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


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.

In document 2018年馬登-朱利安振盪(Madden-Julian Oscillation)活躍期下風所引發之混合層加深 (Page 34-41)

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