TNTI

Continuous layer

Non-turbulen region

Large irrotational scales

Follow a ⟨u2⟩∼x2−yiL11−4 law from the TNTI

Laminar superlayer

Maximum in vorticity

Taylor scale thickness

Elongated microscale vortices

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

Don't control directly the large scales

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

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

Entrainment

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

Flow dependent

Magnitude of the order of rms of turbulence

Direction

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

Engulfing: inviscid ingestion of external fluid

Conversion of irrotational into rotational flow

Local

Large scale fluctuations of the interface with negative curvature

Along the full interface

Viscous diffusion

How to quantify?

How to objectively discriminate?

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

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

Viscous process

Turbulrent region

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

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

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

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 \( \mathbf{u}^{(H)^2}\)

Impinging eddies

Large staining of small-scale motions

Keeps interfacial layer thin