In this study, we use measurements from over 4,735 globally distributed Global Navigation Satellite System receivers to track the progression of traveling ionospheric disturbances (TIDs) associated with the 15 January 2022 Hunga Tonga‐Hunga Ha'apai submarine volcanic eruption. We identify two distinct Large Scale traveling ionospheric disturbances (LSTIDs) and several subsequent Medium Scale traveling ionospheric disturbances (MSTIDs) that propagate radially outward from the eruption site. Within 3,000 km of epicenter, LSTIDs of >1,600 km wavelengths are initially observed propagating at speeds of ∼950 and ∼555 ms−1, before substantial slowing to ∼600 and ∼390 ms−1, respectively. MSTIDs with speeds of 200–400 ms−1 are observed for 6 hrs following eruption, the first of which comprises the dominant global ionospheric response and coincides with the atmospheric surface pressure disturbance associated with the eruption. These are the first results demonstrating the global impact of the Tonga eruption on the ionospheric state.

Abstract.A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Möbius ribbon, for which the central curve is a circle about which the line segment executes a 180 • twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Möbius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

We investigate the effect of large curvature and dipolar energy in thin ferromagnetic films with periodically modulated top and bottom surfaces on magnetization behavior. We predict that the dipolar interaction and surface curvature can produce perpendicular anisotropy which can be controlled by engineering special types of periodic surface structures. Similar effects can be achieved by a significant surface roughness in the film. We demonstrate that, in general, the anisotropy can point in an arbitrary direction depending on the surface curvature. Furthermore, we provide simple examples of these periodic surface structures to show how to engineer particular anisotropies in thin films.

Generalized Lagrangian mean theories are used to analyze the interactions between mean flows and fluctuations, where the decomposition is based on a Lagrangian description of the flow. A systematic geometric framework was recently developed by Gilbert and Vanneste (J. Fluid Mech., 2018) who cast the decomposition in terms of intrinsic operations on the group of volume preserving diffeomorphism or on the full diffeomorphism group. In this setting, the mean of an ensemble of maps can be defined as the Riemannian center of mass on either of these groups. We apply this decomposition in the context of Lagrangian averaging where equations of motion for the mean flow arise via a variational principle from a mean Lagrangian, obtained from the kinetic energy Lagrangian of ideal fluid flow via a small amplitude expansion for the fluctuations.We show that the Euler-α equations arise as Lagrangian averaged Euler equations when using the L 2 -geodesic mean on the volume preserving diffeomorphism group of a manifold without boundaries, imposing a "Taylor hypothesis", which states that first order fluctuations are transported as a vector field by the mean flow, and assuming that fluctuations are statistically isotropic. Similarly, the EPDiff equations arise as the Lagrangian averaged Burgers' equations using the same argument on the full diffeomorphism group. These results generalize an earlier observation by Oliver (Proc. R. Soc. A, 2017) to manifolds in geometrically fully intrinsic terms.

We derive a family of balance models for rotating stratified flow in the primitive equation setting. By construction, the models possess conservation laws for energy and potential vorticity and are formally of the same order of accuracy as Hoskins' semigeostrophic equations. Our construction is based on choosing a new coordinate frame for the primitive equation variational principle in such a way that the consistently truncated Lagrangian degenerates. We show that the balance relations so obtained are elliptic when the fluid is stably stratified and certain smallness assumptions are satisfied. Moreover, the potential temperature can be recovered from the potential vorticity via inversion of a non-standard Monge-Ampère problem which is subject to the same ellipticity condition. While the present work is entirely formal, we conjecture, based on a careful rewriting of the equations of motion and a straightforward derivative count, that the Cauchy problem for the balance models is well posed subject to conditions on the initial data. Our family of models includes, in particular, the stratified analog of the L 1 balance model of R. Salmon.

In this article we derive the equations for a rotating stratified fluid governed by inviscid Euler-Boussinesq and primitive equations that account for the effects of the perturbations upon the mean. Our method is based on the concept of geometric generalized Lagrangian mean recently introduced by Gilbert and Vanneste, combined with generalized Taylor and horizontal isotropy of fluctuations as turbulent closure hypotheses. The models we obtain arise as Euler-Poincaré equations and inherit from their parent systems conservation laws for energy and potential vorticity. They are structurally and geometrically similar to Euler-Boussinesq-α and primitive equations-α models, however feature a different regularizing second order operator.

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.