We examine the motion and tidal dynamics of a nonrotating black hole placed
within a post-Newtonian external spacetime. The tidal perturbation created by
the external environment is treated as a small perturbation. At a large
distance from the black hole, the gravitational field of the external
distribution of matter is assumed to be sufficiently weak to be adequately
described by the (first) post-Newtonian approximation to general relativity.
There, the black hole is treated as a monopole contribution to the total
gravitational field. There exists an overlap in the domains of validity of each
description, and the black-hole and post-Newtonian metrics are matched in the
overlap. The matching procedure produces the equations of motion for the black
hole and the gravito-electric and gravito-magnetic tidal fields acting on the
black hole. We first calculate the equations of motion and tidal fields by
making no assumptions regarding the nature of the post-Newtonian environment;
this could contain a continuous distribution of matter or any number of
condensed bodies. We next specialize our discussion to a situation in which the
black hole is a member of a post-Newtonian two-body system. As an application
of our results, we examine the geometry of the deformed event horizon and
calculate the tidal heating of the black hole, the rate at which it acquires
mass as a result of its tidal interaction with the companion body.Comment: 27 pages, 1 figur
Using primitive equation simulations, a zonally periodic channel is considered. The channel flow is forced by a combination of steady and high-frequency winds. The high-frequency forcing excites near-inertial motion, and the focus is on how this influences the low-frequency, nearly geostrophic part of the flow. In particular, this study seeks to clarify how Reynolds stresses exerted by the near-inertial modes affect the low-frequency kinetic energy. In the system considered, the near-inertial Reynolds stresses (i) serve as a sink term in the low-frequency kinetic energy budget and (ii) transfer low-frequency kinetic energy downward from the mixed layer. Transfer spectra show the bulk of this sink to occur at relatively small horizontal wavenumber (i.e., in the mesoscale, not the submesoscale). The presence of near-inertial motion can also affect the kinetic-to-potential energy exchanges, especially within the low-frequency band.
In the context of Canada's Ocean Protection Plan (OPP), improved coastal and near-shore modelling is needed to enhance marine safety and emergency response capacity in the aquatic environment. In this study, the Nucleus for European Modelling of the Ocean (NEMO) is adopted to develop an ocean forecasting system for Saint John harbour in the Bay of Fundy, on the east coast of Canada. The challenging regional oceanography is characterized by the presence of some of the world's strongest tides, significant river runoff and complicated geometry. A three-level one-way nesting approach is used to downscale from a 1/12°N orth Atlantic-Arctic regional model to very-high-resolution port-scale around Saint John harbour. The three nested grids cover the outer shelf, the Bay of Fundy and finally the approach to the harbour with resolutions of 2.5 km, 500 m and 100 m respectively. Due to the lack of accurate runoff data at the Saint John River outlet, the model's lateral open boundary condition is modified to introduce the river forcing with the observed time series of water level near the mouth of the river. Evaluation with observational data demonstrates the model's accuracy for the simulation of tidal elevation and currents, non-tidal water level and currents, temperature and salinity. Comparison with the observed sea surface temperature demonstrates the improved model accuracy through increasing the horizontal resolution. Virtual Lagrangian trajectories computed using the modelled surface currents and including wind effects show good agreement with the observed trajectories of different types of surface drifters. This study demonstrates the capability of the NEMO modelling framework to provide very-high-resolution modelling at portscale resolution for the Saint John harbour.
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