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Finescale Structure of the Temperature-Salinity Relationship 

Raffaele Ferrari 

Department of Earth, Atmospheric, and Planetary Sciences, 54-1420 
Massachusetts Institute of Technology, 77 Massachusetts Ave. 
Cambridge, MA 02139-4307 USA 

Phone: (617) 253-1291 Fax: (617) 253-4464 Email: rferrari@mit.edu 

Kurt L. Polzin 

Woods Hole Oceanographic Institution 
MS #21 

Woods Hole, MA 02543 

Phone: (508) 289-3368 Fax: (508) 457-2181 Email: kpolzin@whoi.edu 

Award Number: N00014-03-1-0354 
http://mit.edu/raffaele/www/main.htm 


LONG-TERM GOALS 

The long term goal of this project is to understand the processes that establish the temperature-salinity 
relationship in the ocean, with emphasis on the interplay between advection at the large scale, eddy 
stirring at the mesoscale and turbulent mixing at the finescale. 

OBJECTIVES 

The objectives of this proposal are (1) to unfold the processes that participate in the creation of the 
temperature-salinity relationship in two high-resolution data sets, the North Atlantic Tracer Release 
Experiment (NATRE) and the Salt Finger Tracer Release Experiment (SFTRE), and (2) to determine 
the relative importance of eddy stirring and turbulent mixing process in the ocean interior with a 
combination of numerical and theoretical tools. 

APPROACH 

The approach is foremost to analyze and interpret finescale phenomena in high-resolution 
oceanographic data sets, and secondarily to develop simple analytic and numerical representations to 
explain those phenomena. The work is done in collaboration by Raffaele Ferrari, at the Massachusetts 
Institute of Technology, and by Kurt Polzin, at the Woods Hole Oceanographic Institution. Shafer 
Smith, at the New York University, has developed the code to run high-resolution numerical 
experiments on a Beowulf cluster at MIT. Maxim Nikurachine, a student of the Joint Program between 
Woods Hole and MIT, helped with the analysis of the observations. 

WORK COMPLETED 

Ferrari completed the analysis of the temperature variance and eddy kinetic energy budgets for the 
NATRE data set. The analysis was based on an extension of the Oborn-Cox model to account for the 
production of finescale temperature variance by mesoscale eddies. The results are reported in a 


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Finescale Structure of the Temperature-Salinity Relationship 


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Department of Earth, Atmospheric, and Planetary Sciences, 
54-1420„Massachusetts Institute of Technology, 77 Massachusetts 
Ave.„Cambridge„MA, 02139 

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14. ABSTRACT 

The long term goal of this project is to understand the processes that establish the temperature-salinity 
relationship in the ocean, with emphasis on the interplay between advection at the large scale, eddy stirring 
at the mesoscale and turbulent mixing at the finescale. 


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manuscript submitted for publication to Deep Sea Research, a peer-reviewed journal. Polzin completed 
the processing of the SFTRE data set, resulting in estimates of all conventional microstructure 
quantities: vertical profiles of temperature, salinity, shear, thennal dissipation, and kinetic energy 
dissipation. These data will be analyzed with the same approach used for the NATRE data set. The 
quasi-geostrophic model written by Shafer Smith has been modified to run on the Beowulf cluster at 
MIT. 

RESULTS 

The Osbom-Cox model is a simplified temperature variance budget that is the basis for direct estimates 
of diapycnal diffusivities in the ocean. The model assumes that dissipation of thermal variance is due 
to turbulent motions acting on the mean temperature stratification. The model assumes the following 
path for temperature variance, 


Turbulence 

Mean ► Microscale ► Dissipation 


Figure 1. The Osborn-Cox model. 

We extended the Osborn-Cox model to include the variance production by lateral stirring due to 
mesoscale eddy motions, using a triple decomposition scheme proposed by Russ Davis and Chris 
Garrett. The revised model shows that variance at the microscale can be generated by eddy stirring 
acting on the mean T-S profiles, creating finestructure, which is eventually removed by turbulence, 


Fines cale 




Microscale ► Dissipation 


Figure 2. Revised Osborn-Cox model. 

Turbulence and mesoscale eddies act very differently on temperature (T) and salinity (S) distributions. 
First, turbulence is characterized by motions with scales of 0(1-10) m, while mesoscale motions span 
0(10-100) km. Second, turbulence drives fluxes both along and across density surfaces, while 
mesoscale eddy motions are directed along density surfaces (isopycnals). In regions where temperature 
variance production is dominated by turbulence, one expects to find smooth T-S profiles with wiggles 
at small scales. In regions where temperature variance production is dominated by eddy stirring, one 
expects T-S profiles to exhibit structure at the finescale along isopycnals. This paradigm was used to 
analyze microstructure measurements from the North Atlantic Tracer Release Experiment (NATRE). 

The T-S relationship at the Mediterranean Water levels (about 1000 m depth) exhibits a large degree of 
variability along isopycnals. This finestructure is characterized by a lack of horizontal coherence: it is 


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difficult to relate features in one T-S profile with features in a neighboring profile a few kilometers 
apart. This lack of coherence is evident as a 0.2~psu cloud when T-S diagrams for nearby stations are 
overplotted (Figure 3). In contrast, at shallower levels characterized by North Atlantic Central Water, 
the T-S relationship is much tighter. The large amount of T-S variability at the Mediterranean Water 
level and the lack of horizontal coherence are consistent with T-S finestructure being generated by 
mesoscale stirring. The eddy field generates temperature variance by stirring the large-scale isopycnal 
gradients of temperature and salinity associated with the Mediterranean Tongue. The isopycnal 
gradients are much weaker at North Atlantic Central Water levels, and mesoscale stirring cannot 
generate finestructure. 



Figure 3. The T-S relationship in NATRE. 


This interpretation of eddy stirring producing finestructure along isopycnals is supported by the 
temperature variance budget analysis of the NATRE data set. The analysis is based on the Osbom-Cox 
model modified to account for lateral eddy stirring (Figure 4). The budgets are computed for neutral 
layers approximately 100 m thick. The mean depths of the neutral surfaces (close to isopycnals) are 
used as the reference vertical coordinate. Microstructure estimates of temperature variance dissipation 
for each layer are shown in red and the shaded boxes represent the error bars. The production of 
variance by turbulent motions acting on the mean diapycnal gradient is shown in black. The production 
of variance by eddy stirring of the mean isopycnal gradient is represented in blue. At the North 
Atlantic Central Water level, temperature variance is associated with turbulence (i.e. internal wave 
breaking and double diffusion) acting on the mean diapycnal temperature gradient. At the 
Mediterranean Water level, eddy stirring dominates to the production of temperature gradient variance. 


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Preliminary analysis of microstructure data from the Salt Finger Tracer Release Experiment suggests 
that mesoscale eddy stirring plays an important role also in the Western North Atlantic. 




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1010 " 
Variance production/diasipation [m 2 /^ 3 ] 


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26.95 
27.22 
27.46 
27.64 
27.77 
27.85 
27.91 

27.95 
27.99 

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Figure 4. Temperature variance budget in NATRE. 


A main result of this analysis is that eddy stirring contributes substantially to the generation of 
temperature variance at the microscale across water mass fronts, where there are T-S gradients along 
isopycnals. The resulting lincstructurc is characterized by compensating T-S gradients, i.e. T-S 
gradients with no signature on density. Some microscale mixing mechanism must occur to prevent the 
gradients from increasing without limit. Microstructure data suggest that, as the compensated 
gradients develop, they become unstable to double diffusive instabilities which limit the further growth 
of the gradients. This process produces extra diapycnal mixing that would not have occurred in the 
absence of lateral stirring. In this scenario eddy stirring controls the rate of double-diffusive 
turbulence, and hence of diapycnal mixing. This contrasts with the traditional interpretation that the 
rate of diapycnal mixing in regions characterized by water mass contrasts along isopycnals is set by 
double diffusion acting on the mean profiles. 

The result of this analysis is relevant to the study of propagation of acoustic signals in the oceanic 
environment. Acoustic scattering is a product of sound speed anomalies associated with T-S 
finestructure and is extremely sensitive to the spectral distribution of such finestructure. In this work 
we have shown that eddy stirring sets the rate of creation of finestructure, while double diffusive 
instabilities control the spatial scales at which finestructure is dissipated. Thus parameterization of 
mesoscale processes together with parameterizations for double diffusion can be combined to predict 
the spectral distribution of finescale structure. 


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IMPACT/APPLICATIONS 


We anticipate that this work will fonn the basis for future interpretation of microstructure data and for 
the parameterization of the interplay of mesoscale eddy stirring and double diffusive turbulence. 

TRANSITIONS 

Ocean circulation models are extremely sensitive to the rate of diapycnal mixing. Our work has shown 
that finescale structure can trigger double diffusive instabilities and hence diapycnal mixing. Thus the 
predictive ability of ocean models depends upon the parameterization of finestructure phenomena. The 
descriptions of finestructure and physical understanding provided by our simple analysis will help 
improve their skill. 

RELATED PROJECTS 

J. Ledwell, J. Toole and R. Schmitt were leading Pis in the NATRE and SFTRE experiments. The 
insight gained as part of this grant will have a direct impact on the interpretation and comparison of 
microstructure data and tracer release measurements. 

PUBLICATIONS 

Polzin, K. L, and R. Ferrari, 2003: Isopycnal Dispersion in NATRE, Journal of Physical 
Oceanography, [in press, refereed]. 

R. Ferrari, and K. L. Polzin, 2003: Temperature and Salinity Finestructure in NATRE, Deep Sea 
Research, [submitted, refereed]. 

HONORS/AWARDS/PRIZES 

Raffaele Ferrari, Massachusetts Institute of Technology, Victor P. Starr Career Development 
Professorship, Massachusetts Institute of Technology. 


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