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I have some questions about this paper:

Lagrangian/Hamiltonian formalism for description of Navier-Stokes fluids. R. J. Becker. Phys. Rev. Lett. 58 no. 14 (1987), pp. 1419-1422.

After reading the paper, the question arises how far can we investigate turbulence with this approach? With all the mathematical machinery available to us in solving classical field theory and QFT, will it be of any help if we start with a Lagrangian density in taming the turbulence problem?

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So I am not entirely sure what is your question. The last paragraph of the paper is given to explaining why this new(?) approach is advantageous. So far as I recall, Lagrangian approaches tend to give a great deal more latitude to description and analysis than the (often) more complicated Newtonian approaches. The typical "drawback" is that formulating the Lagrangian often requires one to "know" the answer before they start. – honeste_vivere Oct 9 '15 at 11:32

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