Nondimensional parameter regimes of Arctic ice keel-ocean flow interactions

Fangchen Liu, Varvara E Zemskova 

Sea ice keels modulate upper-ocean momentum and mixing through internal wave (IW) generation, yet their effects are difficult to represent in climate models because their spatio-temporal scales are smaller than those of climate models and difficult to study in idealized simulations because geometry, forcing, and stratification span a large parameter space. We construct a compact description of the idealized representation of this problem by deriving five nondimensional parameters: lee-wave radiation potential (χ), IW nonlinearity (J), keel steepness (ζ), mixed-layer depth relative to keel draft (η), and pycnocline strength (Ri). We then calculate these five nondimensional parameters over the Arctic Ocean using monthly data from NEMO–CICE model output over the 2000−2017 time period. After extracting only the data points that fall within the lee wave radiating range (0 < χ < 1) and time-averaging, we apply the unsupervised Gausian Mixture Model (GMM) clustering to find regions with similar nondimensional parameter distributions. GMM reveals mechanically distinct, geographically coherent regions: boundary and marginal seas (Clusters 0−2) versus open-ocean regions that span from the central basin toward shelves (Clusters 3−5). The parameter regimes differ systematically in η and Ri: large η near boundaries implies weak keel–pycnocline coupling, whereas smaller η and steeper keels characterize the central Arctic regions. To diagnose dynamics, we run idealized two-dimensional nonhydrostatic numerical simulations with Boussinesq approximation with nondimensional parameters associated the mean values of each GMM cluster and quantify turbulent kinetic energy dissipation above, within, and below the pycnocline. The boundary regions (Clusters 0−1; η≈27–55) show negligible IW and turbulence response below the pycnocline. The central Arctic regions with larger ζ and J (Clusters 3−5) exhibit enhanced near-pycnocline turbulence, but downward energy propagation is limited where Ri is large (∼290–500) and increases in regions closer to shelves with a smaller Ri value (∼130). Recasting previous IW drag parameterization to a nondimensional form shows it is most sensitive to η, increasing sharply as η →0 and weakly to Ri at fixed η. However, the results of our numerical simulations suggest that there may be some deviations from this parameterization that need to be further explored. Together, the nondimensional framework and clustering bound the physically relevant parameter space, identify where mixed-layer IW-drag parameterizations are credible, and provide concrete target ranges of nondimensional values to use in numerical simulations for calibration of the parameterizations.