Triple-deck theory

Triple-deck theory is a theory that describes a three-layered boundary-layer structure when disturbances are present in the boundary layer. This theory was able to successfully explain the phenomenon of boundary layer separation. James Lighthill, Lev Landau and others were the first to realize that to explain boundary layer separation, different scales other than the normal boundary-layer scales need to be introduced. These scales were first introduced by James Lighthill in 1953[1] The triple-layer structure itself was independently discovered by Keith Stewartson (1969)[2], V. Y. Neiland (1969)[3], and A. F. Messiter (1970)[4].

Suppose ${\displaystyle x}$ and ${\displaystyle y}$ are the streamwise and transverse coordinate with respect to the wall and ${\displaystyle Re}$ be the Reynolds number, the boundary layer thickness is then ${\displaystyle \delta =Re^{-1/2}}$. The boundary layer coordinate is ${\displaystyle \eta =yRe^{1/2}}$. Then the thickness of each deck is

${\displaystyle {\begin{aligned}{\text{Lower deck}}:&\quad y\sim Re^{-5/8}\\{\text{Middle deck}}:&\quad y\sim Re^{-1/2}\\{\text{Upper deck}}:&\quad y\sim Re^{-3/8}.\end{aligned}}}$

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 viscous, irrotational disturbances.

The interaction zone identified by Lighthill in the streamwise direction is

${\displaystyle {\text{Interaction zone}}:\quad x\sim Re^{-3/8}.}$

See also

• Flow separation
• Boundary layer

References

1. Lighthill, M. J. (1953). On boundary layers and upstream influence II. Supersonic flows without separation. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 217(1131), 478-507.
2. Stewartson, K. (1969). On the flow near the trailing edge of a flat plate II. Mathematika, 16(1), 106-121.
3. Neiland, V. Y. (1969). Theory of laminar boundary layer separation in supersonic flow. Fluid Dynamics, 4(4), 33-35.
4. Messiter, A. F. (1970). Boundary-layer flow near the trailing edge of a flat plate. SIAM Journal on Applied Mathematics, 18(1), 241-257.