The influence of front strength on the development and equilibration of symmetric instability. Part 2. Nonlinear evolution

In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.

Energetics and Kinematics of Inertial Oscillations in the Central Northern GOM

Understanding the physics of generation, propagation, and dissipation of inertial currents is important from a variety of aspects. For the Gulf of Mexico, one such aspect is that these oscillations represent an uncertainty in the measurements and forecasting of the longer-period currents, such as those due to the Loop Current (LC) and meso-scale eddies. The Industry has a practice of applying an ‘uplift’ to estimates of current velocity to account for the effect of tidal and inertial currents in cases when observations or model estimates do not resolve the high-frequency current variability. The value of the ‘uplift’ is assumed to be proportional to the intensity of the low-frequency flow. Our analysis aims at testing whether this assumption is valid by providing a detailed description of the space-time variability, including seasonal changes, of inertial oscillations in the central northern Gulf of Mexico. From the analysis of long-term current profile observations and drifter data we found that, on average, near-inertial oscillations have higher amplitudes outside of the areas of strong low-frequency currents associated with a Loop Current Eddy (LCE). Within the upper 200m of the water column, periods characterized by the downward energy propagation dominate. In the layer below 200m, near-inertial waves propagate upward and downward, and the wave trains cannot be traced to a single source of energy. This suggests near-inertial waves within the main part of the water column are of ‘global’ rather than of ‘local’ origin. For most near-inertial wave generation events through wind forcing, the downward energy propagation could not be traced for any extended period of time and no deeper than approximately 200-m depth. The rate of downward energy propagation in the upper pycnocline is on the order of 10-12 m/day. For the near-inertial currents, the first two Empirical Orthogonal Functions (EOF) contribute only 40% into the total current variability for the period of LCE presence and 52% for the period of benign current conditions. The mode shapes vary within a wide range that, most likely, reflects a random distribution of mode shapes that depend on the lateral geometry of the forcing, mixed layer depth, and stratification.

Spontaneous inertia-gravity wave generation from mesoscale eddies

<p>An exact geostrophic vortex generate spontaneously inertia-gravity waves (IGWs) with spiral patterns via singularity instability mechanism. In the vertical direction, the energy of the IGWs is dominated by mode-1 in the generation and propagation processes, leading to weak dissipation and long-distance propagation. The amplitude of the IGWs increases linearly with the Rossby number in the range 0.04–0.1. Additionally, the IGWs emitted from an anticyclonic vortex are stronger than those radiated from the cyclonic vortex. Anticyclonic and cyclonic geostrophic vortices transfer roughly 0.54% and 0.41% of their kinetic energy to IGWs in this transient generation process, respectively. However, quasi-geostrophic mesoscale eddies are decomposed to balanced geostrophic component and unbalanced near-inertial oscillations with different timescales. Near-inertial waves (NIWs) also can be generated as a forced response to the nonlinear coupling of the geostrophic component and high-frequency oscillations of the quasi-geostrophic eddies. Afterwards, the NIWs resonate with the near-inertial oscillations and share the same horizontal wavenumbers with the eddy. Generally, an anticyclonic mesoscale eddy can emit much stronger NIWs than does a cyclonic eddy. The NIW intensity strengthens exponentially with the Rossby number. The spontaneous generated NIWs represent an effective pathway for mesoscale eddy energy skin and non-negligible contribution to the global NIW energy.</p>

Atmospheric drivers of a 4-month drift of an ice buoy in the Antarctic marginal ice zone

<p>Sea-ice drift in the Antarctic marginal ice zone (MIZ) was investigated by using an ice buoy (buoy U1), deployed during the winter sea-ice expansion in July 2017, and drifted for approximately four months from the South Atlantic sector to the Indian Ocean sector of the Southern Ocean. The analysis of this buoy revealed that it remained within the MIZ even during the winter ice expansion, as the mixed pancake-frazil field was maintained. This allowed for a continued assumption of free drift conditions for buoy U1’s full drift, where it continued to respond linearly to the momentum transfer from surface winds. The analysis of buoy U1 also indicated a strong inertial signature at a period of 13.47 hours however, the wavelet analysis indicated majority of the power remained within the lower frequencies. This strong influence at the lower (multi-day) frequencies has therefore been identified as the primary effect of atmospheric forcing. When these lower frequencies were filtered out using the Butterworth high-pass filter it allowed the inertial oscillations to become more significant within the wavelet power spectrum, where it can be seen that these inertial oscillations were often triggered by the passage of cyclones. The initiation of inertial oscillations of sea ice has therefore been identified as the secondary effect of atmospheric forcing, which dominates ice drift at sub-daily timescales and results in the deviation of ice drift from a straight-line path. This comprehensive analysis suggests that the general concentration-based definition of the MIZ is not enough to describe the sea-ice cover, and that the MIZ, where sea ice is in free drift and under the influence of cyclone induced inertial motion, and presumably waves, extends up to »200 km.</p>

Interaction of nonlinear Ekman pumping, near-inertial oscillations and geostrophic turbulence in an idealized coupled model

A new coupled model is developed to investigate interactions among geostrophic, Ekman and near-inertial (NI) flows. The model couples a time-dependent nonlinear slab Ekman layer with a two-layer shallow water model. Wind stress forces the slab layer and horizontal divergence of slab-layer transport appears as a forcing in the continuity equation of the shallow water model. In one version of the slab model, self-advection of slab-layer momentum is retained and in another it is not. The most obvious impact of this explicit representation of the surface-layer dynamics is in the high-frequency part of the flow. For example, near-inertial oscillations are significantly stronger when self-advection of slab-layer momentum is retained, this being true both for the slab-layer flow itself and for the interior flow that it excites. In addition, retaining the self-advection terms leads to a new instability, which causes growth of slab-layer near-inertial oscillations in regions of anticyclonic forcing and decay in regions of cyclonic forcing. In contrast to inertial instability, it is the sign of the forcing, not that of the underlying vorticity that determines stability. High-passed surface pressure fields are also examined and show the surface signature of unbalanced flow to differ substantially depending on whether a slab-layer model is used and, if so, whether self-advection of slab-layer momentum is retained.

Semidiurnal current dynamics in the Arctic Ocean's eastern Eurasian Basin

<p>In the Arctic Ocean, semidiurnal-band processes including tides and wind-forced inertial oscillations are significant drivers of ice motion, ocean currents and shear contributing to mixing. Two years (2013-2015) of current measurements from seven moorings deployed along 125°E from the Laptev Sea shelf (~50 m) down the continental slope into the deep Eurasian Basin (~3900 m) are analyzed and compared with models of baroclinic tides and inertial motion to identify the primary components of semidiurnal-band current (SBC) energy in this region. The strongest SBCs, exceeding 30 cm/s, are observed during summer in the upper ~30 m throughout the mooring array. The largest upper-ocean SBC signal consists of wind-forced oscillations during the ice-free summer. Strong barotropic tidal currents are only observed on the shallow shelf.  Baroclinic tidal currents, generated along the upper continental slope, can be significant. Their radiation away from source regions is governed by critical latitude effects: the S<sub>2</sub> baroclinic tide (period = 12.000 h) can radiate northwards into deep water but the M<sub>2</sub> (~12.421 h) baroclinic tide is trapped to the continental slope. Baroclinic upper-ocean tidal currents are sensitive to varying stratification, mean flows and sea ice cover.  This time-dependence of baroclinic tides complicates our ability to separate wind-forced inertial oscillations from tidal currents. Since the shear from both sources contributes to upper-ocean mixing that affects the seasonal cycle of the surface mixed layer properties, a better understanding of both, inertial motion and baroclinic tides is needed for projections of mixing and ice-ocean interactions in future Arctic climate states.</p>