential temperature data to Munk's vertical advection-diffusion model, upwelling rates of 17±10 m yr −1 and vertical eddy diffusion coefficients of 0.4±0.2 cm 2 s −1 were obtained in the upper water column of the equatorial Atlantic. The downward fluxes of particulate 228Th across the 350-m water depth are about 0.01 to 0.04 dpm cm −2 yr −1 in the Sargasso Sea and in the regions south of 12°N and about 0.06 to 0.11 dpm cm −2 yr −1 in the northern temperate region (excluding the Sargasso Sea). The shorter half-removal time of 228Th in the equatorial (10°S to 20°N) and the northern region (35° to 65°N) are related to higher biological productivity there.

14C distribution in the Atlantic Ocean

The amount of 14C produced by nuclear bomb testing that entered the Atlantic Ocean by late 1972 was 1.71×10−8 μmol/cm2 of ocean surface area for the west Atlantic (36°S–45°N) and 1.18×10−8 μmol/cm2 for the east Atlantic (50°S–28°N) Geochemical Ocean Sections Study stations. There are strong latitudinal differences in the integrated amount of bomb 14C content in Atlantic waters. Bomb‐produced 14C is mostly encountered near the center of the large mid‐latitude gyres, whereas the equatorial region has a lower 14C inventory. The average ocean wide vertical distribution of bomb 14C in the Atlantic can be explained by a vertical eddy diffusion coefficient of 4.0 cm2/s in the surface mixed layer plus thermocline gyre reservoirs. The average 14C activity per unit area measured in the Atlantic yields an CO2 exchange rate of 23 mol/m2 yr, which is equivalent with an atmospheric CO2 residence time of 6.8 years.

The vertical distribution of tropospheric ammonia

A one‐dimensional tropospheric photochemical model is used to simulate measured profiles of NH3 obtained with the Infrared Heterodyne Radiometer. The relative roles of homogeneous loss, heterogeneous loss, and vertical eddy transport are discussed in terms of selecting parameters which best fit the measurements. The best fit was obtained for a vertical eddy diffusion coefficient of 2 × 105 cm−2 sec−1 or greater (corresponding to a characteristic vertical transport time in excess of about 35 days), and a characteristic heterogeneous loss time in excess of 10 days. The characteristic homogeneous chemical loss time was found to be about 40 days at the surface and decreased to about l80 days at 10 km, and not very sensitive to model chemical perturbations. Increased ground level concentrations of NH3 to about 10 ppb, compared to background surface concentrations of about 1 ppb, were measured several weeks after application of ammonium nitrate fertilizer. This suggests that the volatilization of ammonium nitrate fertilizer is rapid, and an important source of NH3. Because of the characteristic times for the loss mechanisms, synoptic time scale phenomena may play an important role in determining the tropospheric distribution of NH3 concentrations.

Whole-Lake Model for the Distribution of Sediment-Derived Chemical Species

The distribution of CH4, ΣCO2, and NH3-N below the thermocline of Lake 227 can be reproduced using a simple numerical model. The model uses a constant vertical eddy diffusion coefficient and assumes the sediments to be the sole source of the chemical species. Analogs dependent on oxygen concentration can effectively represent conditions at the interface of the modeled region and the shallower depths in the lake. The best tit value for the vertical eddy diffusion coefficient is 3.1 × 10−3 cm2∙s−1. This is in good agreement with other independent measurements of this phenomena. The best fit fluxes of CH4, dissolved inorganic carbon and NH3-N are respectively: 13 × 10−3 mol∙m−2∙d−1, 7.5 × 10−3 mol∙m−2∙d−1, and 1.65 × 10−3 mol∙m−2∙d−1. The flux of methane is similar to that found in other small productive northern lakes and the ratio of CH4:ΣCO2 production of 1.73 falls in the range of values established for fermentation of mixed organic materials and sediments. The flux of ΣCO2 is 50–75% of the bicarbonate flux (10–15 × 10−3 mol∙m−2∙d−1) found previously in Linsley Pond, Connecticut.Key words: sediment–water interactions, methane, CO2, and ammonia fluxes, diffusion from sediments, Experimental Lakes Area

Estimates of vertical eddy diffusion through the thermocline from phytoplankton nitrate uptake rates in the mixed layer of the eastern tropical Pacific1

Vertical eddy diffusion coefficients ranging from 0.05–1.1 cm2·s−1 were calculated from phytoplankton nitrate uptake rates in the mixed layer and nitrate gradients at the top of the thermocline of the eastern tropical North Pacific. An empirical relationship was determined between these diffusion coefficients and density gradients in the thermocline. This relationship was used to calculate nitrate fluxes through the thermocline at several stations where nitrate uptake was not measured, and the fluxes indicated that an average of 29% of the primary productivity was supported by the uptake of nitrate‐nitrogen.

Nitric oxide under different constraints imposed on ion-neutral chemistry

The variation of nitric oxide density has been studied on the basis of a currently known ion-neutral chemical scheme under various theoretical constraints, viz. an increase of ionization in photochemical equilibrium, an increase of ionization with vertical transport and different eddy diffusion coefficients, an increase of ionization during nighttime and withdrawal of ionization at night. It is seen that in the absence of a horizontal transport, [NO] increases with increasing ionization. Downward vertical transport which increases with increasing ionization, contributes negligibly in determining the steady-state density of NO. The eddy diffusion has very little effect at heights above 90 km. It is also seen that the present chemical scheme is unable to explain [NO] as large as2× 10 11 cm −3 as observed by Zipf et al. (1970) during an enhanced auroral ionization at Fort Churchill indicating thereby that either the measurement is in error or there is a need of a powerful source of NO. The decay of [NO] is very slow at heights below the peak when ionization is switched off after attaining the maximum value due to the enhancement in ionization.

Nitrate and phytoplankton production in southern California coastal waters1

The transport of nitrate into the euphotic zone appears to be a major factor regulating the standing stock and production of phytoplankton in southern California coastal waters. The evidence is as follows. 1) The rate of photosynthetic carbon assimilation is proportional to the rate of nitrate assimilation and to the ratio of nitrate:total N assimilated. 2) The phytoplankton standing stock (g C·m−3) and its production rate are related to the depth of the vertical nitrate concentration gradient. 3) The chemical composition of the particulate organic matter, as the POC:PON ratio, is related to the carbon:nitrogen assimilation ratio of the phytoplankton. 4) Regenerated production, measured as ammonium assimilation, is proportional to the nitrate assimilation rate, implying parallel and concurrent increases in the production of heterotrophic microplankton and phytoplankton attending new inputs of nitrate into the euphotic zone. 5) The vertical diffusion of nitrate, when calculated from the vertical nitrate concentration gradients and nitrate assimilation rates, appears to give reasonable estimates of the vertical eddy diffusivity coefficient for nitrate.

Venus: Chemistry of the lower atmosphere prior to the Pioneer Venus mission

Using laboratory studies of the high temperature kinetics of a number of sulfur gases together with a simple chemical‐dynamical model of the lower atmosphere of Venus, we conclude that the relative concentrations of photochemically‐produced oxidized sulfur gases (SO2, SO3) and thermochemically‐produced reduced sulfur gases (COS, S2, H2S) are strongly dependent on the rate of vertical mixing. For values of the vertical eddy diffusion coefficient in excess of 104 cm² sec−1 we predict that the reduced gases will dominate over the oxidized gases in the lower atmosphere. Measurements of the important sulfur gases by Pioneer Venus will thus provide valuable knowledge of lower atmospheric mixing in addition to furthering our understanding of the chemistry which maintains the visible sulfuric acid cloud layer.

Daytime nitric oxide at the base of the thermosphere

Nitric oxide profiles are deduced from the analysis of 10 daytime ion composition experiments performed at various latitudes, seasons, and solar conditions, principally over an altitude region from 85 to 100 km. Within a factor of 3, nitric oxide concentrations are found to vary from 1 × 108 cm−3 at 100 km to 2×106 cm−3 at 85 km for various sunspot numbers and seasons, except winter. This strong gradient suggests a vertical eddy diffusion coefficient on the lower side of those thought to be appropriate. The three winter mid‐latitude data sets, all associated with anomalous D region radio absorption, yield higher NO concentrations, two profiles attaining peak values of 109 cm−3.