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gravity waves (60+ TW; Wang and Huang 2004b ), but they are not directly related to the interior flow. Three methods for determining the local rate of wind-power input to the ocean general circulation have been proposed in the literature: 1) the direct rate of work on the geostrophic circulation ( Stern 1975 ); 2) the rate at which the Ekman transport crosses the surface pressure gradient ( Fofonoff 1981 ); and 3) the rate at which Ekman pumping generates potential energy in a stratified fluid ( Gill
gravity waves (60+ TW; Wang and Huang 2004b ), but they are not directly related to the interior flow. Three methods for determining the local rate of wind-power input to the ocean general circulation have been proposed in the literature: 1) the direct rate of work on the geostrophic circulation ( Stern 1975 ); 2) the rate at which the Ekman transport crosses the surface pressure gradient ( Fofonoff 1981 ); and 3) the rate at which Ekman pumping generates potential energy in a stratified fluid ( Gill
, the interaction of uniform wind stress with smaller turbulent vertical viscosity at the front center than periphery (i.e., the internal Ekman pumping) produces an upward buoyancy transport under the upfront-wind forcing, accounting for the enhanced B f TTW in the upfront-wind case. By weakening fronts in the mixed layer, the eddy thermal feedback reduces B f contributed by the geostrophic deformation and TTW. The value of B f at its peaking depth is 12% smaller in the simulation with the
, the interaction of uniform wind stress with smaller turbulent vertical viscosity at the front center than periphery (i.e., the internal Ekman pumping) produces an upward buoyancy transport under the upfront-wind forcing, accounting for the enhanced B f TTW in the upfront-wind case. By weakening fronts in the mixed layer, the eddy thermal feedback reduces B f contributed by the geostrophic deformation and TTW. The value of B f at its peaking depth is 12% smaller in the simulation with the
Brunt–Väisälä frequency at the base of the mixed layer. d. Wind stress and air–sea fluxes We estimate the Ekman transport and Ekman pumping using the Quick Scatterometer Mean Wind Field (QuickSCAT MWF) gridded product [this global half-degree-resolution product is processed and distributed by the Centre European Remote Sensing Satellite (ERS) d’Archivage et de Traitement (CERSAT); available online at http://www.ifremer.fr/cersat/ ]. We used weekly maps of wind stress between 2003 and 2007 to
Brunt–Väisälä frequency at the base of the mixed layer. d. Wind stress and air–sea fluxes We estimate the Ekman transport and Ekman pumping using the Quick Scatterometer Mean Wind Field (QuickSCAT MWF) gridded product [this global half-degree-resolution product is processed and distributed by the Centre European Remote Sensing Satellite (ERS) d’Archivage et de Traitement (CERSAT); available online at http://www.ifremer.fr/cersat/ ]. We used weekly maps of wind stress between 2003 and 2007 to
forth in Gaube et al. (2015) and will refer to this as current-induced Ekman pumping w c . The second term arises because of the horizontal gradient of relative vorticity and has been referred to as the nonlinear Ekman term, but for the reasons described above, we will refer to this term as the vorticity gradient–induced Ekman pumping w ζ . This term can also be written in terms of advection of the vertical component of the absolute vorticity by the classic linear Ekman transport M L : (7) w ζ
forth in Gaube et al. (2015) and will refer to this as current-induced Ekman pumping w c . The second term arises because of the horizontal gradient of relative vorticity and has been referred to as the nonlinear Ekman term, but for the reasons described above, we will refer to this term as the vorticity gradient–induced Ekman pumping w ζ . This term can also be written in terms of advection of the vertical component of the absolute vorticity by the classic linear Ekman transport M L : (7) w ζ
volume flux. In contrast, at 45°N, loss of warmer waters to the north at Θ > 10°C is opposed by a southward transport of cold, deep water at Θ < 10°C, thereby inducing an apparent volume flux of warm water into cold water to the south of 45°N. d. Calculation of Ekman pumping We calculate Ekman pumping as the vertical component of the curl of the wind stress divided by a reference density ( ρ 0 = 1000 kg m −3 ) and f , the Coriolis parameter, assuming an ocean at rest. Integrating in time, we thus
volume flux. In contrast, at 45°N, loss of warmer waters to the north at Θ > 10°C is opposed by a southward transport of cold, deep water at Θ < 10°C, thereby inducing an apparent volume flux of warm water into cold water to the south of 45°N. d. Calculation of Ekman pumping We calculate Ekman pumping as the vertical component of the curl of the wind stress divided by a reference density ( ρ 0 = 1000 kg m −3 ) and f , the Coriolis parameter, assuming an ocean at rest. Integrating in time, we thus
Subantarctic Surface Water along the Antarctic Polar Front Zone ( Marsh et al. 2000 ; Sørensen et al. 2001 ; Sloyan and Rintoul 2001 ; Santoso and England 2004 ). The circumpolar-averaged subduction over the Southern Ocean suggests broad upwelling of Circumpolar Deep Water and AAIW by Ekman pumping, which is then transported northward into a subduction zone of dense SAMW ( Sallée et al. 2010 ). This strong northward Ekman transport is balanced by vigorous processes of eddy diffusion and a southward
Subantarctic Surface Water along the Antarctic Polar Front Zone ( Marsh et al. 2000 ; Sørensen et al. 2001 ; Sloyan and Rintoul 2001 ; Santoso and England 2004 ). The circumpolar-averaged subduction over the Southern Ocean suggests broad upwelling of Circumpolar Deep Water and AAIW by Ekman pumping, which is then transported northward into a subduction zone of dense SAMW ( Sallée et al. 2010 ). This strong northward Ekman transport is balanced by vigorous processes of eddy diffusion and a southward
80°–90°E might block the energy, thus causing the Rossby wave propagating from the east to “break down,” the major mechanisms of this feature are inclined to be the interferences of the localized forcing and free Rossby wave ( Wang et al. 2001 ) or the change in local Ekman pumping across the ridge ( Birol and Morrow 2001 ). Fig . 9. The Hovmöller diagrams at latitude 14.9°S for the surface elevation η and its heaving rate (first row) and depth anomalies of 26.5 σ 0 and 27.4 σ 0 and their
80°–90°E might block the energy, thus causing the Rossby wave propagating from the east to “break down,” the major mechanisms of this feature are inclined to be the interferences of the localized forcing and free Rossby wave ( Wang et al. 2001 ) or the change in local Ekman pumping across the ridge ( Birol and Morrow 2001 ). Fig . 9. The Hovmöller diagrams at latitude 14.9°S for the surface elevation η and its heaving rate (first row) and depth anomalies of 26.5 σ 0 and 27.4 σ 0 and their
interest because SSH variability not only indicates oceanic upwelling but also directly impacts the coasts. Dynamically, SSH and thermocline depth in the south Indian Ocean (SIO) can be forced by a few key processes: local Ekman pumping velocity, Rossby waves originating from the eastern Indian Ocean, and Pacific Ocean variability transmitted through the Indonesian archipelago as Rossby waves. On interannual and seasonal time scales, sea level and thermocline variability in the SIO has been attributed
interest because SSH variability not only indicates oceanic upwelling but also directly impacts the coasts. Dynamically, SSH and thermocline depth in the south Indian Ocean (SIO) can be forced by a few key processes: local Ekman pumping velocity, Rossby waves originating from the eastern Indian Ocean, and Pacific Ocean variability transmitted through the Indonesian archipelago as Rossby waves. On interannual and seasonal time scales, sea level and thermocline variability in the SIO has been attributed
°–80°E. The leading harmonics (annual and semiannual) are shown in red and shading represents plus or minus one standard deviation. (c) The seasonal cycle of Ekman pumping (from QuikSCAT) over the equatorial gyre (5°–10°S, 50°–80°E) and of the SECC ( U g ) are shown. SECC data are from the drifter–altimeter synthesis. For half the year, the EACC feeds directly into the SECC, without crossing the equator. But from April through September, cross-equatorial winds play a role in causing an overshoot of
°–80°E. The leading harmonics (annual and semiannual) are shown in red and shading represents plus or minus one standard deviation. (c) The seasonal cycle of Ekman pumping (from QuikSCAT) over the equatorial gyre (5°–10°S, 50°–80°E) and of the SECC ( U g ) are shown. SECC data are from the drifter–altimeter synthesis. For half the year, the EACC feeds directly into the SECC, without crossing the equator. But from April through September, cross-equatorial winds play a role in causing an overshoot of
further indicated that the upwelling is a seasonal phenomenon, and mainly occurs when the southwest monsoon prevails during June–August. The southwesterly wind, with a direction parallel to the southern coastline of Sri Lanka, is an important factor for the formation of upwelling by inducing offshore Ekman transport ( Vinayachandran et al. 2004 ; Yapa 2012 ; de Vos et al. 2014 ). In addition, the upward Ekman pumping caused by the strong positive wind stress curl around the southern coast during the
further indicated that the upwelling is a seasonal phenomenon, and mainly occurs when the southwest monsoon prevails during June–August. The southwesterly wind, with a direction parallel to the southern coastline of Sri Lanka, is an important factor for the formation of upwelling by inducing offshore Ekman transport ( Vinayachandran et al. 2004 ; Yapa 2012 ; de Vos et al. 2014 ). In addition, the upward Ekman pumping caused by the strong positive wind stress curl around the southern coast during the
