scholarly journals Baroclinic Instability with a Simple Model for Vertical Mixing

2019 ◽  
Vol 49 (12) ◽  
pp. 3273-3300 ◽  
Author(s):  
Matthew N. Crowe ◽  
John R. Taylor
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Simple Model ◽  
Numerical Simulations ◽  
Mixed Layer ◽  
Numerical Models ◽  
Baroclinic Instability ◽  
Vertical Mixing ◽  
Small Scale ◽  
Surface Mixed Layer

AbstractHere, we examine baroclinic instability in the presence of vertical mixing in an idealized setting. Specifically, we use a simple model for vertical mixing of momentum and buoyancy and expand the buoyancy and vorticity in a series for small Rossby numbers. A flow in subinertial mixed layer (SML) balance (see the study by Young in 1994) exhibits a normal mode linear instability, which is studied here using linear stability analysis and numerical simulations. The most unstable modes grow by converting potential energy associated with the basic state into kinetic energy of the growing perturbations. However, unlike the inviscid Eady problem, the dominant energy balance is between the buoyancy flux and the energy dissipated by vertical mixing. Vertical mixing reduces the growth rate and changes the orientation of the most unstable modes with respect to the front. By comparing with numerical simulations, we find that the predicted scale of the most unstable mode matches the simulations for small Rossby numbers while the growth rate and orientation agree for a broader range of parameters. A stability analysis of a basic state in SML balance using the inviscid QG equations shows that the angle of the unstable modes is controlled by the orientation of the SML flow, while stratification associated with an advection/diffusion balance controls the size of growing perturbations for small Ekman numbers and/or large Rossby numbers. These results imply that baroclinic instability can be inhibited by small-scale turbulence when the Ekman number is sufficiently large and might explain the lack of submesoscale eddies in observations and numerical models of the ocean surface mixed layer during summer.

scholarly journals Baroclinic Instability in the Presence of Convection

2018 ◽  
Vol 48 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Jörn Callies ◽  
Raffaele Ferrari
Keyword(s):  
Numerical Simulations ◽  
Mixed Layer ◽  
Baroclinic Instability ◽  
Relative Strength ◽  
Small Scale ◽  
Upper Ocean ◽  
Bulk Properties ◽  
Scale Turbulence ◽  
Balanced Dynamics ◽  
Mixed Layers

AbstractBaroclinic mixed-layer instabilities have recently been recognized as an important source of submesoscale energy in deep winter mixed layers. While the focus has so far been on the balanced dynamics of these instabilities, they occur in and depend on an environment shaped by atmospherically forced small-scale turbulence. In this study, idealized numerical simulations are presented that allow the development of both baroclinic instability and convective small-scale turbulence, with simple control over the relative strength. If the convection is only weakly forced, baroclinic instability restratifies the layer and shuts off convection, as expected. With increased forcing, however, it is found that baroclinic instabilities are remarkably resilient to the presence of convection. Even if the instability is too weak to restratify the layer and shut off convection, the instability still grows in the convecting environment and generates baroclinic eddies and fronts. This suggests that despite the vigorous atmospherically forced small-scale turbulence in winter mixed layers, baroclinic instabilities can persistently grow, generate balanced submesoscale turbulence, and modify the bulk properties of the upper ocean.

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 Quasigeostrophic Diagnosis of Mixed Layer Dynamics Embedded in a Mesoscale Turbulent Field

2016 ◽  
Vol 46 (1) ◽  
pp. 275-287 ◽  
Author(s):  
Cédric P. Chavanne ◽  
Patrice Klein
Keyword(s):  
Surface Layer ◽  
High Resolution ◽  
Mixed Layer ◽  
Finite Thickness ◽  
Vertical Mixing ◽  
Three Dimensional ◽  
Upper Ocean ◽  
Surface Mixed Layer ◽  
Deep Interior ◽  
Quasigeostrophic Model

AbstractA quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation.

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.

scholarly journals The stratification maxima of the seasonally varying Surface layer in the Arctic Ocean’s Beaufort Gyre

2021 ◽  
Author(s):  
◽  
Peter A. Roemer
Keyword(s):  
Mixed Layer ◽  
Vertical Mixing ◽  
Heat Energy ◽  
The Arctic ◽  
Small Scale ◽  
Geographic Variability ◽  
Vertical Diffusivity ◽  
Beaufort Gyre ◽  
The Arctic Ocean ◽  
Initial Evolution

The Beaufort Gyre region of the Arctic Ocean is strongly stratified at the base of the wintertime mixed layer, which impedes the vertical transport of heat, energy, and other tracers. Ice-Tethered Profiler observations during 2004-2018 were used to characterize and investigate the seasonal and interannual variability of the strength, depth, density, and thickness of this highly stratified layer at the base of the mixed layer. This includes investigating the remnant stratification maximum, which formed when the summer mixed layer shoaled. Seasonally, the stratification maximum was never in a steady state. It was largest in October (4.8 × 10−3 rad2/sec2) and decreased during all winter months (to 2.3 × 10−3rad2/sec2 in June), indicating that surface forcing and interior vertical mixing were never in equilibrium during the year. Interannually, the period from 2011-2018 had a higher stratification maximum than then the period from 2005-2010 regardless of the season. The remnant stratification maximum was consistently weaker than the winter stratification maximum from which it formed. The initial evolution of the remnant stratification maximum is used to estimate an effective vertical diffusivity of order 10−6m2/s. No significant geographic variability was found, in part due to high temporal and small scale variability of the stratification maximum layer. Implications for heat transport through to the sea ice cover are discussed.

scholarly journals Diagnosing Surface Mixed Layer Dynamics from High-Resolution Satellite Observations: Numerical Insights

2013 ◽  
Vol 43 (7) ◽  
pp. 1345-1355 ◽  
Author(s):  
Aurelien L. Ponte ◽  
Patrice Klein ◽  
Xavier Capet ◽  
Pierre-Yves Le Traon ◽  
Bertrand Chapron ◽  
...  
Keyword(s):  
High Resolution ◽  
Mixed Layer ◽  
Vertical Mixing ◽  
Mesoscale Eddy ◽  
Three Dimensional ◽  
Satellite Observations ◽  
Scaling Analysis ◽  
Surface Mixed Layer ◽  
Surface Layers ◽  
Velocity Scale

Abstract High-resolution numerical experiments of ocean mesoscale eddy turbulence show that the wind-driven mixed layer (ML) dynamics affects mesoscale motions in the surface layers at scales lower than O(60 km). At these scales, surface horizontal currents are still coherent to, but weaker than, those derived from sea surface height using geostrophy. Vertical motions, on the other hand, are stronger than those diagnosed using the adiabatic quasigeotrophic (QG) framework. An analytical model, based on a scaling analysis and on simple dynamical arguments, provides a physical understanding and leads to a parameterization of these features in terms of vertical mixing. These results are valid when the wind-driven velocity scale is much smaller than that associated with eddies and the Ekman number (related to the ratio between the Ekman and ML depth) is not small. This suggests that, in these specific situations, three-dimensional ML motions (including the vertical velocity) can be diagnosed from high-resolution satellite observations combined with a climatological knowledge of ML conditions and interior stratification.

scholarly journals Submesoscale Baroclinic Instability in the Bottom Boundary Layer

2018 ◽  
Vol 48 (11) ◽  
pp. 2571-2592 ◽  
Author(s):  
Jacob O. Wenegrat ◽  
Jörn Callies ◽  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Baroclinic Instability ◽  
Slope Angle ◽  
Deep Ocean ◽  
Bottom Boundary Layer ◽  
Surface Mixed Layer ◽  
Nonlinear Simulation ◽  
Bottom Boundary ◽  
Topographic Slope

AbstractWeakly stratified layers over sloping topography can support a submesoscale baroclinic instability mode, a bottom boundary layer counterpart to surface mixed layer instabilities. The instability results from the release of available potential energy, which can be generated because of the observed bottom intensification of turbulent mixing in the deep ocean, or the Ekman adjustment of a current on a slope. Linear stability analysis suggests that the growth rates of bottom boundary layer baroclinic instabilities can be comparable to those of the surface mixed layer mode and are relatively insensitive to topographic slope angle, implying the instability is robust and potentially active in many areas of the global oceans. The solutions of two separate one-dimensional theories of the bottom boundary layer are both demonstrated to be linearly unstable to baroclinic instability, and results from an example nonlinear simulation are shown. Implications of these findings for understanding bottom boundary layer dynamics and processes are discussed.

scholarly journals Observations and numerical simulations of large-eddy circulation in the ocean surface mixed layer

2014 ◽  
Vol 41 (21) ◽  
pp. 7584-7590 ◽  
Author(s):  
Miles A. Sundermeyer ◽  
Eric Skyllingstad ◽  
James R. Ledwell ◽  
Brian Concannon ◽  
Eugene A. Terray ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Mixed Layer ◽  
Ocean Surface ◽  
Surface Mixed Layer ◽  
Large Eddy ◽  
Ocean Surface Mixed Layer
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