Realizing Surface Driven Flows in the Primitive Equations

The surface quasi-geostrophic (SQG) model describes the evolution of buoyancy at vertical boundaries in the limit of infinitesimal Rossby number. In this regime, the quasi-geostrophic approximations are expected to hold. Numerical simulation of the SQG model often generate small-scale vortices which may have Rossby numbers that approach unity and may be outside the range of SQG. In this thesis we investigate the evolution of a surface trapped elliptical vortex in both the SQG model and the non-hydrostatic Boussinesq primitive equations (PE) which are better able to describe a wider range of oceanic dynamics. Thus, in the PE, we can vary the Rossby number in order to understand how the surface trapped vortex breaks down at the smaller-scale during its evolution. For small Rossby number, we confirm that the PE match the SQG prediction very well. For larger Rossby number however, we find that the models do not agree and different dynamics begin emerging in the PE. In particular, we find that the thin filament instability in the surface buoyancy field, common to SQG, begins to stabilize as the Rossby number increases and thus the emergence of the secondary small-scale vortices is halted. The core of the vortex spreads out and becomes much more uniform for larger Rossby number. The energy spectrum of the surface trapped vortex steepens from a power law of -5/3 to about -3 and the divergent energy grows as the Rossby number approaches unity. The growing divergent energy is an indication that inertia-gravity waves are generated in the simulation and we do indeed observe these in the vertical velocity field. We conclude that when the Rossby number of the surface trapped elliptical vortex is at least 0.05 new dynamics emerge and the PE must be used to attain an accurate description of the evolution of the flow

Realizing surface driven flows in the primitive equations

© Copyright 2015 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (https://www.ametsoc.org/) or from the AMS at 617-227-2425 or [email protected] surface quasigeostrophic (SQG) model describes flows with surface buoyancy perturbations with no interior quasigeostrophic potential vorticity at small Rossby number Ro and O(1) Burger number, where quasigeostrophic dynamics are expected to hold. Numerical simulations of SQG dynamics have shown that vortices are frequently generated at small scales, which may have O(1) Rossby numbers and therefore may be beyond the limits of SQG. This paper examines the dynamics of an initially geostrophically balanced elliptical surface buoyancy perturbation in both the SQG model and the nonhydrostatic Boussinesq primitive equations (PE). In the case of very small Rossby number, it is confirmed that both models agree, as expected. For larger Ro, non-SQG effects emerge and as a result the solution of the PE deviates significantly from that of SQG. In particular, an increase in the Rossby number has the following effects: (i) the buoyancy filaments at the surface are stabilized in that they generate fewer secondary vortices; (ii) the core of the vortex experiences inertial instability, which results in a uniform buoyancy profile in its interior; (iii) the divergent part of the energy spectrum increases in magnitude; (iv) the PE model has significantly more gravity waves that are radiated from the vortex; (v) the magnitude of the vertical velocity increases; and (vi) in the mature stages of evolution, there are gravitational instabilities that develop because of the complicated dynamics inside the vortex. It is demonstrated that significant non-SQG effects are evident when the large-scale Rossby number of the initial flow is about 0.05 and the local Rossby number is O(1).Natural Sciences and Engineering Research Council || RGPIN/386456-201

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function $Z(t)$ and diffusion coefficient $D$. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for $Z(t)$ and $D$ agree remarkably well with MD simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and cond-mat/0002058 combined Minor changes made to coincide with published versio

Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution

Although fluorescence microscopy provides a crucial window into the physiology of living specimens, many biological processes are too fragile, are too small, or occur too rapidly to see clearly with existing tools. We crafted ultrathin light sheets from two-dimensional optical lattices that allowed us to image three-dimensional (3D) dynamics for hundreds of volumes, often at subsecond intervals, at the diffraction limit and beyond. We applied this to systems spanning four orders of magnitude in space and time, including the diffusion of single transcription factor molecules in stem cell spheroids, the dynamic instability of mitotic microtubules, the immunological synapse, neutrophil motility in a 3D matrix, and embryogenesis in Caenorhabditis elegans and Drosophila melanogaster. The results provide a visceral reminder of the beauty and the complexity of living systems