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By J. C. Burkill

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They are Rds) = f dXI l1 (X - X1)IdX - X 2 x RD(S) = f dx' f I~2C'To(X - Mx' = f + M), dXII1(X-XJldX-X2 +s) xlolI~2{Cllg(x', t f dxlo1CTo(X - Mx) + s), dXI I1 (X-X 1)IdX - X 2 +s) x IOII~2llg(x, t)llg(x', t RF(S) + s) (A-4) ff dxdx'To(X-Mx)To(X-Mx' +s) . (A-5) ff dxdx'to(X-Mx)TO(X-Mx' +s) + M) + C'llg(x, tn. (A-6) The conditional average for each component of R can be determined by using the equation for

11. Lourenco, L. M. , The role of photographic parameters in laser speckle or particle image displacement velocimetry. Experiments in Fluids 5 (1987) 29-32. 12. , Simpkins, P. G. and Dudderar, T. , Speckle measurements of convection in a liquid cooled from above. J. Fluid Mech 182 (1987) 235-254. 13. Prasad, A. , Adrian, R. , Landreth, C. C. and Offutt, P. , Effect of resolution on the speed and accuracy of particle image velocimetry interrogation. Experiments in Fluids 13 (1992) 105-116. 14. , Blackwelder, R.

4 s. In the present experiments this bias is only significant in the very early stages of the decay process and will not affect the discussion in the following sections. (J u 4. Nonrotating turbulence We shall consider first the nonrotating (f = 0) limit as the behaviour of this well known flow will show any major problems with our experimental apparatus or measurement method. There are a wide range of methods of characterising such a flow. For the present we will confine our attention to relatively simple velocity statistics.

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