%====================================================================== % M I X I N G / V A L L E Y . T E X % doc: Tue Apr 4 14:51:09 2000 % dlm: Thu Jun 8 00:12:39 2000 % (c) 2000 A.M. Thurnherr % uE-Info: 180 39 NIL 0 0 72 3 2 4 ofnI %====================================================================== To calculate heat budgets of the rift valley below \m{2000} the corresponding mass (volume) budgets are required. Based on the hydraulic volume flux estimates across sills ``I'' \rsec{F2-inflow} and ``R'' \rsec{hydraulics} the volume budget of \sA below \m{2000} is characterized by inflow from the eastern ridge flank of \mmmps*{95}{3} and outflow across \RS of \mmmps*{65}{3}, leaving a deficit of \mmmps*{30}{3}. While outflow across sill ``O'' can balance this budget, the hydrographic sections of \citeN{JGR/wilson+95} appear more consistent with inflow. Furthermore, there are other potential sinks for the rift-valley water entering \sA (see below). Deriving a similar budget for \A is associated with even greater uncertainties. The deepest sill near the northern end of the segment connects the rift valley to the \FAM segment at \m{2200} (sill ``F''). The available bathymetry does not rule out an additional sill (sill ``W'') connecting \A to the western ridge flank at some depth above \m{2100}. The northernmost rift-valley profiles of both hydrographic surveys indicate higher densities at \m{2100} than in a western ridge-flank background profile, with differences \kgpmmm{<\!10^{-2}}. Applying the hydraulic model of \fullciteN{misc/whitehead+74} (c.f.\ \rsecNP{hydraulics}, with assumed sill and interface depths of \m{2100} and \m{2000}, respectively) yields volume flux estimates \mmmps*{<6}{3}, i.e.\ less than 10\% of the water entering \A across \RS below \m{2000}. %-------------------- \begin{figure}[t] \placeFig{mixing/outflow} \caption[\A/\FAM sill observations]{Hydrographic and light-scattering observations from sill ``F'' connecting the \A and \FAM segments; in the main panel the potential density and nephelometry profiles are plotted; the inset shows the corresponding \ThetaS properties.} \labelFig{mix-outflow} \end{figure} %-------------------- The most likely pathway out of the segment for the bulk of the water flowing across \RS into \A is therefore across sill ``F''. (The hydrographic sections of \citeN{JGR/wilson+95} appear consistent with this view.) \rFigNP{mix-outflow} shows data from a station occupied directly on that sill. Between \m{2020} and \m{2040} the density profile is characterized by a steep gradient. The corresponding \ThetaS properties rule out instrument problems and suggest that the water above and below the density step is most likely of the same origin, i.e.\ eastern North Atlantic water. (The slight change in the \ThetaS slope near \degC{4.2} is consistent with other rift-valley profiles of the 1998 survey, e.g.\ \rfigNP{tscompare}.) The available bathymetric data sets indicate that the \FAM segments are closed below \m{2000} with the exception of sill ``F'' and an additional sill on the eastern rift-valley wall near \latN{36}{25}/\lonW{32}{55} with a minimum depth between \m{2000} and \m{2100}. Inflow of eastern ridge-flank water into \FAM and overflow across sill ``F'' into \A is therefore as consistent with the \ThetaS observations of \rfigNP{mix-outflow} as is flow from \A into \FAM. The increased light-scattering signals observed below the density step suggest two layers of water, possibly flowing in different directions. While no light-scattering data is available from \FAM the observed nephelometry signal is consistent with the rift-valley properties of the \A segments where nearly all nephelometry profiles contain weak maxima of \V{0.01$--$0.02} near \m{2100}. Attempting to infer the flow direction below \m{2000} across sill ``F'' from \rfigNP{sigsec} does not lead to unambiguous conclusions either. The density patterns near the northern and southern ends of the \A segments are similar, i.e.\ consistent with inflow from \FAM into \A. The current-meter measurements on the other hand indicate northward mean flow into the region of the upsloping isopycnal surfaces (c.f.\ \rsecNP{CM-flowstats}). Isopycnal uplifting upstream of \RS was observed in 1997 \rsec{hydraulics} and there are indications for the same effect in \rfigNP{sigsec}. Our data do therefore not allow to infer a mean flow direction across sill ``F'' with confidence. It is nevertheless tentatively assumed that the flow is from \A into \FAM, primarily because added inflow into \A would require a large outflow, presumably across sill ``W'', which does not appear consistent with our density observations. The volume flux across sill ``F'' is estimated with the hydraulic model of \fullciteN{misc/whitehead+74} (c.f.\ \rsecNP{hydraulics}). No cross-sill density section is available, implying that the interface height and density difference between the two layers must be estimated with an alternative method. Using the density step observed on the sill \rfig{mix-outflow} to derive a reduced gravity and interface height yields \mpss*{\gp=3}{-4} and \m{\hu=170} (from the altimeter at \m{2030}, the center of the density step). The Rossby radius of deformation corresponding to these values is \km{2.6}, less than the sill width of \km{5} at \m{2000}, indicating that the hydraulic model can be applied as before, yielding a volume flux estimate of \mmmps*{50}{3}. The corresponding flow velocity estimated from the interfacial wave speed is \mps{0.23}. The most likely volume budget for the \A segment is therefore characterized by inflow across \RS of \mmmps*{65}{3} and outflow into \FAM of \mmmps*{50}{3}, leaving a deficit of \mmmps*{15}{3}. It will be noted that the apparent volume flux deficits of the \A segments are proportional to the lengths (or areas) of the segments. While additional outflows across sills ``O'' and ``W'' can balance the budgets it appears also possible that some of the rift-valley water is lost to the overlying water column (see below). Using the horizontal area of the \A segments at \m{2000} (calculated from the mean rift-valley width of \km{20} at \m{2000} and the length of the segments, i.e.\ \km{100} for \sA and \km{50} for \Ap{}{),} the apparent volume-flux deficits imply a vertical velocity of \mps*{1.5}{-5}. (For comparison, \citeN{JGR/read+pollard99} estimated a value of \mps{10^{-5}} for the entire Mozambique basin.) %-------------------- \begin{table}[t] \begin{center}\begin{tabular}{|l||rrr|rrr|} \hline%------------------------------------------------------------ & \multicolumn{3}{c|}{\sA} & \multicolumn{3}{c|}{\A} \\ & \multicolumn{1}{c}{$Q$} & \multicolumn{1}{c}{$\overline{\theta_2}$} & \multicolumn{1}{c|}{$\rho_0 c_p Q\overline{\theta_2}$} & \multicolumn{1}{c}{$Q$} & \multicolumn{1}{c}{$\overline{\theta_2}$} & \multicolumn{1}{c|}{$\rho_0 c_p Q\overline{\theta_2}$} \\ & \multicolumn{1}{c}{[\mmmps{}]} & \multicolumn{1}{c}{[\degC{}]} & \multicolumn{1}{c|}{[\W{}]} & \multicolumn{1}{c}{[\mmmps{}]} & \multicolumn{1}{c}{[\degC{}]} & \multicolumn{1}{c|}{[\W{}]} \\ \hline\hline%====================================================== Inflow & $95\times10^3$ & 3.634 & $1.45\times10^{12}$ & $65 \times10^3$ & 3.777 & $1.03\times10^{12}$ \\ Outflow& $-65 \times10^3$ & 3.777 & $-1.03\times10^{12}$ & $-50 \times10^3$ & 3.904 & $-0.82\times10^{12}$ \\ Deficit& $-30 \times10^3$ & 3.710 & $-0.47\times10^{12}$ & $-15 \times10^3$ & 3.841 & $-0.24\times10^{12}$ \\ \hline%------------------------------------------------------------ Balance & & \multicolumn{2}{r|}{$4.79\times10^{10}$} & & \multicolumn{2}{r|}{$3.08\times10^{10}$} \\ \hline%------------------------------------------------------------ \end{tabular}\end{center} \caption[\A volume and heat budgets]{Volume and heat budgets of the \A segments; volume fluxes ($Q$) are taken from sills ``I'', ``R'' and ``F''; average temperatures below \m{2000} ($\overline{\theta_2}$) are taken from CTD profiles; ``Balance'' denotes the amount of heat required to close the budgets (LHS of \rexpr{mix-saunders}).} \labelTab{mix-budgets} \end{table} %-------------------- Combining the volume flux budgets of the \A segments with hydrographic data from the 1998 survey, heat budgets are calculated as shown in \rtabNP{mix-budgets}. The average temperatures of the overflows below \m{2000} are taken from the CTD tow-yo across sill ``I'' \rfig{F2-inflow}, from the 1998 CTD stations occupied in the vicinity of \RR \rfig{F2-stations}, and from the profile shown in \rfigNP{mix-outflow}, respectively. The temperatures associated with the volume flux deficits are set to the average values of the inflows and outflows. From these heat balances diapycnal-diffusivity estimates are calculated using \rexpr{mix-saunders} with \degCpm*{\theta_z=1.3}{-3}, estimated from \m{100}-thick layers centered at \m{2000} (c.f.\ \rsecNP{mix-saunders}). The known geothermal contributions (\BHc and \BHp) again have a minor impact on the budgets. The estimates for the diapycnal diffusivities become \mmps*{\Kv=4.1}{-3} \sAp{(}{)} and \mmps*{\Kv=5.6}{-3} \Ap{(}{).} Taking a conservative approach by assuming that the apparent volume flux deficits are caused by overestimates of the inflowing volume fluxes (which is more conservative than assuming that the deficits are caused by additional outflows across sills ``O'' and ``W'') yields \mmps*{\Kv=3.3}{-3} \sAp{(}{)} and \mmps*{\Kv=4.8}{-3} \Ap{(}{).} If the flow below \m{2000} across sill ``F'' is from \FAM into \A no heat budgets and corresponding diffusivities can be estimated for the \A segment.