Triple-deck theory is a theory that describes a three-layered boundary-layer structure when sufficiently large disturbances are present in the boundary layer. This theory is able to successfully explain the phenomenon of

boundary layer separation In fluid dynamics, flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake. A boundary layer exists whenever there is relative movement between a fluid and a solid surface with viscous f ...

, but it has found applications in many other flow setups as well, including the scaling of the lower-branch instability ( T-S) of the Blasius flow, boundary layers in swirling flows, etc.

James Lighthill Sir Michael James Lighthill (23 January 1924 – 17 July 1998) was a British applied mathematician, known for his pioneering work in the field of aeroacoustics and for writing the Lighthill report on artificial intelligence. Biography J ...

Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His a ...

and others were the first to realize that to explain boundary layer separation, different scales other than the classical boundary-layer scales need to be introduced. These scales were first introduced independently by

and E. A. Müller in 1953. The triple-layer structure itself was independently discovered by

Keith Stewartson Keith Stewartson (20 September 1925 – 7 May 1983) was an English mathematician and fellow of the Royal Society. Early life The youngest of three children, Stewartson was born to an English baker in 1925. He was raised in Billingham, County Dur ...

(1969) and V. Y. Neiland (1969) and by A. F. Messiter (1970). Stewartson and Messiter considered considered the separated flow near the trailing edge of a flat plate, whereas Neiland studied the case of a shock impinging on a boundary layer. Suppose

x

and

y

are the streamwise and transverse coordinate with respect to the wall and

Re

be the

Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...

, the boundary layer thickness is then

\delta=Re^

. The boundary layer coordinate is

\eta=y Re^

. Then the thickness of each deck is

\begin
\text: &\quad y \sim Re^\\
\text: &\quad y \sim Re^\\
\text: &\quad y \sim Re^.
\end

The lower deck is characterized by viscous, rotational disturbances, whereas the middle deck (same thickness as the boundary-layer thickness) is characterized by inviscid, rotational disturbances. The upper deck, which extends into the potential flow region, is characterized by inviscid, irrotational disturbances. The interaction zone identified by Lighthill in the streamwise direction is

\text: \quad x \sim Re^.

The most important aspect of the triple-deck formulation is that pressure is not prescribed, and so it has to be solved as part of the boundary-layer problem. This coupling between velocity and pressure reintroduces ellipticity to the problem, which is in contrast to the parabolic nature of the classical boundary layer of

Prandtl Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of ...

References

{{reflist, 30em Fluid dynamics

See also

References