Fluids, Volume 1, Issue 3 (September 2016) – 11 articles

Eddy-driven jets are of importance in the ocean and atmosphere, and to a first approximation are governed by Rossby wave dynamics. This study addresses the time-dependent flux of fluid and a passive tracer between such a jet and an adjacent eddy, with specific regard to determining zonal and meridional wavenumber dependence. The flux amplitude in wavenumber space is obtained, which is easily computable for a given jet geometry, speed and latitude, and which provides instant information on the wavenumbers of the Rossby waves which maximize the flux. This new tool enables the quick determination of which modes are most influential in imparting fluid exchange, which in the long term will homogenize the tracer concentration between the eddy and the jet. The results are validated by computing backward- and forward-time finite-time Lyapunov exponent fields, and also stable and unstable manifolds; the intermingling of these entities defines the region of chaotic transport between the eddy and the jet. The relationship of all of these to the time-varying transport flux between the eddy and the jet is carefully elucidated. The flux quantification presented here works for general time-dependence, whether or not lobes (intersection regions between stable and unstable manifolds) are present in the mixing region, and is therefore also easily computable for wave packets consisting of infinitely many wavenumbers. Full article

This work concerns how two competing mechanisms—eddy backscatter and counter-rotating gyre anomalies—influence the midlatitude ocean dynamics, as described by the eddy-resolving quasi-geostrophic (QG) model of wind-driven gyres. We analyzed dynamical balances and effects of different eddy forcing components, as well as their dependencies on increasing vertical resolution and decreasing eddy viscosity and found that the eastward jet and its adjacent recirculation zones are maintained mostly by the eddy forcing via the eddy backscatter mechanism, whereas the time-mean eddy-forcing component plays not only direct jet-supporting but also indirect jet-inhibiting role. The latter is achieved by inducing zonally elongated anticyclonic/cyclonic Counter-rotating Gyre Anomaly (CGA) in the subpolar/subtropical gyre. The indirect effect of CGAs on the eastward jet is found to be moderate relative to the dominant eddy backscatter mechanism. We also found that the higher the vertical baroclinic mode, the weaker its backscatter role and the stronger its CGA-driving role. Although the barotropic and first baroclinic modes are the most efficient ones in maintaining the backscatter, the higher, up to the fifth baroclinic modes also have significant but reverse impact that reduces the backscatter. Full article

CFD simulations of the multiphase flow in technical equipment are feasible within the framework of interpenetrating continua, the so-called two-fluid modelling. Predictions with multiphase CFD are only possible if a fixed set of closures for the interfacial exchange terms is available that has been validated for a wide range of flow conditions and can therefore reliably be used also for unknown flow problems. To this end, a baseline model, which is applicable for adiabatic bubbly flow, has been specified recently and has been implemented in OpenFOAM. In this work, we compare simulation results obtained using the baseline model with three different sets of experimental data for dispersed gas-liquid pipe flow. Air and water under similar flow conditions have been used in the different experiments, so that the main difference between the experiments is the variation of the pipe diameter from 25 mm to 200 mm. Gas fraction and liquid velocity are reasonably well reproduced, in particular in the bulk of the flow. Discrepancies can be seen in the turbulent kinetic energy, the gas velocity and in the wall peaks of the gas fraction. These can partly be explained by the simplified modelling, but to some extent must be attributed to uncertainty in the experimental data. The need for improved near-wall modelling, turbulence modelling and modelling of the bubble size distribution is highlighted. Full article

The first portion of this paper contains an overview of recent progress in the development of dynamical-systems-based methods for the computation of Lagrangian transport processes in physical oceanography. We review the considerable progress made in the computation and interpretation of key material features such as eddy boundaries, and stable and unstable manifolds (or their finite-time approximations). Modern challenges to the Lagrangian approach include the need to deal with the complexity of the ocean submesoscale and the difficulty in computing fluxes of properties other than volume. We suggest a new approach that reduces complexity through time filtering and that directly addresses non-material, residual scalar fluxes. The approach is “semi-Lagrangian” insofar as it contemplates trajectories of a velocity field related to a residual scalar flux, usually not the fluid velocity. Two examples are explored, the first coming from a canonical example of viscous adjustment along a flat plate and the second from a numerical simulation of a turbulent Antarctic Circumpolar Current in an idealized geometry. Each example concentrates on the transport of dynamically relevant scalars, and the second illustrates how substantial material exchange across a baroclinically unstable jet coexists with zero residual buoyancy flux. Full article

A series of large-scale numerical simulations is presented, which incorporate parameterizations of vertical mixing of temperature and salinity by double-diffusion and by small-scale turbulence. These simulations reveal the tendency of double-diffusion to constrain diapycnal volume transport, both upward and downward. For comparable values of mixing coefficients, the average diapycnal velocity in the double-diffusive thermocline is much less than in the corresponding turbulent regime. The insulating effect of double-diffusion is rationalized using two theoretical models. The first argument is based on the assumed vertical advective-diffusive balance. The second theory uses the Rhines and Young technique to evaluate the net diapycnal transport across regions bounded by closed streamlines at a given density surface. The numerical simulations and associated analytical arguments in this study underscore fundamental differences between double-diffusive mixing and mechanically generated small-scale turbulence. When both double-diffusion and turbulence are taken into account, we find that the constraints on diapycnal velocity loosen (tighten) with the increase (decrease) of the fraction of the overall mixing attributed to turbulence. The range of diapycnal velocities that could be realized in doubly-diffusive fluids is determined by the variation in the heat/salt flux ratio. We hypothesize that the unique ability of double-diffusive mixing to actively control diapycnal volume transport may have significant ramifications for the structure and dynamics of thermohaline circulation in the ocean. Full article

The key element of Geophysical Fluid Dynamics—reorganization of potential vorticity (PV) by nonlinear processes—is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies. Full article

Convection in a partitioned porous layer is considered where the thin partition causes a mechanical isolation of the two identical sublayers from one another, but heat may neveretheless conduct freely. An unsteady solver that employs the multigrid method is employed to determine steady-state strongly nonlinear for values of the Darcy–Rayleigh number up to eight times its critical value. The predictions of linear stability theory are confirmed and the accuracy of the computations are carefully monitored and controlled. It is found that the wavenumber for which the maximum rate of heat transfer is attained at any chosen value of the Darcy–Rayleigh number, $\mathrm{Ra}$ increases quite strongly from roughly $2.33$ at onset to $6.25$ when $\mathrm{Ra}=200$ . It is also found that convection generally cannot take place with wavenumbers which are close to the left-hand branch of the neutral stability curve because nonlinear interactions favour modes selected from higher harmonics. Full article

The nonlinear Schrödinger equation (NLS) is a canonical evolution equation, which describes the dynamics of weakly nonlinear wave packets in time and space in a wide range of physical media, such as nonlinear optics, cold gases, plasmas and hydrodynamics. Due to its integrability, the NLS provides families of exact solutions describing the dynamics of localised structures which can be observed experimentally in applicable nonlinear and dispersive media of interest. Depending on the co-ordinate of wave propagation, it is known that the NLS can be either expressed as a space- or time-evolution equation. Here, we discuss and examine in detail the limitation of the first-order asymptotic equivalence between these forms of the water wave NLS. In particular, we show that the the equivalence fails for specific periodic solutions. We will also emphasise the impact of the studies on application in geophysics and ocean engineering. We expect the results to stimulate similar studies for higher-order weakly nonlinear evolution equations and motivate numerical as well as experimental studies in nonlinear dispersive media. Full article

This work continues development of the framework for dynamically consistent parameterization of mesoscale eddy effects in non-eddy-resolving ocean circulation models. Here, we refine and extend the previous results obtained for the double gyres and aim to account for the eddy backscatter mechanism that maintains eastward jet extension of the western boundary currents. We start by overcoming the local homogeneity assumption and by taking into account full large-scale circulation. We achieve this by considering linearized-dynamic responses to finite-time transient impulses. Feedback from these impulses on the large-scale circulation are referred to as footprints. We find that the local homogeneity assumption yields only quantitative errors in most of the gyres but breaks down in the eastward jet region, which is characterized by the most significant eddy effects. The approach taken provides new insights into the eddy/mean interactions and framework for parameterization of unresolved eddy effects. Footprints provide us with maps of potential vorticity anomalies expected to be induced by transient eddy forcing. This information is used to calculate the equivalent eddy potential vorticity fluxes and their divergences that partition the double-gyre circulation into distinct geographical regions with specific eddy effects. In particular, this allows approximation of the real eddy effects that maintain the eastward jet extension of the western boundary currents and its adjacent recirculation zones. Next, from footprints and their equivalent eddy fluxes and from underlying large-scale flow gradients, we calculate spatially inhomogeneous and anisotropic eddy diffusivity tensor. Its properties suggest that imposing parameterized source terms, that is, equivalent eddy flux divergences, is a better parameterization strategy than implementation of the eddy diffusion. Full article

Venturi flumes are one of the most important flow-measuring structures commonly investigated by physical model tests in the past. The solutions to the Venturi flume flow problems were generally found on the basis of empirical equations arising from such tests. Nonetheless, the overall accuracy and range of applicability of these equations rely on the scope of the tests. Additionally, the hydraulic characteristics of free flows in short-throated flumes cannot be modelled by the conventional hydrostatic pressure approaches. In this study, a one-dimensional model, which incorporates a higher-order dynamic pressure correction for the effects of the sidewalls and streamline vertical curvatures, is applied to simulate such flows and elucidate relevant flow features. The model equations are discretised and solved using the finite difference scheme. The computed results for free surface profiles, pressure distributions at different sections and discharge characteristics are compared to measured data. The computational results exhibit good agreement with measured data. Overall, it is shown that the developed model is capable of accurately simulating the curvilinear flows in short-throated flumes with rounded transition and bottom humps. The results also highlight the detailed dependence of the discharge characteristics of the critical-flow flumes under free flow conditions on the curvature of the streamlines. Full article

This study examined the heat transfer coefficient, friction loss, pressure drop and pumping power needed for the use of nanofluid coolants made of a mixture of suspension of graphene nanoplatelets–silver in water in a rectangular duct. A series of calculations were performed for the coolant volume flow rate in the range of 5000 ≤ Re ≤ 15,000 under a fully developed turbulent flow regime and different nanosheet concentrations up to 0.1 weight percent. The thermo-physical properties of the nanofluids were extracted from the recent experimental work of Yarmand et al. (Graphene nanoplatelets-silver hybrid nanofluids for enhanced heat transfer. Energy Convers. Manag. 2015, 100, 419–428). The presented results indicated that the heat transfer characteristics of the nanofluid coolants improved with the increase in nanosheet concentration as well as the increase in the coolant Reynolds number. However, there was a penalty in the duct pressure drop and an increase in the required pumping power. In summary, the closed conduit heat transfer performance can be improved with the use of appropriate nanofluids based on graphene nanoplatelets–silver/water as a working fluid. Full article