Electromagnetically controlled multi-scale flows

摘要

We generate a class of multi-scale quasi-steady laminar flows in the laboratory by controlling a quasi-two-dimensional shallow-layer brine flow by multi-scale Lorentz body forcing.-The flows' multi-scale topology is invariant over a broad range of Reynolds numbers, Re-2D from 600 to 9900. The key multi-scale aspects of this flow associated with its multi-scale hyperbolic stagnation-point structure are highlighted. Our multi-scale flows are laboratory simulations of quasi-two-dimensional turbulent-like flows, and they have a power-law energy spectrum E(k) similar to k(-p) over a range 2 pi/L < k < 2 pi/eta where p lies between the values 5/3 and 3 which are obtained in a two-dimensional turbulence that is forced at the small scale 71 or at the large scale L, respectively. In fact, in the present set-up, p + D-s = 3 in agreement with a previously established formula; D-s approximate to 0.5 is the fractal dimension of the set of stagnation points and p approximate to 2.5. The two exponents Ds and p are controlled by the multi-scale electromagnetic forcing over the entire range of scales between L and eta for a broad range of Reynolds numbers with separate control over L/eta and Reynolds number. The pair dispersion properties of our multi-scale laminar flows are also controlled by their multi-scale hyperbolic stagnation-point topology which generates a sequence of exponential separation processes starting from the smaller-scale hyperbolic points and ending with the larger ones. The average mean square separation (Delta(2)) over bar has an approximate power law behaviour similar to t(gamma) with 'Richardson exponent' gamma approximate to 2.45 in the range of time scales controlled by the hyperbolic stagnation-points. This exponent is itself controlled by the multi-scale quasi-steady hyperbolic stagnation-point topology of the flow.