5 research outputs found
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Nonlinear hydrodynamic instability and turbulence in eccentric astrophysical discs
The nonlinear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at mean-motion resonances, most prominently via the 3:1 eccentric Lindblad resonance in circumstellar binaries. However, the details of an efficient saturation mechanism for this growth are still not fully understood. Linear theory for the parametric instability of inertial waves in eccentric discs has previously been studied by Barker and Ogilvie (2014), the nonlinear evolution of which dictates the transport rates and may help saturate this unmitigated eccentricity growth. This thesis develops a generalised numerical model for an eccentric quasi-axisymmetric shearing box based on the theoretical model developed by Ogilvie and Barker (2014) which itself generalises the often-used local cartesian shearing box model. The numerical method is an overall 2nd order well-balanced finite volume method which maintains the stratified and oscillatory steady state solution to machine precision.
This implementation is employed to study the nonlinear outcome of this parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the midplane, and localises the effective region of the secondary instability. A saturated marginally sonic turbulent state is then maintained by the breaking of inertial waves cascading energy into smaller scales. The resulting turbulence is quite inefficient at transporting angular momentum through the disc, as might be expected from a restricted axisymmetric instability. Still, the saturation of this parametric instability of inertial waves is shown to damp the eccentricity on the timescale of 50 to 100 orbital periods, and so is a promising mechanism for balancing the exponential growth of eccentricity from the eccentric Lindblad resonances
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On the evolution & equilibration of submesoscale fronts
Submesoscale fronts with large horizontal density gradients and O(1) Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability — a form of convective–inertial instability which occurs when the potential vorticity is of opposite sign to the Coriolis parameter. Symmetric instability is characterised by growing slantwise convection cells nearly aligned with isopycnals and which encourage vertical transport of important biogeochemical tracers in addition to geostrophic momentum. This momentum transport destabilises the balanced thermal wind and can prompt geostrophic adjustment and re-stratification which often leaves remnant inertial oscillations. This thesis sets out to model the impacts of symmetric instability on the structure, evolution, and equilibration of the broad range of submesoscale fronts.
We develop a theory for the linear growth and weakly-nonlinear saturation of symmetric instability in the Eady model. This idealised front configuration is motivated by nearly-uniform symmetrically-unstable frontal zones observed during the SUNRISE field campaign in the Gulf of Mexico. Both the fraction of the balanced thermal wind mixed down by symmetric instability and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of symmetric instability we call 'slantwise inertial instability' by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in 'slantwise convection.' Using a set of direct numerical simulations, we further investigate the non-linear consequences of these flavours of symmetric instability together with the effect of lateral constraints imposed on the growing modes within finite-width fronts by varying the balanced Rossby number. While weak fronts develop narrow frontlets and excite small-amplitude vertically-sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. Furthermore, fronts with a super-critical balanced Rossby number equilibrate to a nearly self-similar profile dependent only on the deformation radius, but for small enough Rossby number, self-similar frontlets form and sub-divide the frontal region. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state. These emergent front properties are incorporated into a scaling model framework to describe the ultimate state of the equilibrated front, and broader implications of these results are discussed in the context of current parameterisations of symmetric instability affecting the upper ocean mixed layer and ultimately climate & earth system models.UKRI EPSRC
Cambridge Trust
Cambridge Philosophical Societ
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Supporting data for: The influence of front strength on the development and equilibration of symmetric instability.
Input files, source code, and a post-processing script used to run the numerical simulations reported in Wienkers et al. Part I and IINatural Environment Research Council, Submesoscales Under Near-Resonant Inertial Shear Experiment (SUNRISE), award number G101793
Rapid vertical exchange at fronts in the Northern Gulf of Mexico.
Over the Texas-Louisiana Shelf in the Northern Gulf of Mexico, the eutrophic, fresh Mississippi/Atchafalaya river plume isolates saltier waters below, supporting the formation of bottom hypoxia in summer. The plume also generates strong density fronts, features of the circulation that are known pathways for the exchange of water between the ocean surface and the deep. Using high-resolution ocean observations and numerical simulations, we demonstrate how the summer land-sea breeze generates rapid vertical exchange at the plume fronts. We show that the interaction between the land-sea breeze and the fronts leads to convergence/divergence in the surface mixed layer, which further facilitates a slantwise circulation that subducts surface water along isopycnals into the interior and upwells bottom waters to the surface. This process causes significant vertical displacements of water parcels and creates a ventilation pathway for the bottom water in the northern Gulf. The ventilation of bottom water can bypass the stratification barrier associated with the Mississippi/Atchafalaya river plume and might impact the dynamics of the region's dead zone