The results of a laboratory experiment designed to study turbulent entrainment at
sheared density interfaces are described. A stratified shear layer, across which a
velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter
upper turbulent layer of depth D from a quiescent, deep lower layer which is either
homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N
(linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk
Richardson number RiB = ΔbD/ΔU2 and
the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the
entrainment process; it is observed that interfacial instabilities locally mix heavy
and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent
eddies in scouring the interface and lifting partially mixed fluid. The nature of the
instability is dependent on RiB, or a related parameter, the local gradient Richardson number
Rig = N2L/
(∂u/∂z)2,
where NL
is the local buoyancy frequency, u is the local streamwise velocity and z
is the vertical coordinate. The transition from the Kelvin–Helmholtz
(K-H) instability dominated regime to a second shear instability, namely
growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8.
The K-H activity completely subsided beyond RiB ∼ 5 or
Rig ∼ 1. The transition period
3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like
features, interacting with each other while breaking and causing intense mixing. The
flux Richardson number Rif or the mixing efficiency peaked during this transition
period, with a maximum of Rif ∼ 0.4 at
RiB ∼ 5 or Rig ∼ 1. The interface at
5 < RiB < 5.8 was dominated by ‘asymmetric’
interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at
RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and
the entrainment rate showed a large disparity (as large as 50%) between the two-layer
and the linearly stratified cases in the range 1.5 < RiB < 5.
In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to
propagate into the deep layer, in which case more energy was available for interfacial
mixing. When the lower layer was linearly stratified, the internal waves appeared to
be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of
groups or packets of K-H billows, their degeneration into turbulence and subsequent
mixing, interfacial thickening and scouring of the thickened interface by turbulent
eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone
for the two-layer case based on the parameter α, where α = (−B + ε)/P,
indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux
B and the dissipation rate ε, except in the range RiB < 5 where
K-H driven mixing was active.
How we compute N matters to estimates of mixing in stratified flows