On the physical dimension of the turbulent sublayer at the turbulent/non-turbulent interface

Abstract

The turbulent/non-turbulent interface (TNTI) is a thin fluid layer that separates rotational and irrotational flows, playing a critical role in the multi-scale process of entrainment. This work examines the TNTI to identify a length scale matching the turbulent sublayer (TS) thickness, (Formula presented.). Since dissipation is governed by η (the Kolmogorov scale) and is facilitated by a larger scale within the inertially-driven TS, this highlights the importance of a scale matching (Formula presented.). Using a kinematic scaling analysis, (Formula presented.) is expressed in terms of appropriately chosen velocity and time scales. By matching the time scales of motion interacting at the TS edge facing the turbulent core, a characteristic mixed-length scale (Formula presented.) is obtained, such that (Formula presented.) (where λ is the Taylor scale). We show that this estimate for (Formula presented.) is quadratically related to (Formula presented.), with only a weak dependence on (Formula presented.) of (Formula presented.). Consequently, if (Formula presented.), then (Formula presented.) for (Formula presented.). More specifically, within the range of (Formula presented.) examined in practice, we find that (Formula presented.). This prediction is validated using the most extensive datasets available, covering a wide range of flow conditions ((Formula presented.)) and types, including wall-bounded, shear-free, and free-shear turbulence. Building on the existing literature, the length scale (Formula presented.) (i) describes (Formula presented.) over a distance along the TNTI corresponding to λ such that the coherent strain along the axial length of scales within the TS should scale with λ instead of η, and (ii) mediates the transition between inertial effects (due to λ) and dissipative effects (governed by η). Practically, this length scale is important for reduced-order models focussed on the TNTI dynamics. Additionally, we demonstrate that this scale falls within the resolution limits of several past TNTI experiments at high (Formula presented.), allowing TS physics to be characterized through measurable statistics in the (Formula presented.) framework.