▪ Abstract Passive scalar behavior is important in turbulent mixing, combustion, and pollution and provides impetus for the study of turbulence itself. The conceptual framework of the subject, strongly influenced by the Kolmogorov cascade phenomenology, is undergoing a drastic reinterpretation as empirical evidence shows that local isotropy, both at the inertial and dissipation scales, is violated. New results of the complex morphology of the scalar field are reviewed, and they are related to the intermittency problem. Recent work on other aspects of passive scalar behavior—its spectrum, probability density function, flux, and variance—is also addressed.

Passive Scalars in Turbulent Flows

https://www.math.nyu.edu/faculty/majda/pdfFiles/PhysRep%201999%20Majda%20Kramer.pdf

Simplified models for turbulent diffusion : theory, numerical modelling, and physical phenomena

Recent advances on the numerical modelling of turbulent flows

[1] Air-water gas transfer influences CO 2 and other climatically important trace gas fluxes on regional and global scales, yet the magnitude of the transfer is not well known. Widely used models of gas exchange rates are based on empirical relationships linked to wind speed, even though physical processes other than wind are known to play important roles. Here the first field investigations are described supporting a new mechanistic model based on surface water turbulence that predicts gas exchange for a range of aquatic and marine processes. Findings indicate that the gas transfer rate varies linearly with the turbulent dissipation rate to the 1/4 power in a range of systems with different types of forcing - in the coastal ocean, in a macro-tidal river estuary, in a large tidal freshwater river, and in a model (i.e., artificial) ocean. These results have important implications for understanding carbon cycling.

/pdf/environmental-turbulent-mixing-controls-on-air-water-gas-34m6hh0rtw.pdf

Environmental turbulent mixing controls on air-water gas exchange in marine and aquatic systems

A free surface may be deformed by fluid motions; such deformation may lead to surface roughness, breakup, or disintegration. This paper describes the wide range of free-surface deformations that occur when there is turbulence at the surface, and focuses on turbulence in the denser, liquid, medium. This turbulence may be generated at the surface as in breaking water waves, or may reach the surface from other sources such as bed boundary layers or submerged jets. The discussion is structured by consideration of the stabilizing influences of gravity and surface tension against the disrupting effect of the turbulent kinetic energy. This leads to a two-parameter description of the surface behaviour which gives a framework for further experimental and theoretical studies. Much of the discussion is necessarily heuristic, and is often limited by a lack of appropriate experimental observations. It is intended that such experiments be stimulated, to test the value or otherwise of our two-parameter description.

The dynamics of strong turbulence at free surfaces. Part 1. Description

The mass transfer mechanism across a sheared air–water interface without bubble entrainment due to wave breaking was experimentally investigated in terms of the turbulence structure of the organized motions in the interfacial region in a wind-wave tank. The transfer velocity of the carbon dioxide (CO2) on the water side was measured through reaeration experiments of CO2, and the fluid velocities in the air and water flows were measured using both a hot-wire anemometer and a laser-Doppler velocimeter. The results show that the mass transfer across a sheared air–water interface is more intensively promoted in wind shear, compared to an unsheared interface. However, the effect of the wind shear on the mass transfer tends to saturate in the high-shear region in the present wind-wave tank, where the increasing rate of mass transfer velocity with the wind shear decreases rapidly. The effect of the wind shear on the mass transfer can be well explained on the basis of the turbulence structure near the air–water interface. That is, surface-renewal eddies are induced on the water side through the high wind shear on the air–water interface by the strong organized motion generated in the air flow above the interface, and the renewal eddies control the mass transfer across a sheared interface. The mass transfer velocity is correlated with the frequency of the appearance of the surface-renewal eddies, as it is in open-channel flows with unsheared interfaces, and it increases approximately in proportion to the root of the surface-renewal frequency. The surface-renewal frequency increases with increasing the wind shear, but for high shear the rate of increase slows. This results in the saturated effect of the wind shear on the mass transfer in the high-shear region in the present wind-wave tank. The mass transfer velocity can be well estimated by the surface-renewal eddy-cell model based on the concept of the time fraction when the surface renewal occurs.

Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence

Surface-renewal motions in the interfacial region below a gas-liquid interface were experimentally investigated in relation to bursting motions in the wall region. To estimate the frequency of the appearance of surface-renewal eddies, mass-transport experiments with methylene-blue solution, together with velocity measurements, were done in an open-channel flow. The instantaneous concentration of methylene-blue tracer emitted from a point source positioned in the buffer layer was measured at the free surface downstream from the source by an optical probe. Instantaneous streamwise velocity was measured using a laser-Doppler velocimeter at a position in the buffer region. Frequencies of both surface-renewal and bursting events were computed from these concentration and velocity signals using a conditional-averaging method. In order to clarify whether the surface-renewal eddies actually dominate mass transfer across the gas-liquid interface, gas-absorption experiments were added. Carbon dioxide was absorbed into the water flow across the calm free surface and its mass-transfer coefficient on the liquid side was measured under the same flow conditions as used in the above mass-transport experiments. The results show that the surface-renewal motions originate in the bursting motions which vigorously occur in the buffer region. That is, the decelerated fluid which is strongly lifted towards the outer layer by bursting almost always arrives at the free surface and renews the free surface. The frequency of the surface renewal, as well as the bursting frequency, is uniquely determined by the wall variables or the outer-flow variables and the Reynolds number. Mass transfer across the gas-liquid interface is dominated by the large-scale surface-renewal eddies, and the mass-transfer coefficient on the liquid side is proportional to the square-root of the surface-renewal frequency.

The relationship between surface-renewal and bursting motions in an open-channel flow

Turbulence structure in an open‐channel flow with a zero‐shear gas–liquid interface was numerically investigated by a three‐dimensional direct numerical simulation (DNS) based on a fifth‐order finite‐difference formulation, and the relationship between scalar transfer across a zero‐shear gas–liquid interface and organized motion near the interface was discussed. The numerical predictions of turbulence quantities were also compared with the measurements by means of a two‐color laser Doppler velocimeter. The results by the DNS show that the vertical motion is restrained in the interfacial region and there the turbulence energy is redistributed from the vertical direction to the streamwise and spanwise directions through the pressure fluctuation. The large‐scale eddies are generated by bursting phenomena in the wall region and they are lifted up toward the interfacial region. Then, the eddies renew the interface and promote the scalar transfer across the gas–liquid interface. Both the damping effect and the generation process of the surface‐renewal motions predicted by the DNS explain well the experimental results deduced in previously published studies. Furthermore, the predicted bursting frequency and mass transfer coefficient are in good agreement with the measurements.

Direct numerical simulation of three‐dimensional open‐channel flow with zero‐shear gas–liquid interface

When two species A and B are introduced through different parts of the bounding surface into a region of turbulent flow, molecules of A and B are brought together by the combined actions of the turbulent velocity field and molecular diffusion. A random flight model is developed to simulate the relative motion of pairs of fluid elements and random motions of the molecules, based on the models of Durbin (1980) and Sawford & Hunt (1986). The model is used to estimate the cross-correlation between fluctuating concentrations of A and B, G, at a point, in non-premixed homogeneous turbulence with a moderately fast or slow second-order chemical reaction. The correlation indicates the effects of turbulent and molecular mixing on the mean chemical reaction rate, and it is commonly expressed as the ‘segregation’ or ‘unmixedness ’ parameter a( = c,C,/cA c,) when normalized by the mean concentrations CA and C,. It is found that a increases from near - 1 to zero with the time (or distance) from the moment (or location) of release of two species in highReynolds-number flow. Also, the model _- (and experiments) agrees with the exact results of Danckwerts (1952) that C,c,I(ci c;); = - 1 for mixing without reaction. The model is then extended to account for the effects on the segregation parameter a of chemical reactions between A and B. This leads to a eventually decreasing, depending on the relative timescales for turbulent mixing and for chemical reaction (i.e. the Damkohler number). The model also indicates how a number of other parameters such as the turbulent scales, the Schmidt number, the ratio of initial concentrations of two reactants and the mean shear affect the segregation parameter a. The model explains the measurements of a in previously published studies by ourselves and other authors, for mixing with and without reactions, provided that the reaction rate is not very fast. Also the model is only strictly applicable for a limited mixing time t, such that t 5 TL where TL is the Lagrangian timescale, because the model requires that the interface between A and B is effectively continuous and thin, even if highly convoluted. Flow visualization results are presented, which are consistent with the physical idea underlying the two-particle model.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112091002847

The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows

An original technique for simultaneous measurements of concentration and velocity in a turbulent liquid flow with and without a chemical reaction is developed by combining a two-component He-Ne laser Doppler velocimeter with a Ar+ laserinduced fluorescence technique. The mass flux and eddy diffusivity of mass are estimated from the simultaneous measurements of concentration and velocity in a liquid shear-free mixing layer downstream of a turbulence grid. The results show that the present measuring technique enables us to simultaneously measure velocity and concentration with high resolutions and that the approximation of the mean gradient diffusion causes about 10% error in estimating the mass flux in a reacting liquid flow.

Yasuhiro Murakami

Papers

Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence

The relationship between surface-renewal and bursting motions in an open-channel flow

Direct numerical simulation of three‐dimensional open‐channel flow with zero‐shear gas–liquid interface

The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows

Measurements of mass flux in a turbulent liquid flow with a chemical reaction