Instability of the halocline at the North Pole

TL;DR

This work analyzes the stability of near-inertial Pollard waves as a model for the Arctic halocline by applying a short-wavelength instability framework to a three-layer Lagrangian flow. The authors derive an explicit instability criterion: instability occurs when the wave steepness $ka e^{-ms}$ exceeds a threshold $\mathscr{T}(\mathfrak{g}, \mathsf{c}_0)$ that is computed from the dispersion relation $c^2 = \frac{f^2}{k^2} + \frac{f^4 \mathsf{c}_0^2}{\mathfrak{g}^2 k^2}$ and water-column properties, where $f=2\Omega$ and $\mathfrak{g}$ is a reduced gravity. The analysis shows that the instability is more likely at the base of the halocline, with the threshold increasing with the mean current $|\mathsf{c}_0|$ and decreasing with $\mathfrak{g}$, and ties these findings to observed halocline weakening and potential mixing between halocline waters and Atlantic Water. The framework provides a direct, parameter-driven way to assess halocline stability from physical properties of the water column.

Abstract

In this paper we address the issue of stability for the near-inertial Pollard waves, as a model for the halocline in the region of the Arctic Ocean centered around the North Pole, derived in Puntini (2025a). Adopting the short-wavelength instability approach, the stability of such flows reduces to study the stability of a system of ODEs along fluid trajectories, leading to the result that, when the steepness of the near-inertial Pollard waves exceeds a specific threshold, those waves are linearly unstable. The explicit dispersion relation of the model allows to easily compute such threshold, knowing the physical properties of the water column.

Figures (4)

• Figure 1: A depiction of the model we are considering developed in mio, consisting of 3 layer: the surface mixed layer (of density $\rho_0$) at which bottom the mean surface current is present, the halocline layer (of density $\rho_1$) and the bottom layer consisting of Atlantic Water (AW) with density $\rho_2$. The halocline layer is described by nonlinear near-inertial Pollard waves with amplitude increasing with depth, and which induce a wave motion at the bottom of the surface layer. The wave amplitude in this picture is not to scale.
• Figure 2: Depiction of the basis at the North Pole, with $\mathbf{e}_x$ aligned with the Transpolar Drift Current and $\mathbf{e}_y$ perpendicular to it. The $\mathbf{e}_z$-axis, as usual, points upward.
• Figure 3: Evolution of a high-frequency wavelet disturbance along the basic flow.
• Figure 4: Graph of the threshold $\mathscr{T}$ as a function of $\mathfrak{g}$ and $\mathsf{c}_0$, with $\mathfrak{g}\in [5\cdot10^{-4},2\cdot10^{-2}]$ (left) and $\mathfrak{g}$ limited to $\mathfrak{g}\in [5\cdot10^{-3},2\cdot10^{-2}]$ (right). In both pictures, $\mathsf{c}_0\in[0, 0.15]$.