An official website of the United States government
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed source, is passively advected and diffused, and exits through the boundary at a fixed temperature. We seek an advecting flow to optimize this exchange. Previous work on energy-constrained cooling with a constant source has conjectured that global optimizers should resemble convection rolls; we prove one-sided bounds on energy-constrained cooling corresponding to, but not resolving, this conjecture. In the case of an enstrophy constraint, our results are more complete: we construct a family of self-similar, tree-like ‘branching flows’ whose cooling we prove is within a logarithm of globally optimal. These results hold for general space- and time-dependent source–sink distributions that add more heat than they remove. Our main technical tool is a non-local Dirichlet-like variational principle for bounding solutions of the inhomogeneous advection–diffusion equation with a divergence-free velocity. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.
more »
« less
Probing gas disc physics with LISA: simulations of an intermediate mass ratio inspiral in an accretion disc
More Like this
-
-
ABSTRACT Magnetically arrested accretion discs (MADs) around black holes (BHs) have the potential to stimulate the production of powerful jets and account for recent ultra-high-resolution observations of BH environments. Their main properties are usually attributed to the accumulation of dynamically significant net magnetic (vertical) flux throughout the arrested region, which is then regulated by interchange instabilities. Here, we propose instead that it is mainly a dynamically important toroidal field – the result of dynamo action triggered by the significant but still relatively weak vertical field – that defines and regulates the properties of MADs. We suggest that rapid convection-like instabilities, involving interchange of toroidal flux tubes and operating concurrently with the magnetorotational instability (MRI), can regulate the structure of the disc and the escape of net flux. We generalize the convective stability criteria and disc structure equations to include the effects of a strong toroidal field and show that convective flows could be driven towards two distinct marginally stable states, one of which we associate with MADs. We confirm the plausibility of our theoretical model by comparing its quantitative predictions to simulations of both MAD and SANE (standard and normal evolution; strongly magnetized but not ‘arrested’) discs, and suggest a set of criteria that could help to distinguish MADs from other accretion states. Contrary to previous claims in the literature, we argue that MRI is not suppressed in MADs and is probably responsible for the existence of the strong toroidal field.more » « less
-
An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed solution technique employs complex potentials to treat the disc’s interior and incremental Lagrangian equations to describe the prestressed elastic rod modelling the coating. The bifurcations of the disc occur with modes characterized by different circumferential wavenumbers, ranging between ovalization and high-order waviness, as a function of the ratio between the elastic stiffness of the disc and the bending stiffness of its coating. The presented results find applications in various fields, such as coated fibres, mechanical rollers, and the growth and morphogenesis of plants and fruits.more » « less
-
ABSTRACT Dippers are a common class of young variable star exhibiting day-long dimmings with depths of up to several tens of per cent. A standard explanation is that dippers host nearly edge-on (id ≈ 70°) protoplanetary discs that allow close-in (<1 au) dust lifted slightly out of the mid-plane to partially occult the star. The identification of a face-on dipper disc and growing evidence of inner disc misalignments brings this scenario into question. Thus, we uniformly (re)derive the inclinations of 24 dipper discs resolved with (sub-)mm interferometry from ALMA. We find that dipper disc inclinations are consistent with an isotropic distribution over id ≈ 0−75°, above which the occurrence rate declines (likely an observational selection effect due to optically thick disc mid-planes blocking their host stars). These findings indicate that the dipper phenomenon is unrelated to the outer (>10 au) disc resolved by ALMA and that inner disc misalignments may be common during the protoplanetary phase. More than one mechanism may contribute to the dipper phenomenon, including accretion-driven warps and ‘broken’ discs caused by inclined (sub-)stellar or planetary companions.more » « less
-
null (Ed.)ABSTRACT Active galactic nuclei (AGN) are powered by the accretion of discs of gas on to supermassive black holes (SMBHs). Stars and stellar remnants orbiting the SMBH in the nuclear star cluster (NSC) will interact with the AGN disc. Orbiters plunging through the disc experience a drag force and, through repeated passage, can have their orbits captured by the disc. A population of embedded objects in AGN discs may be a significant source of binary black hole mergers, supernovae, tidal disruption events, and embedded gamma-ray bursts. For two representative AGN disc models, we use geometric drag and Bondi–Hoyle–Littleton drag to determine the time to capture for stars and stellar remnants. We assume a range of initial inclination angles and semimajor axes for circular Keplerian prograde orbiters. Capture time strongly depends on the density and aspect ratio of the chosen disc model, the relative velocity of the stellar object with respect to the disc, and the AGN lifetime. We expect that for an AGN disc density $$\rho \gtrsim 10^{-11}{\rm g\, cm^{-3}}$$ and disc lifetime ≥1 Myr, there is a significant population of embedded stellar objects, which can fuel mergers detectable in gravitational waves with LIGO-Virgo and LISA.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/mnras/stz1026
