Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

2008 ◽  
Vol 38 (6) ◽  
pp. 1145-1165 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari ◽  
Robert Hallberg
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Climate Impacts ◽  
Surface Mixed Layer ◽  
Rotation Rates ◽  
Wide Range ◽  
Horizontal Density Gradient ◽  
Mixed Layers

Abstract Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

scholarly journals The Scale of Submesoscale Baroclinic Instability Globally

2020 ◽  
Vol 50 (9) ◽  
pp. 2649-2667 ◽  
Author(s):  
Jihai Dong ◽  
Baylor Fox-Kemper ◽  
Hong Zhang ◽  
Changming Dong
Keyword(s):  
Mixed Layer ◽  
Spatial Scales ◽  
Baroclinic Instability ◽  
Ocean Model ◽  
Median Surface ◽  
Surface Mixed Layer ◽  
Vertical Resolution ◽  
High Vertical Resolution ◽  
Mixed Layers ◽  
Strong Seasonality

AbstractThe spatial scale of submesoscales is an important parameter for studies of submesoscale dynamics and multiscale interactions. The horizontal spatial scales of baroclinic, geostrophic-branch mixed layer instabilities (MLI) are investigated globally (without the equatorial or Arctic oceans) based on observations and simulations in the surface and bottom mixed layers away from significant topography. Three high-vertical-resolution boundary layer schemes driven with profiles from a MITgcm global submesoscale-permitting model improve robustness. The fastest-growing MLI wavelength decreases toward the poles. The zonal median surface MLI wavelength is 51–2.9 km when estimated from the observations and from 32, 25, and 27 km to 2.5, 1.2, and 1.1 km under the K-profile parameterization (KPP), Mellor–Yamada (MY), and κ–ε schemes, respectively. The surface MLI wavelength has a strong seasonality with a median value 1.6 times smaller in summer (10 km) than winter (16 km) globally from the observations. The median bottom MLI wavelengths estimated from simulations are 2.1, 1.4, and 0.41 km globally under the KPP, MY, and κ–ε schemes, respectively, with little seasonality. The estimated required ocean model grid spacings to resolve wintertime surface mixed layer eddies are 1.9 km (50% of regions resolved) and 0.92 km (90%) globally. To resolve summertime eddies or MLI seasonality requires grids finer than 1.3 km (50%) and 0.55 km (90%). To resolve bottom mixed layer eddies, grids finer than 257, 178, and 51 m (50%) and 107, 87, and 17 m (90%) are estimated under the KPP, MY, and κ–ε schemes.

On the scaling of stress-driven entrainment experiments

1979 ◽  
Vol 90 (3) ◽  
pp. 509-529 ◽  
Author(s):  
James F. Price
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Side Wall ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Entrainment Rate ◽  
Surface Mixed Layer ◽  
Mean Velocity ◽  
Wide Range ◽  
Conservation Of Momentum

The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is \[ V^{-1} dh/dt = E(R_v), \] where h is the mixed-layer depth, V is the mean velocity of the mixed layer, Rv = B/V2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(Rv) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < Rv < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4R−4v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the wind-driven ocean surface mixed layer (Price, Mooers & Van Leer 1978).The analysis shows that, when forcing is steady, Rv is quasi-steady and, provided that side-wall drag is not large, Rv ≃ 0·6 over a wide range of RT = B/U2*, where U* is the friction velocity of the imposed stress. In the absence of side-wall drag (vanishing h/L) the conservation of momentum then leads to U−1*dh/dt = n(0·6)½R−½T, where n = ½ or 1 if the interior is linearly stratified or homogeneous. The KP, KPA data show this dependence throughout the range 17 < RT < 160 where the effect of side-wall drag is negligible or can be removed by a linear extrapolation. This result, together with the form and magnitude of the observed side-wall effect, suggests that mean momentum conservation is a key constraint upon the entrainment rate in the KP, KPA experiments.

Parameterization of Mixed Layer Eddies. Part II: Prognosis and Impact

2008 ◽  
Vol 38 (6) ◽  
pp. 1166-1179 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Layer Depth ◽  
Mode Water ◽  
Ocean Fronts ◽  
Rotation Rates ◽  
Vertical Fluxes ◽  
Wide Range ◽  
Ocean Atmosphere Interaction ◽  
Critical Regions

Abstract The authors propose a parameterization for restratification by mixed layer eddies that develop from baroclinic instabilities of ocean fronts. The parameterization is cast as an overturning streamfunction that is proportional to the product of horizontal buoyancy gradient, mixed layer depth, and inertial period. The parameterization has remarkable skill for an extremely wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. In this paper a coarse resolution prognostic model of the parameterization is compared with submesoscale mixed layer eddy resolving simulations. The parameterization proves accurate in predicting changes to the buoyancy. The climate implications of the proposed parameterization are estimated by applying the restratification scaling to observations: the mixed layer depth is estimated from climatology, and the buoyancy gradients are from satellite altimetry. The vertical fluxes are comparable to monthly mean air–sea fluxes in large areas of the ocean and suggest that restratification by mixed layer eddies is a leading order process in the upper ocean. Critical regions for ocean–atmosphere interaction, such as deep, intermediate, and mode water formation sites, are particularly affected.

scholarly journals Observations of the Transition Layer

2009 ◽  
Vol 39 (3) ◽  
pp. 780-797 ◽  
Author(s):  
T. M. Shaun Johnston ◽  
Daniel L. Rudnick
Keyword(s):  
Layer Thickness ◽  
Mixed Layer ◽  
Potential Vorticity ◽  
Transition Layer ◽  
Mixed Layer Depth ◽  
Density Ratio ◽  
Horizontal Resolution ◽  
Surface Mixed Layer ◽  
Layer Depth ◽  
Vertical Displacements

Abstract The transition layer is the poorly understood interface between the stratified, weakly turbulent interior and the strongly turbulent surface mixed layer. The transition layer displays elevated thermohaline variance compared to the interior and maxima in current shear, vertical stratification, and potential vorticity. A database of 91 916 km or 25 426 vertical profiles of temperature and salinity from SeaSoar, a towed vehicle, is used to define the transition layer thickness. Acoustic Doppler current measurements are also used, when available. Statistics of the transition layer thickness are compared for 232 straight SeaSoar sections, which range in length from 65 to 1129 km with typical horizontal resolution of ∼4 km and vertical resolution of 8 m. Transition layer thicknesses are calculated in three groups from 1) vertical displacements of the mixed layer base and of interior isopycnals into the mixed layer; 2) the depths below the mixed layer depth of peaks in shear, stratification, and potential vorticity and their widths; and 3) the depths below or above the mixed layer depth of extrema in thermohaline variance, density ratio, and isopycnal slope. From each SeaSoar section, the authors compile either a single value or a median value for each of the above measures. Each definition yields a median transition layer thickness from 8 to 24 m below the mixed layer depth. The only exception is the median depth of the maximum isopycnal slope, which is 37 m above the mixed layer base, but its mode is 15–25 m above the mixed layer base. Although the depths of the stratification, shear, and potential vorticity peaks below the mixed layer are not correlated with the mixed layer depth, the widths of the shear and potential vorticity peaks are. Transition layer thicknesses from displacements and the full width at half maximum of the shear and potential vorticity peak give transition layer thicknesses from 0.11× to 0.22× the mean depth of the mixed layer. From individual profiles, the depth of the shear peak below the stratification peak has a median value of 6 m, which shows that momentum fluxes penetrate farther than buoyancy fluxes. A typical horizontal scale of 5–10 km for the transition layer comes from the product of the isopycnal slope and a transition layer thickness suggesting the importance of submesoscale processes in forming the transition layer. Two possible parameterizations for transition layer thickness are 1) a constant of 11–24 m below the mixed layer depth as found for the shear, stratification, potential vorticity, and thermohaline variance maxima and the density ratio extrema; and 2) a linear function of mixed layer depth as found for isopycnal displacements and the widths of the shear and potential vorticity peaks.

Spiciness Anomalies of Subantarctic Mode Water in the South Indian Ocean

2021 ◽  
Vol 34 (10) ◽  
pp. 3927-3953
Author(s):  
Motoki Nagura
Keyword(s):  
Indian Ocean ◽  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Surface Mixed Layer ◽  
The South ◽  
South Indian Ocean ◽  
Mode Water ◽  
Horizontal Advection ◽  
South Indian ◽  
Subantarctic Mode Water

AbstractThis study investigates spreading and generation of spiciness anomalies of the Subantarctic Mode Water (SAMW) located on 26.6 to 26.8 σθ in the south Indian Ocean, using in situ hydrographic observations, satellite measurements, reanalysis datasets, and numerical model output. The amplitude of spiciness anomalies is about 0.03 psu or 0.13°C and tends to be large along the streamline of the subtropical gyre, whose upstream end is the outcrop region south of Australia. The speed of spreading is comparable to that of the mean current, and it takes about a decade for a spiciness anomaly in the outcrop region to spread into the interior up to Madagascar. In the outcrop region, interannual variability in mixed layer temperature and salinity tends to be density compensating, which indicates that Eulerian temperature or salinity changes account for the generation of isopycnal spiciness anomalies. It is known that wintertime temperature and salinity in the surface mixed layer determine the temperature and salinity relationship of a subducted water mass. Considering this, the mixed layer heat budget in the outcrop region is estimated based on the concept of effective mixed layer depth, the result of which shows the primary contribution from horizontal advection. The contributions from Ekman and geostrophic currents are comparable. Ekman flow advection is caused by zonal wind stress anomalies and the resulting meridional Ekman current anomalies, as is pointed out by a previous study. Geostrophic velocity is decomposed into large-scale and mesoscale variability, both of which significantly contribute to horizontal advection.

Variability of the Oceanic Mixed Layer, 1960–2004

2008 ◽  
Vol 21 (5) ◽  
pp. 1029-1047 ◽  
Author(s):  
James A. Carton ◽  
Semyon A. Grodsky ◽  
Hailong Liu
Keyword(s):  
Mixed Layer ◽  
North Atlantic ◽  
Southern Oscillation ◽  
Mixed Layer Depth ◽  
Global Ocean ◽  
Boreal Summer ◽  
Layer Depth ◽  
The North ◽  
The North Atlantic ◽  
Mixed Layers

Abstract A new monthly uniformly gridded analysis of mixed layer properties based on the World Ocean Atlas 2005 global ocean dataset is used to examine interannual and longer changes in mixed layer properties during the 45-yr period 1960–2004. The analysis reveals substantial variability in the winter–spring depth of the mixed layer in the subtropics and midlatitudes. In the North Pacific an empirical orthogonal function analysis shows a pattern of mixed layer depth variability peaking in the central subtropics. This pattern occurs coincident with intensification of local surface winds and may be responsible for the SST changes associated with the Pacific decadal oscillation. Years with deep winter–spring mixed layers coincide with years in which winter–spring SST is low. In the North Atlantic a pattern of winter–spring mixed layer depth variability occurs that is not so obviously connected to local changes in winds or SST, suggesting that other processes such as advection are more important. Interestingly, at decadal periods the winter–spring mixed layers of both basins show trends, deepening by 10–40 m over the 45-yr period of this analysis. The long-term mixed layer deepening is even stronger (50–100 m) in the North Atlantic subpolar gyre. At tropical latitudes the boreal winter mixed layer varies in phase with the Southern Oscillation index, deepening in the eastern Pacific and shallowing in the western Pacific and eastern Indian Oceans during El Niños. In boreal summer the mixed layer in the Arabian Sea region of the western Indian Ocean varies in response to changes in the strength of the southwest monsoon.

Statistical features of the Oceanographic area off south-western Australia, obtained from Bathythermograph data

1986 ◽  
Vol 37 (4) ◽  
pp. 421 ◽  
Author(s):  
LJ Hamilton
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Sea Surface ◽  
Temperature Fields ◽  
Surface Mixed Layer ◽  
Statistical Features ◽  
Layer Depth ◽  
Leeuwin Current ◽  
South West

A statistical analysis has been made of 26 years of bathythermograph (BT) data to 1980 for the south-west Australian area bounded by 30-35�s. and 110-115�E., a region influenced by the Leeuwin Current. The data indicate that a surface mixed layer exists all year round, with average depth 55 m and standard deviation 37 m. All but 2% of BT casts show a mixed-layer depth (MLD) less than 150 m. MLD are deepest in mid-year, particularly from July to September. Sea surface temperatures (SST) are significantly related to temperature values down to 200 m depth, especially in mid-year, for both eastern and western parts of the area separated by 113�E. Correlations of MLD with SST are significant only in the western part, and then only from January to March, and April to June. Long-term horizontally averaged temperature fields are broadly related through the water column from the surface to 200 m. All results indicate that, especially in mid-year, SST fields are related to subsurface temperature fields, which may be representative of flow structure. Seasonal differences exist between the eastern and western areas, caused by the Leeuwin Current.

scholarly journals Scaling Surface Mixing/Mixed Layer Depth under Stabilizing Buoyancy Flux

2015 ◽  
Vol 45 (1) ◽  
pp. 247-258 ◽  
Author(s):  
Yutaka Yoshikawa
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Mixing Layer ◽  
Buoyancy Flux ◽  
Earth’S Rotation ◽  
Surface Mixed Layer ◽  
Threshold Method ◽  
Layer Depth ◽  
Earth's Rotation ◽  
Surface Buoyancy

AbstractThis study concerns the combined effects of Earth’s rotation and stabilizing surface buoyancy flux upon the wind-induced turbulent mixing in the surface layer. Two different length scales, the Garwood scale and Zilitinkevich scale, have been proposed for the stabilized mixing layer depth under Earth’s rotation. Here, this study analyzes observed mixed layer depth plus surface momentum and buoyancy fluxes obtained from Argo floats and satellites, finding that the Zilitinkevich scale is more suited for observed mixed layer depths than the Garwood scale. Large-eddy simulations (LESs) reproduce this observed feature, except under a weak stabilizing flux where the mixed layer depth could not be identified with the buoyancy threshold method (because of insufficient buoyancy difference across the mixed layer base). LESs, however, show that the mixed layer depth if defined with buoyancy ratio relative to its surface value follows the Zilitinkevich scale even under such a weak stabilizing flux. LESs also show that the mixing layer depth is in good agreement with the Zilitinkevich scale. These findings will contribute to better understanding of the response of stabilized mixing/mixed layer depth to surface forcings and hence better estimation/prediction of several processes related to stabilized mixing/mixed layer depth such as air–sea interaction, subduction of surface mixed layer water, and spring blooming of phytoplankton biomass.

scholarly journals Numerical simulations of the competition between wind-driven mixing and surface heating in triggering spring phytoplankton blooms

2015 ◽  
Vol 72 (6) ◽  
pp. 1926-1941 ◽  
Author(s):  
Rica Mae Enriquez ◽  
John R. Taylor
Keyword(s):  
Heat Flux ◽  
Critical Heat Flux ◽  
Mixed Layer ◽  
Turbulent Mixing ◽  
Phytoplankton Bloom ◽  
Mixed Layer Depth ◽  
Phytoplankton Growth ◽  
Surface Heating ◽  
Surface Mixed Layer ◽  
Critical Depth

Abstract About 60 years ago, Sverdrup formalized the critical depth hypothesis to explain the timing of the spring phytoplankton bloom in terms of the depth of the surface mixed layer. In recent years, a number of refinements and alternatives to the critical depth hypothesis have been proposed, including the critical turbulence hypothesis which states that a bloom can occur when turbulent mixing is sufficiently weak, irrespective of the mixed layer depth. Here, we examine the relative influence of wind-driven mixing and net surface heating on phytoplankton growth. Of particular interest is whether wind-driven mixing can delay the spring bloom after winter convection gives way to net surface warming. We address these questions using high-resolution large-eddy simulations (LES) coupled with a simple phytoplankton model. We also describe an analytical phytoplankton model with a formulation for the turbulent mixing based on the LES results. For a constant, prescribed surface heat flux, net phytoplankton growth is seen when the windstress is smaller than a critical value. Similarly, for a constant windstress, a critical heat flux separates cases with growing and decaying phytoplankton populations. Using the LES results, we characterize the critical windstress and critical heat flux in terms of other physical and biological parameters and propose a simple expression for each based on the analysis of the analytical model. Phytoplankton growth begins when the mixing depth shoals above the critical depth, consistent with the critical depth hypothesis. Our results provide a framework to interpret blooms in other conditions where both the depth and the intensity of turbulent mixing might be crucial factors in influencing phytoplankton growth.

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