scholarly journals A New Look at Richardson Number Mixing Schemes for Equatorial Ocean Modeling

2009 ◽  
Vol 39 (10) ◽  
pp. 2652-2664 ◽  
Author(s):  
Edward D. Zaron ◽  
James N. Moum
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Mixed Layer ◽  
Richardson Number ◽  
Large Scale ◽  
Ocean Modeling ◽  
Depth Range ◽  
Surface Mixed Layer ◽  
Flux Divergence ◽  
Equatorial Undercurrent

Abstract A reexamination of turbulence dissipation measurements from the equatorial Pacific shows that the turbulence diffusivities are not a simple function of the gradient Richardson number. A widely used mixing scheme, the K-profile parameterization, overpredicts the turbulent vertical heat flux by roughly a factor of 4 in the stably stratified region between the surface mixed layer and the Equatorial Undercurrent (EUC). Additionally, the heat flux divergence is of the incorrect sign in the upper 80 m. An alternative class of parameterizations is examined that expresses the mixing coefficients in terms of the large-scale kinetic energy, shear, and Richardson number. These representations collapse the turbulence diffusivities above and below the Equatorial Undercurrent, and a tuned version is able to reproduce the vertical turbulence heat flux within the 50–180-m depth range. Kinetic energy is not Galilean invariant, so the collapse of the data with the new parameterization suggests that oceanic turbulence responds to boundary forcing at depths well below the surface mixed layer.

scholarly journals Cold-Water Events and Dissipation in the Mixed Layer of a Lake

2006 ◽  
Vol 36 (10) ◽  
pp. 1928-1939 ◽  
Author(s):  
B. Ozen ◽  
S. A. Thorpe ◽  
U. Lemmin ◽  
T. R. Osborn
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Large Scale ◽  
Cold Water ◽  
Velocity Shear ◽  
Surface Mixed Layer ◽  
Near Surface ◽  
Law Of The Wall ◽  
Upward Direction

Abstract Measurements of temperature, velocity, and microscale velocity shear were made from the research submarine F. A. Forel in the near-surface mixed layer of Lake Geneva under conditions of moderate winds of 6–8 m s−1 and of net heating at the water surface. The submarine carried arrays of thermistors and a turbulence package, including airfoil shear probes. The rate of dissipation of turbulent kinetic energy per unit mass, estimated from the variance of the shear, is found to be lognormally distributed and to vary with depth roughly in accordance with the law of the wall at the measurement depths, 15–20 times the significant wave height. Measurements revealed large-scale structures, coherent over the 2.38-m vertical extent sampled by a vertical array of thermistors, consisting of filaments tilted in the wind direction. They are typically about 1.5 m wide, decreasing in width in the upward direction, and are horizontally separated by about 25 m in the downwind direction. Originating in the upper thermocline, they are characterized in the mixed layer by their relatively low temperature and low rates of dissipation of turbulent kinetic energy and by an upward vertical velocity of a few centimeters per second.

scholarly journals Weakening of Cold Halocline Layer Exposes Sea Ice to Oceanic Heat in the Eastern Arctic Ocean

2020 ◽  
Vol 33 (18) ◽  
pp. 8107-8123 ◽  
Author(s):  
Igor V. Polyakov ◽  
Tom P. Rippeth ◽  
Ilker Fer ◽  
Matthew B. Alkire ◽  
Till M. Baumann ◽  
...  
Keyword(s):  
Heat Flux ◽  
Sea Ice ◽  
Arctic Ocean ◽  
Mixed Layer ◽  
Winter Season ◽  
Atlantic Water ◽  
The Arctic ◽  
Surface Mixed Layer ◽  
Winter Convection ◽  
Oceanic Heat Flux

AbstractA 15-yr duration record of mooring observations from the eastern (>70°E) Eurasian Basin (EB) of the Arctic Ocean is used to show and quantify the recently increased oceanic heat flux from intermediate-depth (~150–900 m) warm Atlantic Water (AW) to the surface mixed layer and sea ice. The upward release of AW heat is regulated by the stability of the overlying halocline, which we show has weakened substantially in recent years. Shoaling of the AW has also contributed, with observations in winter 2017–18 showing AW at only 80 m depth, just below the wintertime surface mixed layer, the shallowest in our mooring records. The weakening of the halocline for several months at this time implies that AW heat was linked to winter convection associated with brine rejection during sea ice formation. This resulted in a substantial increase of upward oceanic heat flux during the winter season, from an average of 3–4 W m−2 in 2007–08 to >10 W m−2 in 2016–18. This seasonal AW heat loss in the eastern EB is equivalent to a more than a twofold reduction of winter ice growth. These changes imply a positive feedback as reduced sea ice cover permits increased mixing, augmenting the summer-dominated ice-albedo feedback.

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.

A Parameterization of Shear-Driven Turbulence for Ocean Climate Models

2008 ◽  
Vol 38 (5) ◽  
pp. 1033-1053 ◽  
Author(s):  
L. Jackson ◽  
R. Hallberg ◽  
S. Legg
Keyword(s):  
Time Scale ◽  
Richardson Number ◽  
Large Scale ◽  
Climate Models ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Length Scale ◽  
Equatorial Undercurrent ◽  
Elliptic Equilibrium ◽  
Critical Requirement

Abstract This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state. The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N 2/|uz|2, where N is the buoyancy frequency and |uz| is the vertical shear) and the buoyancy length scale over which the turbulence decays [Lb = Q1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself. High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.

scholarly journals Topographic and Mixed Layer Submesoscale Currents in the Near-Surface Southwestern Tropical Pacific

2017 ◽  
Vol 47 (6) ◽  
pp. 1221-1242 ◽  
Author(s):  
Kaushik Srinivasan ◽  
James C. McWilliams ◽  
Lionel Renault ◽  
Hristina G. Hristova ◽  
Jeroen Molemaker ◽  
...  
Keyword(s):  
Heat Flux ◽  
Surface Layer ◽  
Kinetic Energy ◽  
Wind Stress ◽  
Mixed Layer ◽  
Surface Heat Flux ◽  
Seasonal Cycle ◽  
Surface Heat ◽  
Near Surface ◽  
Coral Sea

AbstractThe distribution and strength of submesoscale (SM) surface layer fronts and filaments generated through mixed layer baroclinic energy conversion and submesoscale coherent vortices (SCVs) generated by topographic drag are analyzed in numerical simulations of the near-surface southwestern Pacific, north of 16°S. In the Coral Sea a strong seasonal cycle in the surface heat flux leads to a winter SM “soup” consisting of baroclinic mixed layer eddies (MLEs), fronts, and filaments similar to those seen in other regions farther away from the equator. However, a strong wind stress seasonal cycle, largely in sync with the surface heat flux cycle, is also a source of SM processes. SM restratification fluxes show distinctive signatures corresponding to both surface cooling and wind stress. The winter peak in SM activity in the Coral Sea is not in phase with the summer dominance of the mesoscale eddy kinetic energy in the region, implying that local surface layer forcing effects are more important for SM generation than the nonlocal eddy deformation field. In the topographically complex Solomon and Bismarck Seas, a combination of equatorial proximity and boundary drag generates SCVs with large-vorticity Rossby numbers (Ro ~ 10). River outflows in the Bismarck and Solomon Seas make a contribution to SM generation, although they are considerably weaker than the topographic effects. Mean to eddy kinetic energy conversions implicate barotropic instability in SM topographic wakes, with the strongest values seen north of the Vitiaz Strait along the coast of Papua New Guinea.

Turbulent mixing in a shear-free stably stratified two-layer fluid

1998 ◽  
Vol 354 ◽  
pp. 175-208 ◽  
Author(s):  
DAVID A. BRIGGS ◽  
JOEL H. FERZIGER ◽  
JEFFREY R. KOSEFF ◽  
STEPHEN G. MONISMITH
Keyword(s):  
Kinetic Energy ◽  
Froude Number ◽  
Internal Waves ◽  
Mixed Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Source Region ◽  
Buoyancy Flux ◽  
Mixing Efficiency ◽  
Principal Mechanism

Direct numerical simulation is used to examine turbulent mixing in a shear-free stably stratified fluid. Energy is continuously supplied to a small region to maintain a well-developed kinetic energy profile, as in an oscillating grid flow (Briggs et al. 1996; Hopfinger & Toly 1976; Nokes 1988). A microscale Reynolds number of 60 is maintained in the source region. The turbulence forms a well-mixed layer which diffuses from the source into the quiescent fluid below. Turbulence transport at the interface causes the mixed layer to grow under weakly stratified conditions. When the stratification is strong, large-scale turbulent transport is inactive and pressure transport becomes the principal mechanism for the growth of the turbulence layer. Down-gradient buoyancy flux is present in the large scales; however, far from the source, weak counter-gradient fluxes appear in the medium to small scales. The production of internal waves and counter-gradient fluxes rapidly reduces the mixing when the turbulent Froude number is lower than unity. When the stratification is weak, the turbulence is strong enough to break up the density interface and transport fluid parcels of different density over large vertical distances. As the stratification intensifies, turbulent eddies flatten against the interface creating anisotropy and internal waves. The dominant entrainment mechanism is then scouring. Mixing efficiency, defined as the ratio of buoyancy flux to available kinetic energy, exhibits a similar dependence on Froude number to other stratified flows (Holt et al. 1992; Lienhard & Van Atta 1990). However, using the anisotropy of the turbulence to define an alternative mixing efficiency and Froude number improves the correlation and allows local scaling.

Large-Eddy Simulation of Deep-Cycle Turbulence in an Equatorial Undercurrent Model

2013 ◽  
Vol 43 (11) ◽  
pp. 2490-2502 ◽  
Author(s):  
Hieu T. Pham ◽  
Sutanu Sarkar ◽  
Kraig B. Winters
Keyword(s):  
Large Eddy Simulation ◽  
Mixed Layer ◽  
Buoyancy Frequency ◽  
Surface Mixed Layer ◽  
Equatorial Undercurrent ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Model Components ◽  
Surface Buoyancy ◽  
Les Model

Abstract Dynamical processes leading to deep-cycle turbulence in the Equatorial Undercurrent (EUC) are investigated using a high-resolution large-eddy simulation (LES) model. Components of the model include a background flow similar to the observed EUC, a steady westward wind stress, and a diurnal surface buoyancy flux. An LES of a 3-night period shows the presence of narrowband isopycnal oscillations near the local buoyancy frequency N as well as nightly bursts of deep-cycle turbulence at depths well below the surface mixed layer, the two phenomena that have been widely noted in observations. The deep cycle of turbulence is initiated when the surface heating in the evening relaxes, allowing a region with enhanced shear and a gradient Richardson number Rig less than 0.2 to form below the surface mixed layer. The region with enhanced shear moves downward into the EUC and is accompanied by shear instabilities and bursts of turbulence. The dissipation rate during the turbulence bursts is elevated by up to three orders of magnitude. Each burst is preceded by westward-propagating oscillations having a frequency of 0.004–0.005 Hz and a wavelength of 314–960 m. The Rig that was marginally stable in this region decreases to less than 0.2 prior to the bursts. A downward turbulent flux of momentum increases the shear at depth and reduces Rig. Evolution of the deep-cycle turbulence includes Kelvin–Helmholtz-like billows as well as vortices that penetrate downward and are stretched by the EUC shear.

scholarly journals Restratification of the Surface Mixed Layer with Submesoscale Lateral Density Gradients: Diagnosing the Importance of the Horizontal Dimension

2008 ◽  
Vol 38 (11) ◽  
pp. 2438-2460 ◽  
Author(s):  
P. J. Hosegood ◽  
M. C. Gregg ◽  
M. H. Alford
Keyword(s):  
Density Gradient ◽  
Mixed Layer ◽  
Large Scale ◽  
Acoustic Doppler Current Profiler ◽  
Small Scale ◽  
Density Gradients ◽  
Surface Mixed Layer ◽  
Vertical Scale ◽  
Current Profiler ◽  
Dimensional Measurements

Abstract A depth-cycling towed conductivity–temperature–depth (CTD) and vessel-mounted acoustic Doppler current profiler (ADCP) were used to obtain four-dimensional measurements of the restratification of the surface mixed layer (SML) at a submesoscale lateral density gradient near the subtropical front. With the objective of studying the role of horizontal processes in restratification, the thermohaline and velocity fields were monitored for 33 h by 16 small-scale (≤15 km2) surveys centered on a drogued float. Daytime warming by insolation caused a unidirectional displacement of the initially vertical isopycnals toward increasing density. Across the entire SML (50-m vertical scale), solar insolation accounted for 60% of observed restratification, but over 10-m scales, the percentage decreased with depth from 80% at 25–35 m to ≤25% at 55–65 m. Below 35 m, stratification was enhanced by the vertically sheared horizontal advection of the lateral density gradient due to a near-inertial wave of ∼100-m vertical wavelength that rotated anticyclonically at the inertial frequency. The phase and similar period (25.4 h) of the local inertial period to the diurnal cycle ensured constructive interference with isopycnal displacements due to insolation. Restratification by sheared advection matched that predicted due to vertically sheared inertial oscillations generated during the geostrophic adjustment of a density front, but direct wind forcing may also have generated the wave that was subsequently modified by interaction with mesoscale vorticity associated with a nearby large-scale front. By further including the effects of lateral uncompensated thermohaline inhomogeneity, the authors can account for 100% ± 20% of the observed N 2 during daytime restratification. No detectable restratification due to the slumping of horizontal density gradients under gravity alone was found.

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