Robert A. Handler

Direct numerical simulation of the turbulent channel flow of a polymer solution

In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consi...

Direct numerical simulation of turbulent flow over a modeled riblet covered surface

An immersed boundary technique is used to model a riblet covered surface on one wall of a channel bounding fully developed turbulent flow. The conjecture that the beneficial drag reduction effect of riblets is a result of the damping of cross-flow velocity fluctuations is then examined. This possibility has been discussed by others but is unverified. The damping effect is explicitly modelled by applying a cross-flow damping force field in elongated streamwise zones with a height and spacing corresponding to the riblet crests. The same trends are observed in the turbulence profiles above both riblet and damped surfaces, thus supporting cross-flow damping as a beneficial mechanism. It is found in the examples presented that the effect of the riblets on the mean flow field quantities (mean velocity profile, velocity fluctuations, Reynolds shear stress, and low–speed sreak spacing) is small. The riblests cause a relatively small drag reduction of about 4%, a figure that is in rough agreement with experiments and other computations. The simulations also suggest a mechanism for the observed displacement of the turbulence quantities away from the wall. The immersed boundary technique used to model the riblets consists of creating an externally imposed spatially localized body force which opposes the flow velocity and creates a riblet-like surface. For unstead viscous flow the calculation of the force is done with a feedback scheme in which the velocity is used to iteratively determine the desired value. In particular, the surface body force is determined by the relation f ( x s , t ) = α ∫ t 0 U ( x s , t ′)d t ′ + β U ( x s , t ) for surface points x s , velocity U time t and negative constants α and β. All simulations are done with a spectral code in a single computational domain without any mapping of the mesh. The combination of the immersed boundary and spectral techniques can potentially be used to solve other problems having complex geometry and flow physics.

Vortex dynamics and the production of Reynolds stress

The physical mechanisms by which the Reynolds shear stress is produced from dynamically evolving vortical structures in the wall region of a direct numerical simulation of turbulent channel flow are explored. The complete set of quasistreamwise vortices are systematically located and tracked through the flow by the locus of the points of intersection of their centres of rotation with the (y, z) numerical grid planes. This approach assures positive identification of vortices of widely differing strengths, including those whose amplitude changes significantly in time. The process of vortex regeneration, and the means by which vortices grow, distort and interact over time are noted. Ensembles of particle paths arriving on fixed planes in the flow are used to represent the physical processes of displacement and acceleration transport (Bernard & Handler 1990a) from which the Reynolds stress is produced. By interweaving the most dynamically significant of the particle paths with the evolving vortical structures, the dynamical role of the vortices in producing Reynolds stress is exposed. This is found to include ejections of low-speed fluid particles by convecting structures and the acceleration and deceleration of fluid particles in the cores of vortices. Sweep dominated Reynolds stress close to the wall appears to be a manifestation of the regeneration process by which new vortices are created in the flow.

Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow

The budgets of the Reynolds stress, turbulent kinetic energy and streamwise enstrophy are evaluated through direct numerical simulations for the turbulent channel flow of a viscoelastic polymer solution modeled with the Finitely Extensible Nonlinear Elastic with the Peterlin approximation (FENE-P) constitutive equation. The influence of viscoelasticity on the budgets is examined through a comparison of the Newtonian and the viscoelastic budgets obtained for the same constant pressure drop across the channel. It is observed that as the extensional viscosity of the polymer solution increases there is a consistent decrease in the production of Reynolds stress in all components, as well as in the other terms in the budgets. In particular, the effect of the flow elasticity, which is associated with the reduction in the intensity of the velocity-pressure gradient correlations, potentially leads to a redistribution of the turbulent kinetic energy among the streamwise, the wall-normal and the spanwise directions....

Empirical Orthogonal Function Analysis of Ocean Surface Currents Using Complex and Real-Vector Methods*

Empirical orthogonal function (EOF) analysis has been widely used in meteorology and oceanography to extract dominant modes of behavior in scalar and vector datasets. For analysis of two-dimensional vector fields, such as surface winds or currents, use of the complex EOF method has become widespread. In the present paper, this method is compared with a real-vector EOF method that apparently has previously been unused for current or wind fields in oceanography or meteorology. It is shown that these two methods differ primarily with respect to the concept of optimal representation. Further, the real-vector analysis can easily be extended to threedimensional vector fields, whereas the complex method cannot. To illustrate the differences between approaches, both methods are applied to Ocean Surface Current Radar data collected off Cape Hatteras, North Carolina, in June and July 1993. For this dataset, while the complex analysis ‘‘converges’’ in fewer modes, the real analysis is better able to isolate flows with wide cross-shelf structures such as tides.

Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow

Direct numerical simulations of fully developed turbulence in an open channel geometry were performed in which a passive scalar was introduced. The simulations were intended to explore transport at free surfaces in two cases for which (1) the free surface was maintained at constant temperature and (2) the interfacial flux was fixed. These cases can be considered models for mass and evaporative heat transport where buoyancy and surface deformation effects are negligible. Significant differences were found in the thermal fields in these two cases. The turbulent statistics reveal that the surface flux in the constant temperature case was significantly more intermittent compared to the surface temperature field in the constant flux case. The surface temperature field in the latter case formed large patches of warm fluid, reminiscent of the so-called fish scale patterns revealed in recent infrared imagery of the air–water interface. The wake-like structure of the patches was evident despite the absence of surf...

Statistical analysis of coherent vortices near a free surface in a fully developed turbulence

The dynamics of coherent vortices, their interactions with an unsheared gas–liquid interface, i.e., free surface, and their contribution to turbulent heat transfer has been investigated in a fully developed turbulence using the results from a direct numerical simulation. Fully resolved free surface turbulence simulations were performed at Reynolds numbers of 150 and 300 based on the wall shear velocity and water depth. Passive heat transfer at a Prandtl number of 1 is enforced by imposing a constant temperature difference between the bottom no-slip boundary and free surface. Instantaneous turbulent flow realizations are stored and used to establish a database from which the statistical properties of the flow can be established. The three-dimensional two-point correlations between the total heat flux at the free surface and the subsurface hydrodynamics are evaluated to determine the spatial extent of the coherent vortices which contribute to the enhancement of heat transport at the free surface. A conditio...

The Karhunen–Loéve decomposition of minimal channel flow

Minimal channel flow is analyzed by means of the Karhunen–Loeve (KL) decomposition. It is shown that the most energetic modes are streamwise rollers followed by outward tilted quasi-streamwise vortices. Both of these mode types have a strong similarity to structures seen in physical experiments. Temporal plots of roll energy, propagating energy, bulk velocity, and representational entropy have been obtained. Study of the evolution of these variables shows a consistent pattern of growth and decay in which entropy plays a key role in describing the events in the turbulent process. The roll and propagating modes are also shown to make independent contributions to the Reynolds stress with the roll modes dominating the profile near the walls and the propagating modes having larger values towards the channel center. A comparison of the KL dimension of this flow and a full channel flow shows that the dimension scales with box size, i.e., it confirms the assertion that dimension is an extensive variable.

Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow

In this work we study, using the results of direct numerical simulations [Housiadas and Beris, “Polymer-induced drag reduction: Viscoelastic and inertia effects of the variations in viscoelasticity and inertia,” Phys. Fluids 15, 2369 (2003)], the effects of changes in the flow viscoelasticity and the friction Reynolds number on several higher order statistics of turbulence, such as the Reynolds stress, the enstrophy, the averaged equations for the conformation tensor, as well as on the coherent structures through a Karhunen–Loeve (K-L) analysis and selected flow and conformation visualizations. In particular, it is shown that, as the zero friction Weissenberg number Weτ0 increases (for a constant zero friction Reynolds number Reτ0) dramatic reductions take place in many terms in the averaged equations for the Reynolds stresses and in all terms of the averaged enstrophy equations. From a Karhunen–Loeve analysis of the eigenmodes of the flow we saw that the presence of viscoelasticity increases significantl...

Direct numerical simulations of free convection beneath an air–water interface at low Rayleigh numbers

Direct numerical simulations of a cooling air–water interface were employed to determine the structure of the temperature, velocity, and vorticity fields in the thin thermal boundary layer formed at the free surface. The simulations were performed at low to moderate Rayleigh numbers. In this flow, the turbulence is initiated by the Rayleigh instability at the interface and is maintained by buoyant production. Visualizations of the flow reveal that the temperature field at the interface is composed of large warm patches surrounded by cooler dense fluid which accumulates in thin bands. The cool fluid associated with the bands initially falls in sheets, but rapidly forms descending tubes and plumes. The turbulence statistics were scaled both with outer and inner variables. The latter scaling is based on the so-called surface strain model which is essentially consistent with Townsend’s inner scaling. It is found that the temperature statistics collapse well using inner variables. On the other hand, the vertical velocity scales well with inner variables within the thermal boundary layer, but at greater depths it becomes more appropriate to use outer scaling. The anisotropic nature of the velocity statistics in the core of the flow is ascribed to the relatively low Rayleigh numbers used in the simulations. An explanation for this anisotropy is offered based on a detailed examination of the turbulence kinetic energy balances.