scholarly journals Destruction of Potential Vorticity by Winds

2005 ◽  
Vol 35 (12) ◽  
pp. 2457-2466 ◽  
Author(s):  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Potential Vorticity ◽  
Ekman Layer ◽  
Buoyancy Flux ◽  
Coriolis Parameter ◽  
Mode Water ◽  
Ocean Fronts ◽  
Secondary Circulations ◽  
Frictional Forces

Abstract The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FBatm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe)(FBwind/FBatm), where H and δe are the mixed layer and Ekman layer depths, FBwind = S2τo/(ρof ), S2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.

scholarly journals Intensification of Ocean Fronts by Down-Front Winds

2005 ◽  
Vol 35 (6) ◽  
pp. 1086-1102 ◽  
Author(s):  
Leif N. Thomas ◽  
Craig M. Lee
Keyword(s):  
Potential Vorticity ◽  
Buoyancy Flux ◽  
Ekman Transport ◽  
Ekman Pumping ◽  
Vertical Circulation ◽  
Ocean Fronts ◽  
Front Width ◽  
Secondary Circulations ◽  
Frontal Interface ◽  
Mixed Layers

Abstract Many ocean fronts experience strong local atmospheric forcing by down-front winds, that is, winds blowing in the direction of the frontal jet. An analytic theory and nonhydrostatic numerical simulations are used to demonstrate the mechanism by which down-front winds lead to frontogenesis. When a wind blows down a front, cross-front advection of density by Ekman flow results in a destabilizing wind-driven buoyancy flux (WDBF) equal to the product of the Ekman transport with the surface lateral buoyancy gradient. Destabilization of the water column results in convection that is localized to the front and that has a buoyancy flux that is scaled by the WDBF. Mixing of buoyancy by convection, and Ekman pumping/suction resulting from the cross-front contrast in vertical vorticity of the frontal jet, drive frontogenetic ageostrophic secondary circulations (ASCs). For mixed layers with negative potential vorticity, the most frontogenetic ASCs select a preferred cross-front width and do not translate with the Ekman transport, but instead remain stationary in space. Frontal intensification occurs within several inertial periods and is faster the stronger the wind stress. Vertical circulation is characterized by subduction on the dense side of the front and upwelling along the frontal interface and scales with the Ekman pumping and convective mixing of buoyancy. Cross-front sections of density, potential vorticity, and velocity at the subpolar front of the Japan/East Sea suggest that frontogenesis by down-front winds was active during cold-air outbreaks and could result in strong vertical circulation.

Nonlinear stratified spin-up

2002 ◽  
Vol 473 ◽  
pp. 211-244 ◽  
Author(s):  
LEIF N. THOMAS ◽  
PETER B. RHINES
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Wind Stress ◽  
Thermal Boundary Layer ◽  
Ekman Layer ◽  
Ekman Transport ◽  
Ekman Pumping ◽  
Vertical Diffusion ◽  
Vertical Vorticity ◽  
Horizontal Advection

Both a weakly nonlinear analytic theory and direct numerical simulation are used to document processes involved during the spin-up of a rotating stratified fluid driven by wind-stress forcing for time periods less than a homogeneous spin-up time. The strength of the wind forcing, characterized by the Rossby number ε, is small enough (i.e. ε[Lt ]1) that a regular perturbation expansion in ε can be performed yet large enough (more specifically, ε∝E1/2, where E is the Ekman number) that higher-order effects of vertical diffusion and horizontal advection of momentum/density are comparable in magnitude. Cases of strong stratification, where the Burger number S is equal to one, with zero heat flux at the upper boundary are considered. The Ekman transport calculated to O(ε) decreases with increasing absolute vorticity. In contrast to nonlinear barotropic spin-up, vortex stretching in the interior is predominantly linear, as vertical advection negates stretching of interior relative vorticity, yet is driven by Ekman pumping modified by nonlinearity. As vertical vorticity is generated during the spin-up of the fluid, the vertical vorticity feeds back on the Ekman pumping/suction, enhancing pumping and vortex squashing while reducing suction and vortex stretching. This feedback mechanism causes anticyclonic vorticity to grow more rapidly than cyclonic vorticity. Strict application of the zero-heat-flux boundary condition leads to the growth of a diffusive thermal boundary layer E−1/4 times thicker than the Ekman layer embedded within it. In the Ekman layer, vertical diffusion of heat balances horizontal advection of temperature by extracting heat from the thermal boundary layer beneath. The flux of heat extracted from the top of the thermal boundary layer by this mechanism is proportional to the product of the Ekman transport and the horizontal gradient of the temperature at the surface. The cooling caused by this heat flux generates density inversions and intensifies lateral density gradients where the wind-stress curl is negative. These thermal gradients make the potential vorticity strongly negative, conditioning the fluid for ensuing symmetric instability which greatly modifies the spin-up process.

scholarly journals Buoyancy Effects in a Stratified Ekman Layer

2009 ◽  
Vol 39 (10) ◽  
pp. 2581-2599 ◽  
Author(s):  
James C. McWilliams ◽  
Edward Huckle ◽  
Alexander F. Shchepetkin
Keyword(s):  
Boundary Layer ◽  
Ekman Layer ◽  
Buoyancy Flux ◽  
Buoyancy Frequency ◽  
Surface Cooling ◽  
Mean Velocity ◽  
Vertical Scale ◽  
Viscosity Profile ◽  
The Mean ◽  
Surface Buoyancy

Abstract The K-profile parameterization scheme is used to investigate the stratified Ekman layer in a “fair weather” regime of weak mean surface heating, persistently stable density stratification, diurnal solar cycle, and broadband fluctuations in the surface stress and buoyancy flux. In the case of steady forcing, the boundary layer depth typically scales as h ∼ u*/Nf, where u* is the friction velocity, f is the Coriolis frequency, and N is the interior buoyancy frequency that confirms empirical fits. The diurnal cycle of solar forcing acts to deepen the boundary layer because of net interior absorption and compensating surface cooling. Parameterized mesoscale and submesoscale eddy-induced restratification flux compresses the boundary layer. With transient forcing, the mean boundary layer profiles are altered; that is, rectification occurs with a variety of causes and manifestations, including changes in h and in the Ekman profile u(z). Overall, stress fluctuations tend to deepen the mean boundary layer, especially near the inertial frequency. Low- and high-frequency surface buoyancy-flux fluctuations have net shallowing and deepening effects, respectively. Eddy-induced interior profile fluctuations are relatively ineffective as a source of boundary layer rectification. Rectification effects in their various combinations lead to a range of mean velocity and buoyancy profiles. In particular, they lead to a “rotated” effective eddy-viscosity profile with misalignment between the mean turbulent stress and mean shear and to a “flattening” of the velocity profile with a larger vertical scale for the current veering than the speed decay; both of these effects from rectification are consistent with previous measurements.

scholarly journals Effects of the Submesoscale on the Potential Vorticity Budget of Ocean Mode Waters

2018 ◽  
Vol 48 (9) ◽  
pp. 2141-2165 ◽  
Author(s):  
Jacob O. Wenegrat ◽  
Leif N. Thomas ◽  
Jonathan Gula ◽  
James C. McWilliams
Keyword(s):  
Boundary Layer ◽  
Ocean Circulation ◽  
Potential Vorticity ◽  
Realistic Model ◽  
Small Scale ◽  
Mode Water ◽  
Mode Waters ◽  
Boundary Layer Turbulence ◽  
Water Formation ◽  
Surface Buoyancy

AbstractNonconservative processes change the potential vorticity (PV) of the upper ocean and, later, through the subduction of surface waters into the interior, affect the general ocean circulation. Here we focus on how boundary layer turbulence, in the presence of submesoscale horizontal buoyancy gradients, generates a source of potential vorticity at the ocean surface through a balance known as the turbulent thermal wind. This source of PV injection at the submesoscale can be of similar magnitude to PV fluxes from the wind and surface buoyancy fluxes, and hence can lead to a net injection of PV onto outcropped isopycnals even during periods of surface buoyancy loss. The significance of these dynamics is illustrated using a high-resolution realistic model of the North Atlantic Subtropical Mode Water (Eighteen Degree Water), where it is demonstrated that injection of PV at the submesoscale reduces the rate of mode water PV removal by a factor of ~2 and shortens the annual period of mode water formation by ~3 weeks, relative to air–sea fluxes alone. Submesoscale processes thus provide a direct link between small-scale boundary layer turbulence and the gyre-scale circulation, through their effect on mode water formation, with implications for understanding the variability and biogeochemical properties of ocean mode waters globally.

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

scholarly journals Multi-symplectic formulation of near-local Hamiltonian balanced models

2011 ◽  
Vol 467 (2136) ◽  
pp. 3424-3442 ◽  
Author(s):  
Sylvain Delahaies ◽  
Peter E. Hydon
Keyword(s):  
Potential Vorticity ◽  
Contact Structure ◽  
Fluid Motion ◽  
Local Model ◽  
Contact Transformation ◽  
Geometric Features ◽  
Coriolis Parameter ◽  
New Class

We transform near-local Hamiltonian balanced models (HBMs) describing nearly geostrophic fluid motion (with constant Coriolis parameter) into multi-symplectic (MS) systems. This allows us to determine conservation of Lagrangian momentum, energy and potential vorticity for Salmon's L 1 dynamics; a similar approach works for other near-local balanced models (such as the -model). The MS approach also enables us to determine a class of systems that have a contact structure similar to that of the semigeostrophic model. The contact structure yields a contact transformation that makes the problem of front formation tractable. The new class includes the first local model with a variable Coriolis parameter that preserves all of the most useful geometric features of the semigeostrophic model.

scholarly journals Subantarctic Mode Water Formation, Destruction, and Export in the Eddy-Permitting Southern Ocean State Estimate

2013 ◽  
Vol 43 (7) ◽  
pp. 1485-1511 ◽  
Author(s):  
Ivana Cerovečki ◽  
Lynne D. Talley ◽  
Matthew R. Mazloff ◽  
Guillaume Maze
Keyword(s):  
Southern Ocean ◽  
Buoyancy Flux ◽  
Differential Heat ◽  
Diapycnal Mixing ◽  
Mode Water ◽  
State Estimate ◽  
Surface Formation ◽  
Subantarctic Mode Water ◽  
The Pacific ◽  
The Difference

Abstract Subantarctic Mode Water (SAMW) is examined using the data-assimilating, eddy-permitting Southern Ocean State Estimate, for 2005 and 2006. Surface formation due to air–sea buoyancy flux is estimated using Walin analysis, and diapycnal mixing is diagnosed as the difference between surface formation and transport across 30°S, accounting for volume change with time. Water in the density range 26.5 < σθ < 27.1 kg m−3 that includes SAMW is exported northward in all three ocean sectors, with a net transport of (18.2, 17.1) Sv (1 Sv ≡ 106 m3 s−1; for years 2005, 2006); air–sea buoyancy fluxes form (13.2, 6.8) Sv, diapycnal mixing removes (−14.5, −12.6) Sv, and there is a volume loss of (−19.3, −22.9) Sv mostly occurring in the strongest SAMW formation locations. The most vigorous SAMW formation is in the Indian Ocean by air–sea buoyancy flux (9.4, 10.9) Sv, where it is partially destroyed by diapycnal mixing (−6.6, −3.1) Sv. There is strong export to the Pacific, where SAMW is destroyed both by air–sea buoyancy flux (−1.1, −4.6) Sv and diapycnal mixing (−5.6, −8.4) Sv. In the South Atlantic, SAMW is formed by air–sea buoyancy flux (5.0, 0.5) Sv and is destroyed by diapycnal mixing (−2.3, −1.1) Sv. Peaks in air–sea flux formation occur at the Southeast Indian and Southeast Pacific SAMWs (SEISAMWs, SEPSAMWs) densities. Formation over the broad SAMW circumpolar outcrop windows is largely from denser water, driven by differential freshwater gain, augmented or decreased by heating or cooling. In the SEISAMW and SEPSAMW source regions, however, formation is from lighter water, driven by differential heat loss.

scholarly journals Surface signature of Mediterranean water eddies in the Northeastern Atlantic: effect of the upper ocean stratification

Ocean Science ◽  
2012 ◽  
Vol 8 (6) ◽  
pp. 931-943 ◽  
Author(s):  
I. Bashmachnikov ◽  
X. Carton
Keyword(s):  
Potential Vorticity ◽  
Initial Period ◽  
Relative Vorticity ◽  
Sea Surface ◽  
Upper Ocean ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Ocean Stratification ◽  
Surface Signature ◽  
Mediterranean Water

Abstract. Meddies, intra-thermocline eddies of Mediterranean water, can often be detected at the sea surface as positive sea-level anomalies. Here we study the surface signature of several meddies tracked with RAFOS floats and AVISO altimetry. While pushing its way through the water column, a meddy raises isopycnals above. As a consequence of potential vorticity conservation, negative relative vorticity is generated in the upper layer. During the initial period of meddy acceleration after meddy formation or after a stagnation stage, a cyclonic signal is also generated at the sea-surface, but mostly the anticyclonic surface signal follows the meddy. Based on geostrophy and potential vorticity balance, we present theoretical estimates of the intensity of the surface signature. It appears to be proportional to the meddy core radius and to the Coriolis parameter, and inversely proportional to the core depth and buoyancy frequency. This indicates that surface signature of a meddy may be strongly reduced by the upper ocean stratification. Using climatic distribution of the stratification intensity, we claim that the southernmost limit for detection in altimetry of small meddies (with radii on the order of 10–15 km) should lie in the subtropics (35–45° N), while large meddies (with radii of 25–30 km) could be detected as far south as the northern tropics (25–35° N). Those results agree with observations.

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