Based on the buoy and floats measurement, the increase of wind and the acceleration
of horizontal current in the upper 40 m occur simultaneously. The stronger current may
destabilize ocean stratification via shear instability. This section will therefore explore
factors for causing the change in surface MLD.
4.1 Mixed layer depth deepening
Multiple MLD criteria are proposed, including temperature and density-based criteria
such as temperature difference near the ocean surface (Wyrtki 1964) or density gradient
criteria (Lukas and Lindstrom 1991). Here, we compute the MLD by exploring the
difference of potential density between MLD and reference depth z0 that exceed a
constant. The z0 is choose arbitrarily to exclude the unknown spikes on density gradient
caused by turbulence near the sea surface. In this study, the MLD is estimated by fulfilling
density difference larger than 0.15 kg m-3 that is Δρ = ρ(MLD) – ρ(z0) > 0.15 kg m-3
where z0 = 15 m. The z0 chosen in the study is to avoid the warm layer in the upper 10 m
to 12 m formed on the 13th, which may be associated with sudden wind precipitous fall.
The Brunt-Väisälä frequency (N2) is often used for discussing the density
stratification and express as:
N2 =−g ∂ρ ρ0∂z
N2 was estimated by temperature and salinity measurements of four floats. High N2
from 25 m to 50 m was consistent with the change of MLD in the concerning period (Fig.
9). During the MJO active phase from 14th to 17th Dec 2018, the MLD was deepened
rapidly from 25 m to 50 m in five consecutive days which was captured by the four floats
simultaneously. Strong vertical turbulent mixing might cause the rapid decline of MLD,
thereby the upper ocean cooling. According to the negative N2 ubiquitous above MLD,
i.e., the inversion of seawater density, the upper ocean was under the unstable conditions.
The major forcing for the instability will be discussed in the next part.
Fig. 9: (a)–(d) Surface MLD (magenta lines) and buoyancy frequency N2 (shading)
derived from two ALAMO floats and two EM-APEX floats measurements AL9207,
AL9209, EM8487, and EM8488, respectively. The negative values of N2 are expressed
with pink dots. The missing data are expressed with gray dots.
4.2 Gradient Richardson number
The study discusses the stability within the stratified shear flow by computing the
gradient Richardson number (Ri), which also aims to find where the probable turbulent
mixing happened. It is defined as
Ri = 𝑁2 𝑆2 =
−g ∂ρ ρ0∂z (𝜕𝑈
𝜕𝑧)2+ (𝜕𝑉
𝜕𝑧)2
where N2 is buoyancy frequency, g is the gravity acceleration, ρ is the situ density, ρ0 is
the reference density, S is the vertical shear term, U is eastward components, V is
eastward component of current, and z is the vertical coordinate. Ri is the proportion of
stratified layer and shear flow. If the shear flow supplies sufficient kinetic energy,
turbulence can overcome the stratified barrier, and mixing occurs. Miles (1961) and
Howard (1961) demonstrated that Ri, of 0.25, is a linear stability threshold. Weak
stratified or strong shear within the stratified shear flow can result in Ri < 0.25 and
generate shear instability. The enhanced shear production term in the TKE budget will
favor the growth of turbulence and thereby turbulent mixing. Contrastingly, when Ri >
0.25 everywhere in the fluid, flows are stable.
Ri was computed by EM8487 and EM8488 velocity and density measurements (Fig.
10). When the MJO convective arrived, Ri less than 0.25 occurred frequently above the
MLD on EM8487 and EM8488. Within the MLD, the horizontal current was accelerated
by stronger wind MJO brought, making the shear term in Ri large enough to reach the
threshold of 0.25. Namely, due to the stronger current and night time surface cooling,
instability occurred above the MLD. The instability might contribute to the density
inversion in the ML, and the deepening of MLD should result from the corresponding
turbulent mixing.
Fig. 10: (a) and (d) are the buoyancy stratification N2 (shading) derived from EM8487
and EM8488. The negative values of N2 are expressed with pink dots. (b) and (e) are
vertical sheer square of EM8487 and EM8488 (c) and (f) are (1/Ri) – 4 and surface MLD
(black lines) of EM8487 and EM8488. The missing data are expressed with gray dots.
4.3 Thorpe scale method and dispassion rate
Based on the observed N2 and small Ri at the floats, strong turbulent mixing occurred
and related to the passage of MJO’s deep convection. Here, we will estimate the turbulent
kinetic energy (TKE) dissipation rate to quantify the magnitude of turbulent mixing.
Thorpe (1977) assumes the kinetic energy of turbulent eddy transfers to potential energy,
resulting in the displacement of a fluid particle. Explaining more, the density
measurements profile is reordered to a gravitationally stable profile in which density
increase with depth. The fluid particles' vertical distance must be moved adiabatically in
this process, and the density displacement is Thorpe displacement. The Thorpe scale is
computed by using the root mean square of Thorpe displacement. The turbulent
dissipation rate is estimated by Thorpe scale (Fig. 11), using EM8487 and EM8488
density profiles. The estimation of turbulent dissipation rate is approximately between
10-8 to 10-6 W kg-1 above the MLD during the MJO active phase. The number is more
significant than the estimated value of low wind conditions in the area, which was about
10-11 to 10-10 W kg-1 within the thermocline.
When current shear is strong enough or stratification is weak enough, the Ri will
decrease to reach the threshold of < 0.25. It will result in Kelvin-Helmholtz instability.
Because of the westerly wind (Section 3), the vertical shear of horizontal current could
be 3 × 10-4 s-2. Despite strong stratification within the thermocline, Ri lowered by the
strong vertical shear was typically below 0.25 in the upper ocean. The shear instability
associated with the low Ri might enhance turbulence kinetic energy, which would
ultimately become potential energy or heat. The momentum from wind stress contributed
to current shear that countered the stabilizing effect of density stratification, thereby
generating the shear instability. To sum up, the change of MLD during our experiments
was forced by the momentum transition from wind to current flow. The entrainment of
cold water might then cool the SST.
Fig. 11: (a) and (b) are TKE dispassion rate and MLD (black lines) estimated by Thorpe
scale method. The value below 10-11 are denoted with gray dots. (c) and (d) are (1/Ri) –
4 and surface MLD (black lines).
4.4 Summary of mixed layer depth deepening
When the MJO convection event arrived, the wind accelerated the horizontal current
to around 0.4 m s-1. The enhanced vertical shear due to the significant current velocity
will decrease Ri to less than 0.25 in the ML. In other words, the enhanced vertical shear
should be the major factor causing the deepening of ML by inducing the shear instability.
Thorpe scale method was used to estimate the turbulent dissipation rate during this
turbulent mixing event. The estimated turbulent dissipation rate within the MLD was
about 10-8 to 10-6 W kg-1, more significant than that within the typical thermocline of
about 10-10 to 10-9 W kg-1. Strong turbulent mixing might be the major factor leading to
the MLD deepening from 25 m to 50 m via the shear instability in this event.