This paper describes a method for measuring distributions of turbulent diffusivity in less than an hour. The measurement is rapid enough to aid in designing devices that make use of the turbulent diffusion of mass, heat, or momentum. It may be useful as a measurement of the degree of turbulence in the blood of patients with cardiovascular diseases. It consists of subtracting the natural logarithms of the pixel values of a magnetic-resonance image of turbulent fluid from those of stationary fluid. The pixel values of the resulting image are multiplied by a constant to yield diffusivities. The accuracy of the measurement is within the range of diffusivities (1) upstream as far as the speed of the fluid multiplied by the time $T_E$ between exciting the spin system and recording the signal, (2) in the direction of the gradient of diffusivity as far as $T_E$ multiplied by 5 times the gradient of the diffusivity, and (3) in the direction of the phase-encoding magnetic field gradient as far as the negative of the component of velocity in the phase-encoding direction multiplied by the time between phase encoding and recording the signal. In a 32×32-${\mathrm{cm}}^2$ image of a jet of water with a nozzle velocity of 4.5 m ${\mathrm{s}}^{\mathrm{-}1}$ and Reynolds number of 18 000, made with a $T_E$ of 15 ms, the distance of (1) ranged from 0 to 6.7 cm, of (2) ranged from 0 to 0.3 cm, and of (3) ranged from 0 to 0.4 cm. These distances are bounds; the actual spatial misregistration was less. The signal-to-noise ratio ranged from 10 to 15 for diffusivities from 0.02 to 0.7 ${\mathrm{cm}}^2$ ${\mathrm{s}}^{\mathrm{-}1}$. .AE

• Received 17 April 1989

DOI:https://doi.org/10.1103/PhysRevA.40.4542