Turbulence and waves in a rotating tank
TL;DR: A turbulent field is produced with an oscillating grid in a deep, rotating tank as discussed by the authors, which consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer.
Abstract: A turbulent field is produced with an oscillating grid in a deep, rotating tank. Near the grid, the Rossby number is kept large, 0(3-33), and the turbulence is locally unaffected by rotation. Away from the grid, the scale of the turbulence increases, the r.m.s. turbulent velocity decreases, and rotation becomes increasingly important. The flow field changes dramatically at a local Rossby number of about 0.20, and thereafter remains independent of depth. The flow consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer. The number of vortices per unit area is a function of the grid Rossby number. The local vorticity within cores can be a factor of 50 larger than the tank vorticity 2Ω. The total relative circulation contained in the vortices remains, however, a small fraction of the tank circulation.The concentrated vortex cores support waves consisting of helical distortions, which travel along the axes of individual vortices. Isolated, travelling waves seem well-described by the vortex-soliton theory of Hasimoto (1972). The nonlinear waves transport mass, momentum and energy from the vigorously turbulent region near the grid to the rotation-dominated flow above. Interactions between waves, which are frequent occurrences, almost always result in a local breakdown of the vortex core, and small-scale turbulence production. Usually the portions of broken core reform within ½−1 rotation periods, but occasionally cores are destroyed and reformed on a much longer timescale.
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TL;DR: The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments.
Abstract: Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament This twist can then significantly alter the dynamics of the filament This paper explores this dynamics via numerical simulation After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)) The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment However this decay is suppressed by uniformly decreasing excitability Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed Results are contrasted with other mechanisms of fibrillation and future prospects are summarized (c)1998 American Institute of Physics
818 citations
TL;DR: A variety of observations of intense, long-lived oceanic vortices are interpreted as examples of a distinct phenomenon, which is given the name Submesoscale, Coherent Vortices (SCV's).
Abstract: A variety of observations of intense, long-lived oceanic vortices are interpreted as examples of a distinct phenomenon, which is given the name Submesoscale, Coherent Vortices (SCV's). The distinguishing characteristics of SCV's are defined and illustrated by example, and a survey is made of the different SCV types presently known. On the basis of extant theoretical and modeling solutions, interpretations are made of the dynamics associated with SCV existence, movement, endurance, interactions with other currents, generation, and contributions to the transport of chemical properties in the ocean.
427 citations
TL;DR: Forced turbulence in a rotating frame is studied using numerical simulations in a triply periodic box in this article, where the random forcing is three dimensional and localized about an intermediate wavenumber kf, and energy is transferred to scales larger than the forcing scale when the rotation rate is large enough.
Abstract: Forced turbulence in a rotating frame is studied using numerical simulations in a triply periodic box. The random forcing is three dimensional and localized about an intermediate wavenumber kf. The results show that energy is transferred to scales larger than the forcing scale when the rotation rate is large enough. The scaling of the energy spectrum approaches E(k)∝k−3 for k
379 citations
TL;DR: In this article, a quantitative experimental study of the two-dimensional inverse energy cascade is presented, where the flow is electrically driven in a horizontal layer of mercury and three-dimensional perturbations are suppressed by means of a uniform magnetic field.
Abstract: A quantitative experimental study of the two-dimensional inverse energy cascade is presented. The flow is electrically driven in a horizontal layer of mercury and three-dimensional perturbations are suppressed by means of a uniform magnetic field, so that the flow can be well approximated by a two-dimensional Navier–Stokes equation with a steady forcing term and a linear friction due to the Hartmann layer. Turbulence is produced by the instability of a periodic square network of 36 electrically driven alternating vortices. The inverse cascade is limited at large scales, either by the linear friction or by the finite size of the domain, depending on the experimental parameters. In the first case, spectra are measured and the corresponding two-dimensional Kolmogorov constant is in the range 3–7. In the second case, a condensation of the turbulent energy in the lowest mode, corresponding to a spontaneous mean global rotation, is observed. Such a condensation was predicted by Kraichnan (1967) from statistical thermodynamics arguments, but without the symmetry breaking. Random reversals of the rotation sense, owing to turbulent fluctuations, are more and more sparse as friction is decreased. The lowest mode fluctuations and the small scales are statistically independent.
371 citations
TL;DR: In this article, the structures of the vorticity fields in several homogeneous irrotational straining flows and a homogeneous turbulent shear flow were examined using a database generated by direct numerical simulation of the unsteady Navier-Stokes equations.
Abstract: The structures of the vorticity fields in several homogeneous irrotational straining flows and a homogeneous turbulent shear flow were examined using a database generated by direct numerical simulation of the unsteady Navier-Stokes equations. In all cases, strong evidence was found for the presence of coherent vortical structures. The initially isotropic vorticity fields were rapidly affected by imposed mean strain and the rotational component of mean shear and developed accordingly. In the homogeneous turbulent shear-flow cases, the roll-up of mean vorticity into characteristic hairpin vortices was clearly observed, supporting the view that hairpin vortices are an important vortical structure in all turbulent shear flows; the absence of mean shear in the homogeneous irrotational straining flows precludes the presence of hairpin-like vortices.
348 citations
References
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01 Jan 1967TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.
11,187 citations
TL;DR: In this article, the application of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention in recent years, and the authors investigated a complicated system of nonlinear equations, in order to find out enough about the properties of the solutions of these equations that insight can be obtained into the various patterns exhibited by the field and that data can be derived concerning the relative frequencies of these patterns in the hope that in this way a basis may be found for the calculation of important values.
Abstract: Publisher Summary This chapter discusses that the application of methods of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention in recent years. It investigated a complicated system of nonlinear equations, in order to find out enough about the properties of the solutions of these equations that insight can be obtained into the various patterns exhibited by the field and that data can be derived concerning the relative frequencies of these patterns in the hope that in this way a basis may be found for the calculation of important values. The difficulties encounter are of a twofold nature: in part they are connected with the complicated geometrical character of the hydrodynamical equations; in part they are dependent upon the presence of nonlinear terms, containing derivatives of the first order of the velocity components, along with derivatives of the second order multiplied by the very small coefficient of viscosity. The latter feature is responsible for a number of important, characteristics of turbulence, among which are prominent those connected with the balance of energy and with the appearance of dissipation layers. These layer an important part in the energy exchange, as they represent the main regions where energy is dissipated.
2,202 citations
TL;DR: In this article, the intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrodinger equation.
Abstract: The intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrodinger equation
\[
\frac{{\rm l}}{i}\frac{\partial \psi}{\partial t} = \frac{\partial^2\psi}{\partial s^2}+{\textstyle\frac{1}{2}}(|\psi|^2+A)\psi,
\]
where t is the time, s the length measured along the filament, ψ is the complex variable
\[
\psi = \kappa\exp\left(i\int_0^{s}\tau \,ds\right)
\]
and is a function oft. It is found that this equation yields a solution describing the propagation of a loop or a hump of helical motion along a line vortex, with a constant velocity 2τ. The relation to the system of intrinsic equations derived by Betchov (1965) is discussed.
968 citations
TL;DR: In this article, the authors describe some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed, viz. mild (double helix) breakdown, spiral breakdown, and axisymmetric breakdown.
Abstract: This paper describes some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed.In one set of experiments, the position of the breakdown, axial component of the velocity of the vortex core, swirl angle distribution ahead of the breakdown, and the pressure distribution along the tube were determined for various flow rates and for various values of circulation imparted to the fluid (water). Basically, three types of vortex breakdown were observed, viz. mild (double helix) breakdown, spiral breakdown (followed by turbulent mixing), and axisymmetric breakdown (followed by a thicker vortex core, then a spiral breakdown, and finally by turbulent mixing). The type and the location of the stationary breakdowns were found to be dependent, for the particular vortex tube used, upon the Reynolds and circulation numbers of the flow. In a spiral breakdown, the vortex core filament maintained the same sense of rotation as the upstream fluid elements. In an axisymmetric breakdown, the bubble included an inclined vortex-ring whose axis gyrated about the axis of the tube.In a second set of experiments, the response of the abrupt structural change along the axis of flow to gradual and abrupt changes in the upstream and downstream flow conditions was examined. The axisymmetric breakdown responded in a manner analogous to the hydraulic jump in open-channel flow before if reached a new stationary position along the axis of the tube.The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is a finite transition between two sequent states of flow as proposed by Benjamin (1962, 1965, 1967) on theoretical grounds.
554 citations
TL;DR: In this paper, the decay law of the turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally.
Abstract: The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law , the Peclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.
378 citations