Turbulent mixing at a stable density interface : the variation of the buoyancy flux–gradient relation

Experiments conducted on mixing across a stable density interface in a turbulent Taylor–Couette flow show, for the first time, experimental evidence of an increase in mixing efficiency at large Richardson numbers. With increasing buoyancy gradient the buoyancy flux first passes a maximum, then decreases and at large values of the buoyancy gradient the flux increases again. Thus, the curve of buoyancy flux versus buoyancy gradient tends to be N-shaped (rather than simply bell shaped), a behaviour suggested by the model of Balmforth et al. (J. Fluid Mech. vol. 428, 1998, p. 349). The increase in mixing efficiency at large Richardson numbers is attributed to a scale separation of the eddies active in mixing at the interface; when the buoyancy gradient is large mean kinetic energy is injected at scales much smaller than the eddy size fixed by the gap width, thus decreasing the eddy turnover time. Observations show that there is no noticeable change in interface thickness when the mixing efficiency increases; it is the mixing mechanism that changes. The curves of buoyancy flux versus buoyancy gradient also show a large variability for identical experimental conditions. These variations occur at time scales one to two orders of magnitude larger than the eddy turnover time scale

Inherent work suit buoyancy distribution:effects on lifejacket self-righting performance

Introduction: Accidental immersion in cold water is an occupational risk. Work suits and life jackets (LJ) should work effectively in combination to keep the airway clear of the water (freeboard) and enable self-righting. We hypothesized that inherent buoyancy, in the suit or LJ, would be beneficial for enabling freeboard, but its distribution may influence LJ self-righting. Methods: Six participants consented to complete nine immersions. Suits and LJ tested were: flotation suit (FLOAT; 85 N inherent buoyancy); oilskins 1 (OS-1) and 2 (OS-2), both with no inherent buoyancy; LJs (inherent buoyancy/buoyancy after inflation/total buoyancy), LJ-1 50/150/200 N, LJ-2 0/290/290 N, LJ-3 80/190/270 N. Once dressed, the subject entered an immersion pool where uninflated freeboard, self-righting performance, and inflated freeboard were measured. Data were compared using Friedman’s test to the 0.05 alpha level. Results: All suits and LJs enabled uninflated and inflated freeboard, but differences were seen between the suits and LJs. Self-righting was achieved on 43 of 54 occasions, irrespective of suit or LJ. On all occasions that self-righting was not achieved, this occurred in an LJ that included inherent buoyancy (11/54 occasions). Of these 11 failures, 8 occurred (73% of occasions) when the FLOAT suit was being worn. Discussion: LJs that included inherent buoyancy, that are certified as effective on their own, worked less effectively from the perspective of self-righting in combination with a work suit that also included inherent buoyancy. Equipment that is approved for use in the workplace should be tested in combination to ensure adequate performance in an emergency scenario

The Nusselt numbers of horizontal convection

We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $\kappa$ is the molecular diffusivity of buoyancy $b$. This connection between $\mathbf{J}$ and $\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $\kappa\langle|\boldsymbol{\nabla} b|^2\rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent "surface Nusselt number", defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{\rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|\mathbf{\nabla}b|^2$ demanded by $\kappa\langle|\mathbf{\nabla}b|^2\rangle$.Comment: 16 pages, 7 figure

Double-diffusive instabilities of a shear-generated magnetic layer

Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely.Comment: Submitted to ApJ

Fishing for drifts : detecting buoyancy changes of a top marine predator using a step-wise filtering method

This research was partly funded by a Natural Environment Research Council grant [NE/E018289/1]. Further, a PhD studentship in Marine Biology partially funded by the Natural Environment Research Council [NE/L501852/1] and the University of St Andrews 600th Scholarship supported this work.In southern elephant seals (Mirounga leonina), fasting and foraging related fluctuations in body composition are reflected by buoyancy changes which can be monitored by changes in drift rate. Here, we present an improved knowledge-based method for detecting buoyancy changes from compressed and abstracted dive profiles received through telemetry. We applied this step-wise filtering method to the dive records of 11 southern elephant seals, which identified 0.8% to 2.2% of all dives as drift dives. At the beginning of the migration, all individuals were strongly negatively buoyant. Over the following 75 to 150 days, the buoyancy reached a peak close to or at neutral buoyancy, indicative of a seal’s foraging success. Ground-truthing confirmed that this new knowledge-based method is capable to reliably detect buoyancy changes in the dive records of drift diving species using abstracted dive profiles. This affirms that the abstraction algorithm conveys sufficient detail of the geometric shape of drift dives for them to be identified. It also suggest that using this step-wise filtering method, buoyancy changes could be detected even in old datasets with compressed dive information, for which conventional drift dive classification previously failed.Publisher PDFPeer reviewe

The Dominance of Neutrino-Driven Convection in Core-Collapse Supernovae

Multi-dimensional instabilities have become an important ingredient in core-collapse supernova (CCSN) theory. Therefore, it is necessary to understand the driving mechanism of the dominant instability. We compare our parameterized three-dimensional CCSN simulations with other buoyancy-driven simulations and propose scaling relations for neutrino-driven convection. Through these comparisons, we infer that buoyancy-driven convection dominates post-shock turbulence in our simulations. In support of this inference, we present four major results. First, the convective fluxes and kinetic energies in the neutrino-heated region are consistent with expectations of buoyancy-driven convection. Second, the convective flux is positive where buoyancy actively drives convection, and the radial and tangential components of the kinetic energy are in rough equipartition (i.e. K_r ~ K_{\theta} + K_{\phi}). Both results are natural consequences of buoyancy-driven convection, and are commonly observed in simulations of convection. Third, buoyant driving is balanced by turbulent dissipation. Fourth, the convective luminosity and turbulent dissipation scale with the driving neutrino power. In all, these four results suggest that in neutrino-driven explosions, the multi-dimensional motions are consistent with neutrino-driven convection.Comment: Accepted by the Astrophysical Journa

The lightness of water vapor helps to stabilize tropical climate.

Moist air is lighter than dry air at the same temperature, pressure, and volume because the molecular weight of water is less than that of dry air. We call this the vapor buoyancy effect. Although this effect is well documented, its impact on Earth's climate has been overlooked. Here, we show that the lightness of water vapor helps to stabilize tropical climate by increasing the outgoing longwave radiation (OLR). In the tropical atmosphere, buoyancy is horizontally uniform. Then, the vapor buoyancy in the moist regions must be balanced by warmer temperatures in the dry regions of the tropical atmosphere. These higher temperatures increase tropical OLR. This radiative effect increases with warming, leading to a negative climate feedback. At a near present-day surface temperature, vapor buoyancy is responsible for a radiative effect of 1 W/m2 and a negative climate feedback of about 0.15 W/m2 per kelvin

The role of diffusion on the interface thickness in a ventilated filling box

We examine the role of diffusivity, whether molecular or turbulent, on the steady-state stratification in a ventilated filling box. The buoyancy-driven displacement ventilation model of Linden et al. (J. Fluid Mech., vol. 212, 1990, p. 309) predicts the formation of a two-layer stratification when a single plume is introduced into an enclosure with vents at the top and bottom. The model assumes that diffusion plays no role in the development of the ambient buoyancy stratification: diffusion is a slow process and the entrainment of ambient fluid into the plume from the diffuse interface will act to thin the interface resulting in a near discontinuity of density between the upper and lower layers. This prediction has been corroborated by small-scale salt bath experiments; however, full-scale measurements in ventilated rooms and complementary numerical simulations suggest an interface that is not sharp but rather smeared out over a finite thickness. For a given plume buoyancy flux, as the cross-sectional area of the enclosure increases the volume of fluid that must be entrained by the plume to maintain a sharp interface also increases. Therefore the balance between the diffusive thickening of the interface and plume-driven thinning favours a thicker interface. Conversely, the interface thickness decreases with increasing source buoyancy flux, although the dependence is relatively weak. Our analysis presents two models for predicting the interface thickness as a function of the enclosure height, base area, composite vent area, plume buoyancy flux and buoyancy diffusivity. Model results are compared with interface thickness measurements based on previously reported data. Positive qualitative and quantitative agreement is observed

Use of cryogenic buoyancy systems for controlled removal of heavy objects from the seabed

The concept design of a lightweight cryogenic marine heavy lift buoyancy system has been investigated. The approach makes use of a novel cryogenic system for provision of buoyancy within the ocean environment. The objective is to be able to lift or lower large displacement objects under full remote control. The nature of subsea lifting and lowering operations requires a high degree of precise control for operational safety, reasons and to preserve the structural integrity of the load. The lift operation occurs in two phases: Development of lift to overcome seabed suction, and then rapid reduction of buoyancy to maintain a controlled ascent. Descent involves controlled release of the buoyancy. The proposed buoyancy system consists of a buoyancy chamber and an integral cryogenic gas generation unit. The application of an on-board gas generation unit allows the removal of the engineering challenges associated with use of compressors and the concomitant complex manifold of connecting umbilical pipe work. It provides for a fully remote system completely eliminating all risk associated with extensive physical surface to subsea connection throughout the entire lift operation. The opening stages of the project work include the development of a system that will operate efficiently and effectively to a depth of 350m. An initial general arrangement for the buoyancy system has been developed. A number of these systems involve considerable design and development, these include: structural design of the buoyancy chamber, mechanical systems to control and connection to the lift device, the cryogenic system itself and overall process control systems. As part of the design process for such an arrangement, numerical simulation of the complete system has been undertaken in order to develop mechanical, cryogenic and process control systems efficiently and effectively. This system simulation has been developed using Matlab Simulink. This paper considers the overall design concept and associated system development issues. These are illustrated through use of the time accurate simulation of alternative design configurations that confirm the viability of the concept. A main conclusion is that minimisation of the dry weight of the system is critical to cost-effective operation of the project