Vertical turbulent mixing

In [48], it was shown that, in order to simulate the cold intermediate layer of the Black Sea (see [3]), one should take into account the dependence of the vertical turbulent mixing coefficient on the density stratification of the waters. In this case, the optimal coefficients in the well-known formula by Munk-Anderson for the Black Sea occurred to be an order of magnitude lower than those for the World Ocean. 

The chapter also addresses whether changes in trace metal trends are a result of enhanced or reduced input to the Baltic Sea, or if they are related to a feedback mechanism including the stabihzation of the anoxic deepwater regime and resulting trace metal export by vertical turbulent mixing across the oxic-anoxic interface. 

Between 1999 and 2005, a negative trend of -8.6%/year (-0.01 nmol/(kg year)) was calculated for Cddiss in waters Above Halocline. It was assumed that this phenomenon was due to the stabilization of anoxic conditions in the deep water, which led to the increase in the export of Cddiss from surface waters by time lag. To support this idea, the exchange of dissolved metals by vertical turbulent mixing at the oxic-anoxic interface has been calculated, as described later. 

Quantification of Trace Metal Fluxes across the Redox Interface Caused by Vertical Turbulent Mixing... 

About 25% of Cd, 12% of Cu, and 8% of Zn, which were supplied by rivers and atmosphere, were eliminated by vertical turbulent mixing across the oxic-anoxic interface and subsequent sulfide precipitation. For Pbjiss, the flux at the redox interface was negligible. Comparing the sum of the internal fluxes (dissolved and particulate) in relation to the total... 

The determination of nitrate in seawater is not subject to interferences. It has been claimed that nitrate might occur together with small amounts of hydrogen sulphide. For thermodynamic reasons this can only be true for waters from the transition layers between oxic and anoxic environments where intense vertical turbulent mixing processes occur. In this case the hydrogen sulphide is precipitated on top of the reductor as copper or cadmium sulphide and does not interfere in the nitrate analysis. Nitrate values observed together with hydrogen sulphide should be interpreted with care. 

The mechanism of turbulent mixing which brings air into the buoyant plume is called entrainment. It has been described empirically by relating the momentum of the induced air proportionally to the vertical momentum (mean or centerline),... 

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

Nci exchange. The top 2 m of the lake are well mixed. Vertical turbulent diffusivity... 

While molecular diffusivity is commonly independent of direction (isotropic, to use the correct expression), turbulent diffusivity in the horizontal direction is usually much larger than vertical diffusion. One reason is the involved spatial scales. In the troposphere (the lower part of the atmosphere) and in surface waters, the vertical distances that are available for the development of turbulent structures, that is, of eddies, are generally smaller than the horizontal distances. Thus, for pure geometrical reasons the eddies are like flat pancakes. Needless to say, they are more effective in turbulent mixing along their larger axes than along their smaller vertical extension. 

Radioactive or stable isotopes of noble gases are also used to determine vertical turbulent diffusion in natural water bodies. For instance, the decay of tritium (3H)— either produced by cosmic rays in the atmosphere or introduced into the hydrosphere by anthropogenic sources—causes the natural stable isotope ratio of helium, 3He/ 4He, to increase. Only if water contacts the atmosphere can the helium ratio be set back to its atmospheric equilibrium value. Thus the combined measurement of the 3H-concentration and the 3He/4He ratio yields information on the so-called water age, that is, the time since the analyzed water was last exposed to the atmosphere (Aeschbach-Hertig et al., 1996). The vertical distribution of water age in lakes and oceans allows us to quantify vertical mixing. 

In Illustrative Example 19.4, the dissolution of a non-aqueous-phase liquid (NAPL) into groundwater was discussed. Here we consider a similar (although somewhat hypothetical) case. Assume that a mixture of chlorinated solvents totally covers the flat bottom of a small pond (maximum depth zmax = 4 m, surface area Asurface = 104 m2) forming a dense non-aqueous-phase liquid (DNAPL). The DNAPL is contaminated by benzene which dissolves into the water column and is vertically transported by turbulent diffusion. The pond is horizontally well mixed. The vertical turbulent diffusion coefficient is , = 0.1 cm2s l and approximately constant over the whole water column. 

First, recall that the nondimensional Damkohler number, Da (Eq. 22-11 b), allows us to decide whether advection is relevant relative to the influence of diffusion and reaction. As summarized in Fig. 22.3, if Da 1, advection can be neglected (in vertical models this is often the case). Second, if advection is not relevant, we can decide whether mixing by diffusion is fast enough to eliminate all spatial concentration differences that may result from various reaction processes in the system (see the case of photolysis of phenanthrene in a lake sketched in Fig. 21.2). To this end, the relevant expression is L (kr / Ez)1 2, where L is the vertical extension of the system, Ez the vertical turbulent diffusivity, and A, the first-order reaction rate constant (Eq. 22-13). If this number is much smaller than 1, that is, if... 

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