Albion Lawrence

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.

Upper-ocean flows are a multi-scale jigsaw puzzle of turbulence and waves. Characterizing these flows is essential for understanding their role in redistributing heat, carbon, and nutrients, yet power spectral analysis cannot always distinguish between types of motion. We show that the scattering transform (ST), a wavelet convolution method, can extract geometric information from flow fields, offering insights beyond the power spectrum. The ST distinguishes balanced dynamics, internal waves, and types of turbulence -- even when their power spectra are identical. Applied to sea surface height (SSH) fields from ocean models, the ST differentiates regions with distinct underlying dynamics. Our analysis offers a framework for interpreting SSH from satellite altimetry missions and for analyzing other spatial maps (e.g., from airborne and coastal radar). More generally, the ST is an appealing way to characterize complex fluid motion in a variety of geophysical contexts.

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 which provide an efficient pathway for NIW propagation to depth. Here we analyse the eigenmodes of NIWs in the presence of mesoscale eddies and heavily draw on parallels with quantum mechanics. Whether the eddies are effective at modulating the behaviour of NIWs depends on the wave dispersiveness $\varepsilon ^2 = f\lambda ^2/\varPsi$, where $\lambda$ is the deformation radius and $\varPsi$ is a scaling for the eddy streamfunction. If $\varepsilon \gg 1$, 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 $\varepsilon \ll 1$, NIWs are weakly dispersive, and the wave evolution is strongly modulated by the eddy field. In this weakly dispersive limit, the Wentzel–Kramers–Brillouin approximation, from which ray tracing emerges, is 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 we find that this effect should be small under oceanic conditions.

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python’s lunch conjecture of Brown et al., the bulge’s area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS _p× S^q p × S q . These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions in terms of collapsing dust shells in the black hole interior. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the statistical origin of the Bekenstein-Hawking entropy.

Final technical report for he DOE QuantISED grant "Structure and Dynamics of Entanglement in Large Quantum Systems", awarded to Profs. Albion Lawrence and Matthew Headrick a Brandeis University. The work on this grant included entanglement in "matrix quantum mechanics", a system wih large numbers of degrees of freedom; the dynamics of a system coupled to a large environment; and the formulation of he "bit threads" picture of entanglement in quantum systems which are equivalent to a theory of quantum gravity.

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 k0 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 [2k0,4k0] and [k0,2k0] peak ∼2 and ∼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 of kinetic energy 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.

Submesoscale flows have been seen in simulations and shipboard data to exhibit qualitative seasonal changes, consistent with submesoscale baroclinic instabilities being activated in deep winter mixed layers. To further test and understand this, we use Jason-2/OSTM satellite data to compute along-track sea surface height (SSH) spectra across the global ocean, for each calendar month. The balanced flow is modeled by a low-wavenumber plateau transitioning to a submesoscale power-law falloff. When tides are weak, we find statistically significant variation with location and season in the parameters describing balanced motion. Our model of the signal and altimeter noise produces a power-law falloff which is closer to the results of numerical models and in situ measurements as compared to prior altimetry-based studies. The power law exponent decreases in the winter and increases in the summer, and there is evidence of kinetic energy moving upwards to larger scales in the months following the month of maximum mixed layer depth. This correlates with the deepening and shoaling of the mixed layer (computed from climatology) and is consistent with shipboard ADCP data.

We study the open system dynamics of a harmonic oscillator "system" coupled to an "environment" of oscillators with an exponential density of states, motivated by holographic models of non-gravitational "little" string theories. We present the Heisenberg equations of motion and the quantum master equation for the system, and develop a renormalization procedure to manage the divergences, which are exponential in the cutoff. We provide evidence that the renormalized system dynamics is Markovian even when the initial state of the environment is the instantaneous ground state.