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TNTI (

TNTI

Continuous layer

Bisset et al. 2002

Westerweel et al. 2005

Laminar superlayer

Corrsin & Kistler 1955

Maximum in vorticity

Taylor scale thickness

Influenced by the flow region within one one integral scale from the TNTI

Entrainment

Entrainment velocity (towards the TNTI): \( E_v \)
Defined in a Galilean referance frame

Flow dependent

Hunt et al.

Turner et al. 1986

Magnitude of the order of rms of turbulence

Direction

Conversion of irrotational into rotational flow

Viscous process

Shear free TNTI
\( \frac{\partial U_1}{ \partial x_2}=0 \); \( \frac{\partial U_3}{\partial x_2}=0\);
\(x_2 \) direction normal to the TNTI

Matching conditions at the TNTI:
\( \mathbf{u_n} \) and \( p \) are continuous

\( \nabla \phi_{x_2 \rightarrow \infty } \rightarrow 0 \)

\( \mathbf{u_n} \) decreases close to the TNTI

\( \mathbf{u_\tau} \) increase close to the TNTI, then discontinuously decrease by \( \mathbf{u}^{(H)^2}\)

Bisset et al. 2002

Non-turbulen region

Large irrotational scales

Hussain & Clark 1981

Follow a \( \langle u^2 \rangle \sim \frac{x_2 - y_i}{L_{11}}^{-4} \) law from the TNTI

Phillips 1955

Teixeira & Silva 2012

\( \mathbf{u} = \nabla \phi \)

\( \nabla^2 \phi = 0\)

.

As flow evolves the TNTI moves outwards
(normal into irrotational flow)

Interface velocity:
\( E_b = \frac{d \langle y_i \rangle}{dt} \)

Nibbling: partially viscous process, caused by irregular small scale motions near the TNTI

Along the full interface

Viscous diffusion

Engulfing: inviscid ingestion of external fluid

Local

Large scale fluctuations of the interface with negative curvature

How to quantify?

Mathew & Basu 2002

Westerweel et al. 2005

Dahm & Dimotakis 1987

Ferré et al. 1990

Mungal et al. 1991

Dimotakis 2000

How to objectively discriminate?

Turbulrent region

\( \mathbf{u} = \mathbf{u}^{(H)} + \nabla \phi \)
\( \mathbf{u}^{(H)} = \) homogeneous isotropic field

Elongated microscale vortices

da Silva et al. 2011

Move at at the characterisc microscale speed relative to the large scales

Holzner et al. 2011

Don't control directly the large scales

Hunt et al. 2011

Impinging eddies

Large staining of small-scale motions

Keeps interfacial layer thin