Effect of near-inertial pumping on subduction at an ocean front

TL;DR

This study investigates how wind-driven near-inertial waves (NIWs) interact with submesoscale fronts to drive vertical transport of tracers. Using a high-resolution, non-hydrostatic PSOM model of a CALYPSO-like western Mediterranean front, the authors force NIWs for four inertial periods and analyze tracer covariance and energy spectra after forcing ceases. They demonstrate that inertial pumping is not fully reversible: phase differences between NIWs and front-induced vorticity yield net downward tracer transport, with enhanced transport on subinertial and inertial time scales and energy transfer to higher vertical modes. The findings imply that NIW-front interactions amplify vertical exchange and nutrient/cargo cycling at fronts, suggesting that coarse-resolution models may underestimate this transport and that accurate representation of NIWs is essential for biogeochemical predictions.

Abstract

The interactions between near-inertial waves (NIWs) and submesoscale currents in the surface ocean are challenging to deconvolve due to their overlapping temporal and spatial scales. The frequency of NIW is modulated by the relative vorticity, $ζ$, of submesoscale currents, which varies between positive and negative $ζ$ of $O(f)$ on spatial scales of 1 -- 10~$km$, particularly across fronts where the horizontal buoyancy gradient, $\nabla_H b$, is intensified. The effective NIW frequency $f_{\small{eff}} = f + ζ/2$ can therefore also vary by $O(f)$ on these scales, causing the waves to be out of phase. This generates periodic convergence and divergence in the surface layer, particularly at fronts. The resulting vertical motion, known as inertial pumping, is traditionally considered to be reversible. However, the strong vertical shear of the horizontal velocity at fronts, $v_z \sim |\nabla_H b|/f$, implies that not all of the water that is pumped downward will return. We examine the effect of this asymmetry on the vertical transport of tracers with an ambient vertical gradient, analogous to biogeochemical tracers, such as oxygen and dissolved organic carbon. Using numerical simulations of an unstable front forced by NIW, we demonstrate that inertial pumping can lead to net vertical transport of tracers. Spectral analysis of the vertical tracer flux -- given by the covariance between tracer anomaly and vertical velocity -- reveals that the interaction of strong NIW with submesoscale currents enhances the vertical exchange at the front on both the sub-inertial and inertial time scales.

Figures (23)

• Figure 1: Panels (a–c) show the relative vorticity, $\zeta$, normalized by $f$, overlaid with potential density contours at a depth of 3.5 $m$ on Day 60 for the three cases: the front (F), front with weak waves (F+WW), and front with strong waves (F+SW). By Day 60, the wave energy has greatly attenuated. Panels (d–f) are time series of the vertical velocity (w) in the upper 100 $m$ with potential density contours (black) at the domain center marked by a star, for the same cases: (d) F, (e) F+WW, and (f) F+SW. In panels (e) and (f), the vertical dashed lines indicate days 5–8, during which time the inertial wind stress is applied. The solid red lines in panels (e) and (f) correspond to a group velocity on the order of 3-5 $m$$day^{-1}$.
• Figure 2: Panels (a–c) show the spatial distribution of tracer deficit ($D$, in %) on Day 60 relative to Day 8 when the tracer is initialized, for the three cases: Front (F), front with weak waves (F+WW), and front with strong waves (F+SW). Potential density anomaly contours at 3.5 $m$ are overlaid in each panel for day 60. The horizontal dashed lines indicate $y=48\:km$ and 144 $km$, which mark the meridional extent of the region used for horizontal averaging. Panels (d–f) horizontally averaged vertical profiles of the tracer deficit, $D$%, over the upper 100 $m$. The averaged isopycnal depths for 28.7 (red), 28.8 (blue), and 28.9 $kg$$m^{-3}$ (green), computed relative to 3.5 $m$ depth on Day 60, are also shown for all three cases.
• Figure 3: Probability density functions (PDFs) of (a–c) normalized relative vorticity $\zeta/f$; (d–f) horizontal divergence $\delta/f$, where $\delta= u_x +v_y$; and (g–i) ratio of magnitude of the horizontal buoyancy gradient ($M^2$) and vertical stratification ($N^2$) given by $M^2/N^2= |\nabla_H b|/\partial b/\partial z~$, $b$ is the buoyancy. The left column is the front-only case (F), the middle column -- front with weak waves (F+WW), and the right column -- front with strong waves (F+SW). The PDFs are computed over the period from Day 8 to Day 60, after the winds are turned off, at depths of 3.5 $m$ (red), 20 $m$ (blue), and 60 $m$ (green).
• Figure 4: Panels (a–c) show the isotropic power spectral density (PSD) of horizontal kinetic energy, (d–f) vertical kinetic energy, and (g–i) the ratio of PSD of relative vorticity (RV) to PSD of divergence (DIV), all averaged over Days 8–60. The spectra are plotted as a function of horizontal wavenumber ($K=\sqrt{k^2_x+k^2_y}$, where $k_x$ and $k_y$ are the zonal and meridional wavenumbers, respectively, at depths of 3.5 $m$ (red), 20 $m$ (blue), and 60 $m$ (green). Results are shown for the three cases: the front (F), the front with weak-wave forcing (F+WW), and the front with strong-wave forcing (F+SW). Reference slopes of {-3, -2} for horizontal kinetic energy (a–c) and {-1,0} for vertical kinetic energy (d–f) are indicated. The grey-shaded region to the right of 8 $km$ (thick black vertical dashed line) marks the unreliable part of the PSD based on visual inspection. The red dashed line denotes the Rossby radius of deformation ($L_R$).
• Figure 5: Panels (a–c) and (d–f) show the zonal wavenumber ($k_x$)–frequency ($\omega/f$) power spectral density of vertical velocity, meridionally averaged, for the F, F+WW, and F+SW experiments at 20 $m$ (top row) and 60 $m$ (bottom row), over days 8–60. Overlaid dispersion curves correspond to channel mode $n=8$, with baroclinic phase speeds ($c_m$) for modes $m=3-5$ in F (upper to lower curves), and modes $m=7-10$ in F+WW and F+SW (upper to lower curves). In the F+SW case, the black dashed line marks the baroclinic phase speed of the Kelvin wave along the channel boundary, empirically fitted as 0.063 $m$$s^{-1}$.