arXiv subjects

Jörn Callies

Publications and source records attributed to Jörn Callies.

13 recordsLinked to original sources

arXiv2026

Energetics of frontogenesis in simple balanced models

Submesoscale fronts have been proposed to act as conduits funneling kinetic energy from geostrophically constrained mesoscale eddies down to small scales, where the energy can be dissipated. Realistic primitive-equation simulations suggest that the downscale energy transfer at submesoscales is strongly concentrated in sharpening fronts, with convergence on the cyclonic side playing a dominant role. This study explores how much of this phenomenology can be captured by simple quasi-geostrophic (QG) and semi-geostrophic (SG) theories of frontogenesis. An analysis of the kinetic energy budget of classical strain-induced frontogenesis shows that there is downscale transfer in both QG and SG fronts. In QG frontogenesis, the narrowing jet along the sharpening front is powered by buoyancy production, but geostrophic downscale transfer due to the strain field plays an important role. In SG frontogenesis, where frontal sharpening is accelerated by the ageostrophic cross-frontal circulation, ageostrophic advection enhances this downscale transfer on the cyclonic side of the front, where the surface flow is convergent. On the anticyclonic side, where the ageostrophic circulation is divergent, the ageostrophic scale transfer of kinetic energy is upscale and partially offsets the geostrophic downscale transfer. While matching patterns in realistic primitive-equation simulations, the ageostrophic scale transfers remain important but not dominant in the adiabatic and frictionless theory considered here. This suggests that processes absent from these theories may play an important role. For example, mixed-layer turbulence may enhance the ageostrophic circulation and the associated dipole of scale transfers. The advection of ageostrophic momentum may also be important in some circumstances.

physics.ao-ph↗

arXiv2026

Orthogonality of coastal trapped waves

Coastal trapped wave modes are shown to be orthogonal in the sense that they make independent contributions to the energy of the wave field. The hydrostatic Boussinesq dynamics on an $f$-plane, linearized around a state of rest, are formulated as a (generalized) Schrödinger equation, which exposes the Hermitian structure of the wave operator that implies the orthogonality of eigenmodes. This formulation, which becomes particularly simple in weak form, is parlayed into a finite-element discretization that preserves the symmetries of the original problem and therefore the energy conservation and orthogonality of modes. The geostrophic momentum approximation, under which the orthogonality of modes has been recognized previously, is reprised and discussed in the present context to emphasize that low-frequency coastal trapped waves are edge waves. Their dynamics are governed by boundary potential-vorticity anomalies, both Bretherton-type contributions familiar from the quasi-geostrophic equations and lateral contributions that are important for steep slopes and coastal walls.

physics.ao-ph↗

arXiv2025

Isolating Balanced Ocean Dynamics in SWOT Data

The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional sea surface height (SSH) maps at unprecedented resolution, but its signal is a combination of balanced meso- and submesoscale turbulence, unbalanced internal waves, and small-scale noise. Interpreting the meso- and submesoscale flow features captured by SWOT requires a careful isolation of the balanced signal. We present a statistical method to do so in regions where internal-wave signals are negligible, such as western boundary current regions and the Southern Ocean. Our method assumes Gaussian statistics for both the balanced flow and the noise, which we infer by fitting parametric models to the observed SSH wavenumber spectrum. Using these inferred parameters, we perform a Bayesian inversion to reconstruct swath-aligned SSH maps that fill the nadir gap. We evaluate the method using synthetic data from a high-resolution simulation with realistic SWOT-like noise added. Comparisons with the underlying model data show that our reconstruction successfully removes small-scale noise while preserving meso- and submesoscale eddies, fronts, and filaments down to a feature scale of 10km. The comparison also demonstrates that the posterior uncertainty is a reliable estimate of the error.

physics.ao-ph↗

arXiv2025

Assessing submesoscale sea surface height signals from the SWOT mission

The sea surface height (SSH) field measured by Surface Water and Ocean Topography (SWOT) mission's wide-swath altimeter is analyzed with a focus on submesoscale features. Along-track wavenumber spectra of SSH variance are estimated for the global ocean using the 1-day repeat period from March 26 to July 10, 2023. In regions with an energetic mesoscale eddy field, the spectra have a mesoscale plateau, a steep drop-off due to balanced submesoscale turbulence, and a much flatter power-law tail at small scales. These spectra are characterized by fitting a spectral model. For the balanced signal, this fit yields a power law exponent between -4 and -6 for most regions, broadly consistent with expectations and previous observations. The amplitude of the distinct small-scale signal, which typically dominates at wavelengths less than 30 to 50 km, is strongly correlated in time and space with the height of surface gravity waves, suggesting aliased wave signals as the most likely source. A simple method is proposed to isolate the balanced signal in regions with negligible internal tides. Maps of the balanced signal in the Antarctic Circumpolar Current show compact cyclones with geostrophic relative vorticities frequently in excess of the local planetary vorticity, challenging the quasi-geostrophic framework commonly used to interpret altimetric data.

physics.ao-ph↗

arXiv2025

Closure of the sea surface height budget with a Stokes offset

The sea surface height budget, obtained by integrating hydrostatic balance over the water column, relates sea surface height variations to variations of the seafloor pressure, density in the water column, and atmospheric surface pressure. This budget is crucial for calibrating and interpreting satellite altimetry measurements. It only holds once non-hydrostatic surface gravity waves are averaged out, however, which complicates an observational closure of the budget. Using data from the California Current System, this study demonstrates that the budget closes to within understood uncertainties if GPS buoy measurements of surface height are interpreted as Lagrangian measurements. The buoy largely follows wave motion and spends slightly more time near wave crests than troughs. The associated Stokes offset, which reaches a maximum of 16 cm in these observations, must be accounted for in the Eulerian sea surface height budget.

physics.ao-ph↗

arXiv2025

Global Near-Inertial Wave Spectra Shaped by Mesoscale Eddies

Wind-forced near-inertial waves (NIWs) propagate through a sea of mesoscale eddies, which can fundamentally alter their evolution. The nature of this NIW--mesoscale interaction depends on how dispersive the waves are. For weakly dispersive waves, ray tracing suggests that the NIW frequency should be shifted by $\frac{1}{2}ζ$, where $ζ$ is the mesoscale vorticity, and that the waves are refracted into anticyclones. Strongly dispersive waves, in contrast, retain the large-scale structure of the wind forcing and exhibit a small negative frequency shift. Previous in situ observational studies have indeed revealed varying degrees of NIW--mesoscale interaction. Here, observations of NIWs from drifters are used to map the geography of NIW--mesoscale interactions globally, and idealized simulations and a simple model are used to identify the underlying physical processes. Almost everywhere in the ocean, with the notable exception of the North Pacific, the NIW frequency is strongly modulated by the mesoscale vorticity, with the slope of the frequency shift vs. vorticity taking values of approximately $0.4$. Concentration of NIW energy into anticyclones is a common feature throughout the ocean. Other aspects of the observations, however, show signatures of strongly dispersive waves: a negative frequency shift and weaker concentration into anticyclones in regions with strong eddies as well as weak modulation of the NIW frequency by mesoscale eddies in the North Pacific. The signatures of both weakly and strongly dispersive NIW behavior can be rationalized by the geography of the wave dispersiveness and the fact that wind forcing excites multiple vertical modes with different wave dispersiveness. These results have implications for NIW-induced mixing in the upper-ocean.

physics.ao-ph↗

arXiv2024

Regimes of Near-Inertial Wave Dynamics

When atmospheric storms pass over the ocean, they resonantly force near-inertial waves (NIWs); internal waves with a frequency close to the local Coriolis frequency $f$. It has long been recognised that the evolution of NIWs is modulated by the ocean's mesoscale eddy field. This can result in NIWs being concentrated into anticyclones and provide an efficient pathway for their propagation to depth. Whether mesoscale eddies are effective at modulating the behaviour of NIWs depends on the wave dispersiveness $\varepsilon^2 = fλ^2/Ψ$, where $λ$ is the deformation radius and $Ψ$ is a scaling for the eddy streamfunction. If $\varepsilon\gg1$, NIWs are strongly dispersive, and the waves are only weakly affected by the eddies. We calculate the perturbations away from a uniform wave field and the frequency shift away from $f$. If $\varepsilon\ll1$, NIWs are weakly dispersive, and the wave evolution is strongly modulated by the eddy field. In this weakly dispersive limit, ray-tracing emerges as a valid description of the NIW evolution even if the large-scale atmospheric forcing apparently violates the requisite assumption of a scale separation between the waves and the eddies. The large-scale forcing excites many wave modes, each of which varies on a short spatial scale and is amenable to asymptotic analysis analogous to the semi-classical analysis of quantum systems. The strong modulation of weakly dispersive NIWs by eddies has the potential to modulate the energy input into NIWs from the wind, but under oceanic conditions, this effect should be small.

physics.ao-ph↗

arXiv2024

Interpreting Observed Interactions between Near-Inertial Waves and Mesoscale Eddies

The evolution of wind-generated near-inertial waves (NIWs) is known to be influenced by the mesoscale eddy field, yet it remains a challenge to disentangle the effects of this interaction in observations. Here, the model of Young and Ben Jelloul (YBJ), which describes NIW evolution in the presence of slowly evolving mesoscale eddies, is compared to observations from a mooring array in the Northeast Atlantic Ocean. The model captures the evolution of both the observed NIW amplitude and phase much more accurately than a slab mixed layer model. The YBJ model allows for the identification of specific physical processes that drive the observed evolution. It reveals that differences in the NIW amplitude across the mooring array are caused by the refractive concentration of NIWs into anticyclones. Advection and wave dispersion also make important contributions to the observed wave evolution. Stimulated generation, a process by which mesoscale kinetic energy acts as a source of NIW potential energy, is estimated to be 20$μ$W/m$^2$ in the region of the mooring array, which is two orders of magnitude smaller than the global average input to mesoscale kinetic energy and likely not an important contribution to the mesoscale kinetic energy budget in this region. Overall, the results show that the YBJ model is a quantitatively useful tool to interpret observations of NIWs.

physics.ao-ph↗

arXiv2023

Vertical-slice ocean tomography with seismic waves

Seismically generated sound waves that propagate through the ocean are used to infer temperature anomalies and their vertical structure in the deep East Indian Ocean. These T waves are generated by earthquakes off Sumatra and received by hydrophone stations off Diego Garcia and Cape Leeuwin. Between repeating earthquakes, a T wave's travel time changes in response to temperature anomalies along the wave's path. What part of the water column the travel time is sensitive to depends on the frequency of the wave, so measuring travel time changes at a few low frequencies constrains the vertical structure of the inferred temperature anomalies. These measurements reveal anomalies due to equatorial waves, mesoscale eddies, and decadal warming trends. By providing direct constraints on basin-scale averages with dense sampling in time, these data complement previous point measurements that alias local and transient temperature anomalies.

physics.ao-ph↗

arXiv2023

Coupling Between Abyssal Boundary Layers and the Interior Ocean in the Absence of Along-Slope Variations

To close the overturning circulation, dense bottom water must upwell via turbulent mixing. Recent studies have identified thin bottom boundary layers (BLs) as locations of intense upwelling, yet it remains unclear how they interact with and shape the large-scale circulation of the abyssal ocean. The current understanding of this BL--interior coupling is shaped by 1D theory, suggesting that variations in locally produced BL transport generate exchange with the interior and thus a global circulation. Until now, however, this picture has been based on a 1D theory that fails to capture the local evolution in even highly idealized 2D geometries. The present work applies BL theory to revised 1D dynamics, which more naturally generalizes to two and three dimensions. The BL is assumed to be in quasi-equilibrium between the upwelling of dense water and the convergence of downward buoyancy fluxes. The BL transport, for which explicit formulae are presented, exerts an influence on the interior by modifying the bottom boundary condition. In 1D, this BL transport is independent of the interior evolution, but in 2D the BL and interior are fully coupled. Once interior variables and the bottom slope are allowed to vary in the horizontal, the resulting convergences and divergences in the BL transport exchange mass with the interior. This framework allows for the analysis of previously inaccessible problems such as the BL--interior coupling in the presence of an exponential interior stratification, laying the foundation for developing a full theory for the abyssal circulation.

physics.ao-ph↗

arXiv2022

Rapid Spin Up and Spin Down of Flow Along Slopes

The near-bottom mixing that allows abyssal waters to upwell tilts isopycnals and spins up flow over the flanks of mid-ocean ridges. Meso- and large-scale currents along sloping topography are subjected to a delicate balance of Ekman arrest and spin down. These two seemingly disparate oceanographic phenomena share a common theory, which is based on a one-dimensional model of rotating, stratified flow over a sloping, insulated boundary. This commonly used model, however, lacks rapid adjustment of interior flows, limiting its ability to capture the full physics of spin up and spin down of along-slope flow. Motivated by two-dimensional dynamics, the present work extends the one-dimensional model by constraining the vertically integrated cross-slope transport and allowing for a barotropic cross-slope pressure gradient. This produces a closed secondary circulation by forcing Ekman transport in the bottom boundary layer to return in the interior. The extended model can thus capture Ekman spin up and spin down physics: the interior return flow is turned by the Coriolis acceleration, leading to rapid \linelabel{ll:slowdiff}rather than slow diffusive adjustment of the along-slope flow. This transport-constrained one-dimensional model accurately describes two-dimensional mixing-generated spin up over an idealized ridge and provides a unified framework for understanding the relative importance of Ekman arrest and spin down of flow along a slope.

physics.ao-ph↗

arXiv2022

Seasonality and spatial dependence of meso- and submesoscale ocean currents from along-track satellite altimetry

Along-track wavenumber spectral densities of sea surface height (SSH) are estimated from Jason-2 altimetry data as a function of spatial location and calendar month, to understand the seasonality of meso- and submesoscale balanced dynamics across the global ocean. Regions with significant mode-1 and mode-2 baroclinic tides are rejected, restricting the analysis to the extratropics. Where balanced motion dominates, the SSH spectral density is averaged over all pass segments in a region for each calendar month, and is fit to a 4-parameter model consisting of a flat plateau at low wavenumbers, a transition at wavenumber $k_0$ to a red power law spectrum $k^{-s}$, and a white spectrum at high wavenumbers that models the altimeter noise. The monthly time series of the model parameters are compared to the evolution of the mixed layer. The annual mode of the spectral slope $s$ reaches a minimum after the mixed layer deepens, and the annual mode of the bandpassed kinetic energy in the ranges $[2k_0,4 k_0]$ and $[k_0,2 k_0]$ peak $\sim$2 and $\sim$4 months, respectively, after the maximum of the annual mode of the mixed layer depth. This analysis is consistent with an energization of the submesoscale by a winter mixed layer instability followed by an inverse cascade to the mesoscale, in agreement with prior modeling studies and in situ measurements. These results are compared to prior modeling, in situ, and satellite investigations of specific regions, and are broadly consistent with them within measurement uncertainties.

physics.ao-ph↗

arXiv2021

Direct numerical simulation of low Reynolds number oscillating boundary layers on adiabatic slopes

We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. Such conditions are typical of the boundary layers generated by low wavenumber internal tides sloshing up and down adiabatic abyssal slopes in the absence of mean flows, high wavenumber internal tides, and resonant tide-bathymetry interactions. We examine flows within a region of non-dimensional parameter space typical of the mid- to low-latitude oceanic $M_2$ tides on hydraulically smooth abyssal slopes by direct numerical simulation. We find that at low Reynolds numbers transition-to-turbulence pathways arise from both shear and gravitational instabilities, and we find that the boundary layers are stabilized by increased outer boundary layer stratification during the downslope oscillation phase. However, if rotation is significant (low slope Burger numbers) we find that boundary layer turbulence is sustained throughout the oscillation period, resembling Stokes-Ekman layer turbulence. Our results suggest that oscillating boundary layers on smooth abyssal slopes created by low wavenumber $M_2$ tides do not cause significant irreversible turbulent buoyancy flux (mixing) and that flat-bottom dissipation rate models derived from the tide amplitude are accurate within an order of magnitude.

physics.flu-dyn↗