Electromagnetically controlled multi-scale flows

Abstract

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 multiscale flows are laboratory simulations of quasi-two-dimensional turbulent-like flows, and they have a power-law energy spectrum E(k) ∼ k −p over a range 2π/L < k < 2π/η 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 η 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 ≈ 0.5 is the fractal dimension of the set of stagnation points and p ≈ 2.5. The two exponents D s and p are controlled by the multi-scale electromagnetic forcing over the entire range of scales between L and η for a broad range of Reynolds numbers with separate control over L/η 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 ∆ 2 has an approximate power law behaviour ∼t γ with 'Richardson exponent' γ ≈ 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.

Multiscale Laminar Flows with Turbulentlike Properties

“…[6] showed that the number density n s of stagnation points is a power-law function of the outer to inner length-scale ratio L/η, n s = C s L −d (L/η) Ds where the fractal dimension D s is such that p + 2D s /d = 3 and d=2, 3 for 2D, 3D turbulence. [13] generated a Q2D multi-scale laminar flow with an imposed multi-scale spatial distribution of stagnation points and corroborated that such a flow has a powerlaw energy spectrum in agreement with p + D s = 3. The same rig and family of flows (p ≈ 2.5) are used here.…”

“…This leads to a measurement grid containing 287x287 velocity vectors. For full details on the rig and experiments, see [13] who also show that the flow at the free surface of the brine is Q2D.…”

“…identify most stagnation points and follow their paths whilst measuring their length-scales and following fluid element pairs at the same time), we propose to test this new theory in bespoke multi-scale flows with electromagnetically imposed turbulent-like multi-scale stagnation point topology following the recent work of [13]. An important first case of such bespoke multi-scale flow design is the case of the steady quasi-two-dimensional (Q2D) laminar flow.…”

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

“…Different generic setups, including 2-and 3-magnet configurations with different orientations with respect to the imposed electric DC currents, were analysed. In contrast to the previously mentioned studies, of Honji et al [16] and Rossi et al [40,41], Verdoold et al [45] applied electric currents that were sufficiently strong (up to I = 10 A) to locally create transient and turbulent flow regimes. Experimental studies were based on dye visualisations similar to that presented in Honji et al [16], but without velocity measurements.…”

“…Rossi et al [40,41] addressed electromagnetically driven steady quasi-two-dimensional laminar flows with multi-scale point topology. The authors introduced an interesting concept of imposed electromagnetic forcing originating from the fractal-structure based geometry of the permanent magnets with opposite polarities.…”