Short-wave vortex instability in stratified flow

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.euromechflu.2015.08.005. © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we investigate a new instability of the Lamb–Chaplygin dipole in a stratified fluid. Through numerical linear stability analysis, a secondary peak in the growth rate emerges at vertical scales about an order of magnitude smaller than the buoyancy scale Lb=U/NLb=U/N where U is the characteristic velocity and N is the Brunt–Väisälä frequency. This new instability exhibits a growth rate that is similar to, and even exceeds, that of the zigzag instability, which has the characteristic length of the buoyancy scale. This instability is investigated for a wide range of Reynolds numbers, Re=2000–20000, and horizontal Froude numbers, Fh=0.05–0.2, where Fh=U/NR, Re=UR/ν, R is the radius of the dipole, and ν is the kinematic viscosity. A range of vertical scales is explored from above the buoyancy scale to the viscous damping scale. Additionally, evidence is presented that the length scale and growth rate of this new instability are partially determined by the buoyancy Reynolds number, Reb=Fh^2Re.Natural Sciences and Engineering Research Council || RGPIN/386456-201

Short-wave vortex instabilities in stratified flow

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio

Constraining alternative theories of gravity using GW150914150914 and GW151226151226

The recently reported gravitational wave events GW$150914$ and GW$151226$ caused by the mergers of binary black holes [arXiv:1602.03841],[arXiv:1606.04855],[arXiv:1606.04856] provide a formidable way to set constraints on alternative metric theories of gravity in the strong field regime. In this paper, we develop an approach where an arbitrary theory of gravity can be parametrised by an effective coupling $G_{eff}$ and an effective gravitational potential $\Phi(r)$. The standard Newtonian limit of General Relativity is recovered as soon as $G_{eff}\rightarrow G_N$ and $\Phi(r)\rightarrow \Phi_{N}$. The upper bound on the graviton mass and the gravitational interaction length, reported by the LIGO-VIRGO collaboration, can be directly recast in terms of the parameters of the theory which allows an analysis where the gravitational wave frequency modulation sets constraints on the range of possible alternative models of gravity. Numerical results based on published parameters for the binary black hole mergers are also reported. Comparison of the observed phase of the GW$150914$ and GW$151226$ with the modulated phase in alternative theories of gravity does not give reasonable constraints due the large uncertainties in the estimated parameters for the coalescing black holes. In addition to these general considerations, we obtain limits for the frequency dependence of the $\alpha$ parameter in scalar tensor theories of gravity.Comment: 11 pages, 3 figures, accepted for publication in Phys. Rev. D. arXiv admin note: text overlap with arXiv:gr-qc/0412088 by other author

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wide range of application areas. Applications powered by ExaHyPE can be run on a student’s laptop, but are also able to exploit thousands of processor cores on state-of-the-art supercomputers. The engine is able to dynamically increase the accuracy of the simulation using adaptive mesh refinement where required. Due to the robustness and shock capturing abilities of ExaHyPE’s numerical methods, users of the engine can simulate linear and non-linear hyperbolic PDEs with very high accuracy. Users can tailor the engine to their particular PDE by specifying evolved quantities, fluxes, and source terms. A complete simulation code for a new hyperbolic PDE can often be realised within a few hours — a task that, traditionally, can take weeks, months, often years for researchers starting from scratch. In this paper, we showcase ExaHyPE’s workflow and capabilities through real-world scenarios from our two main application areas: seismology and astrophysics

Macroscopic and microscopic post-merger dynamics in binary neutron stars

In this thesis I develop a new technique of the use of tracers to study problems in the micro- and macroscopic aspects of post-merger dynamics in binary neutron star mergers, with particular attention to the dynamical ejecta and resulting r-process nucleosynthesis

Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers

Inferring the properties of dense matter is one of the most exciting prospects from the measurement of gravitational waves from neutron star mergers. However, it requires reliable numerical simulations that incorporate viscous dissipation and energy transport as these can play a significant role in the survival time of the post-merger object. We calculate time scales for typical forms of dissipation and find that thermal transport and shear viscosity will not be important unless neutrino trapping occurs, which requires temperatures above 10 MeV and gradients over length scales of 0.1 km or less. On the other hand, if direct-Urca processes remain suppressed, leaving modified-Urca processes to establish flavor equilibrium, then bulk viscous dissipation could provide significant damping to density oscillations right after merger. When comparing with data from state-of-the-art merger simulations, we find that the bulk viscosity takes values close to its resonant maximum in a typical merger, motivating a more careful assessment of the role of bulk viscous dissipation in the gravitational-wave signal from merging neutron stars