arXiv subjects

Christian Puntini

Publications and source records attributed to Christian Puntini.

8 recordsLinked to original sources

arXiv2026

Why a mid-depth stress-free boundary condition is incorrect for Ekman flows

We show that the assumption of a stress-free boundary condition at a finite intermediate depth, namely, at the bottom of the Ekman layer, in the analysis of wind-driven ocean flows necessarily leads to an unphysical current profile. Indeed, if the $z$-derivative of the fluid velocity vanishes at a given depth, then this depth necessarily corresponds to a minimum of the velocity profile, with the velocity increasing beneath it. Using a WKB ansatz based on the small variations of the ocean's water density at great depths, we also argue that a no-slip condition at the bottom of the ocean, if sufficiently deep, still effectively implies (up to a very small error) the orthogonality of the Ekman transport and the wind-stress.

physics.flu-dyn↗

arXiv2026

Instability of the halocline at the North Pole

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 (2026). 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.

physics.geo-ph↗

arXiv2026

Near-Inertial Pollard Waves Modeling the Arctic Halocline

We present an explicit and exact solution to the governing equations describing the vertical structure of the Arctic Ocean region centred around the North Pole. The solution describes a stratified water column with three constant-density regions: a motionless bottom layer, a middle layer -- the halocline -- described by nonhydrostatic, near-inertial Pollard waves, and an upper layer presenting a mean current and a wave motion associated with the one in the halocline layer.

physics.ao-ph↗

arXiv2026

On the instability of some upward propagating, exact, nonlinear mountain waves

Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. A: Math. Theor.} (2023), under the assumption of a dry adiabatic flow. Within this approach, the stability problem reduces to analysing a system of ordinary differential equations along fluid trajectories. Our results show that the flow becomes unstable when the wave steepness exceeds the critical threshold of $\frac{1}{3}$. Given the representation of the solution in Lagrangian coordinates, the instability analysis will show the existence of an unstable layer beneath the tropopause, where instability may occur, finally leading to a chaotic 3-dimensional fluid motion.

physics.ao-ph↗

arXiv2026

On large-scale wind-drift ocean currents: An asymptotic approach in spherical coordinates

Starting from the Navier--Stokes equations in rotating spherical coordinates with depth-varying density and eddy viscosity, we derive an asymptotic model describing non-equatorial wind-generated ocean drift currents. Our approach allows for large-scale flows that cannot be captured by classical tangent-plane approximations. The strategy is to perform a careful scaling and to perform a double asymptotic expansion with respect to two small parameters arising from the scaling: the Rossby number and the ratio between the Ekman depth and the Earth's radius. We obtain a system of linear ordinary differential equations with nonlinear boundary conditions governing the leading-order dynamics, highlighting that the dynamics is governed by the linear terms, whereas the nonlinear ones, related to the injection and dissipation of kinetic energy, appear only at higher order. We use the leading-order equations to compare our model with the simplest theory of ocean circulation due to Sverdrup and note that, even at this level of simplification, our equations have the potential to provide deeper insight. Subsequently, focusing on Ekman flows, we prove existence and uniqueness of the leading-order solution, which retains the classical Ekman spiral structure for arbitrary eddy viscosity profiles. Finally, we compute the surface deflection angle of the wind-driven current for three explicit eddy viscosity profiles, obtaining results consistent with observations. In addition, we derive the governing equations for the first-order correction with respect to the Rossby number and provide a priori bounds for its solution.

physics.flu-dyn↗

arXiv2025

Nonlinear Dynamics of Wind-Drift Currents at Mid-Latitudes

Starting from the Navier-Stokes equation in the $f$-plane approximation, we provide an exact and explicit solution of the governing equations at leading order for fluid flows in the upper layer of the ocean at mid-latitudes, driven by a wind stress. Such a solution highlights the presence of a mean Ekman current superimposed to trochoidal oscillations and a background geostrophic current.

physics.flu-dyn↗

arXiv2025

On the modeling of nonlinear wind-induced ice-drift ocean currents at the North Pole

Starting from the governing equations for geophysical flows, by means of a thin-shell approximation and a tangent plane approximation, we derive the equations describing, at leading order, the nonlinear ice-drift flow for regions centered around the North Pole. An exact solution is derived in the material/Lagrangian formalism, describing a superposition of oscillations, a mean Ekman flow and a geostrophic current.

physics.flu-dyn↗

arXiv2025

Shielding of breathers for the focusing nonlinear Schrödinger equation

We study a deterministic gas of breathers for the Focusing Nonlinear Schrödinger equation. The gas of breathers is obtained from a $N$-breather solution in the limit $N\to \infty$.\\ The limit is performed at the level of scattering data by letting the $N$-breather spectrum to fill uniformly a suitable compact domain of the complex plane in the limit $N\to\infty$. The corresponding norming constants are interpolated by a smooth function and scaled as $1/N$. For particular choices of the domain and the interpolating function, the gas of breathers behaves as finite breathers solution. This extends the shielding effect discovered in "M. Bertola, T. Grava, and G. Orsatti - Physical Review Letters, 130.12 (2023): 1" for a soliton gas also to a breather gas.

nlin.SI↗