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Orlandi, P, Carnevale GF, Lele SK, Shariff K.  2001.  Thermal perturbation of trailing vortices. European Journal of Mechanics B-Fluids. 20:511-524.   10.1016/s0997-7546(01)01131-1   AbstractWebsite

The possibility of diminishing the danger of trailing vortices through thermal forcing is investigated. It is shown that heating the vortices would have two beneficial effects. First, it would cause the vortices to descend more rapidly thus clearing the flight path more quickly. Second, it would cause the vortices to draw closer together, thus greatly increasing the growth rate of the short-wave instabilities that can ultimately destroy the vortices through cross-diffusion. (C) 2001 Editions scientifiques et medicales Elsevier SAS.

Orlandi, P, Carnevale GF.  1999.  Evolution of isolated vortices in a rotating fluid of finite depth. Journal of Fluid Mechanics. 381:239-269.   10.1017/s0022112098003693   AbstractWebsite

Laboratory experiments have shown that monopolar isolated vortices in a rotating flow undergo instabilities that result in the formation of multipolar vortex states such as dipoles and tripoles. In some cases the instability is entirely two-dimensional, with the vortices taking the form of vortex columns aligned along the direction of the ambient rotation at all times. In other cases, the vortex first passes through a highly turbulent three-dimensional state before eventually reorganizing into vortex columns. Through a series of three-dimensional numerical simulations, the roles that centrifugal instability, barotropic instability, and the bottom Ekman boundary layer play in these instabilities are investigated. Evidence is presented that the centrifugal instability can trigger the barotropic instabilities by the enhancement of vorticity gradients. It is shown that the bottom Ekman layer is not essential to these instabilities but can strongly modify their evolution.

Orlandi, P, Pirozzoli S, Carnevale GF.  2012.  Vortex events in Euler and Navier-Stokes simulations with smooth initial conditions. Journal of Fluid Mechanics. 690:288-320.   10.1017/jfm.2011.430   AbstractWebsite

We present high-resolution numerical simulations of the Euler and Navier-Stokes equations for a pair of colliding dipoles. We study the possible approach to a finite-time singularity for the Euler equations, and contrast it with the formation of developed turbulence for the Navier-Stokes equations. We present numerical evidence that seems to suggest the existence of a blow-up of the inviscid velocity field at a finite time (t(s)) with scaling vertical bar u vertical bar(infinity) similar to (t(s) - t)(-1/2), vertical bar omega vertical bar(infinity) similar to (t(s) - t)(-1). This blow-up is associated with the formation of a k(-3) spectral range, at least for the finite range of wavenumbers that are resolved by our computation. In the evolution toward t(s), the total enstrophy is observed to increase at a slower rate, Omega similar to (t(s) - t)(-3/4), than would naively be expected given the behaviour of the maximum vorticity, omega(infinity) similar to (t(s) - t)(-1). This indicates that the blow-up would be concentrated in narrow regions of the flow field. We show that these regions have sheet-like structure. Viscous simulations, performed at various Re, support the conclusion that any non-zero viscosity prevents blow-up in finite time and results in the formation of a dissipative exponential range in a time interval around the estimated inviscid t(s). In this case the total enstrophy saturates, and the energy spectrum becomes less steep, approaching k(-513). The simulations show that the peak value of the enstrophy scales as Re-3/2, which is in accord with Kolmogorov phenomenology. During the short time interval leading to the formation of an inertial range, the total energy dissipation rate shows a clear tendency to become independent of Re, supporting the validity of Kolmogorov's law of finite energy dissipation. At later times the kinetic energy shows a t(-1.2) decay for all Re, in agreement with experimental results for grid turbulence. Visualization of the vortical structures associated with the stages of vorticity amplification and saturation show that, prior to ts, large-scale and the small-scale vortical structures are well separated. This suggests that, during this stage, the energy transfer mechanism is non-local both in wavenumber and in physical space. On the other hand, as the spectrum becomes shallower and a k(-5/3) range appears, the energy-containing eddies and the small-scale vortices tend to be concentrated in the same regions, and structures with a wide range of sizes are observed, suggesting that the formation of an inertial range is accompanied by transfer of energy that is local in both physical and spectral space.

Orlandi, P, Carnevale GF.  2007.  Nonlinear amplification of vorticity in inviscid interaction of orthogonal Lamb dipoles. Physics of Fluids. 19   10.1063/1.2732438   AbstractWebsite

Dynamical arguments based on the structure of the Euler equations suggest the possibility of rapid amplification of vorticity in which the vorticity and the rate of strain grow proportionately. During such growth, the vorticity is expected to amplify as a (t(s)-t)(-1) power-law in time. This behavior is difficult to demonstrate numerically, in part, because initial transients tend to obscure it. Lamb dipoles are used here to construct the initial vorticity. This helps to avoid these transients and results in a flow exhibiting the expected power-law vorticity amplification for a period of time. The spatial region where the vorticity growth rate is maximal is investigated in detail using a decomposition of the vorticity along the principal axes of the rate-of-strain tensor. It is demonstrated that the vorticity and strain rate in one direction in this decomposition are proportional during the period of rapid vorticity growth. These findings suggest that, during this period, the Euler equations can be reduced to a one-dimensional model equation for vorticity in the rate-of-strain coordinate system. (C) 2007 American Institute of Physics.

Orlandi, P, Pirozzoli S, Bernardini M, Carnevale GF.  2014.  A minimal flow unit for the study of turbulence with passive scalars. Journal of Turbulence. 15:731-751.   10.1080/14685248.2014.927066   AbstractWebsite

The concept of a minimal flow unit (MFU) for the study of the basic physics of turbulent flows is introduced. The MFU is an initial vorticity configuration that consists of a few simple well-defined large-scale vortex structures. The form and position of these structures are chosen so that their interaction produces turbulence capturing many of the essential characteristics of isotropic homogeneous turbulence produced from random-phase initial conditions or that produced by continual random-phase forcing. The advantage of using the MFU is that the evolution of the vortex structures can be followed more clearly and the relationship between the evolving vortex structures and the various ranges in the energy spectrum can be more clearly defined. The addition of passive scalar fields to the MFU permits an investigation of passive scalar mixing that is relevant to the study of combustion. With a particular choice of the MFU, one that produces a trend to a finite-time singularity in the vorticity field, it is demonstrated that passive scalar distributed in the original large-scale vortices will develop intense gradients in the region where the vorticity is tending toward a singularity. In viscous flow, the evolution of the MFU clearly shows how the volume of the regions where originally well-separated passive scalars come into contact increases with increasing Reynolds number.

Vallis, GK, Carnevale GF, Young WR.  1989.  Extremal energy properties and construction of stable solutions of the Euler equations. Journal of Fluid Mechanics. 207:133-152.   10.1017/s0022112089002533   AbstractWebsite

Certain modifications of the Euler equations of fluid motion lead to systems in which the energy decays or grows monotonically, yet which preserve other dynamically important characteristics of the field. In particular, all topological invariants associated with the vorticity field are preserved. In cases where isolated energy extrema exist, a stable steady flow can be found. In two dimensions, highly constrained by vorticity invariants, it is shown that the modified dynamics will lead to at least one non-trivial stationary, generally stable, solution of the equations of motion from any initial conditions. Numerical implementation of the altered dynamics is straightforward, and thus provides a practical method for finding stable flows. The method is sufficiently general to be of use in other dynamical systems.Insofar as three-dimensional turbulence is characterized by a cascade of energy, but not topological invariants, from large to small scales, the procedure has direct physical significance. It may be useful as a parameterization of the effects of small unresolved scales on those explicitly resolved in a calculation of turbulent flow.

Verzicco, R, Orlandi P, Eisenga AHM, vanHeijst GJF, Carnevale GF.  1996.  Dynamics of a vortex ring in a rotating fluid. Journal of Fluid Mechanics. 317:215-239.   10.1017/s0022112096000730   AbstractWebsite

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier-Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a 'degree of polarization'. If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown. Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.

Weiss, J, Tabor M, Carnevale G.  1983.  The Painlevé property for partial differential equations. Journal of Mathematical Physics. 24:522-526.   10.1063/1.525721   AbstractWebsite

In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well‐known partial differential equations (Burgers’ equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.

Zavala Sanson, L, Serravall R, Carnevale GF, vanHeijst GJF.  2005.  Experiments and simulations on coastal flows in the presence of a topographic slope. Journal of Physical Oceanography. 35:2204-2218.   10.1175/jpo2815.1   AbstractWebsite

The evolution of a barotropic coastal current in the presence of a bottom ramp-shaped topography is studied by means of laboratory experiments and numerical simulations. The experiments are performed in a rectangular rotating tank filled with freshwater. The fluid depth is shallow at one side of the domain and deeper at the other side, and both regions are divided by a narrow slope, whose depth contours are perpendicular to the long sides of the tank. A current approaching the slope is produced along one of the vertical walls, having the boundary at its right. Two configurations are analyzed: when the current flows from shallow to deep water and when flowing in the opposite direction. In the first scenario, the current is divided in two parts, one of them following the coastline. The other part of the current pairs with a cell of negative relative vorticity generated at the slope due to squeezing effects, forming a dipolar structure moving offshore, back toward the shallow side. In addition, a weak current moving inshore along the slope is clearly formed. In the second configuration, when the flow goes from deep to shallow water, a part of or even the whole current might be forced to move along the contours of the topography, away from the coast. In this case there is no dipole formation. The experiments are well reproduced by means of quasigeostrophic numerical simulations, which allow a more detailed systematic study of the influence of flow parameters such as the topography height and the width of the slope.