ALBERT

Notes: A Reynolds stress closure is developed for homogeneous shear-free turbulence subjected to a strong magnetic field at low magnetic Reynolds numbers. A scalar dimensionality anisotropy parameter is introduced to carry information about the distribution of energy in spectral space. This information is vital in modeling MHD turbulence, as it determines both magnitude and anisotropy of the Joule dissipation tensor. The Joule dissipation tensor is modeled by a tensor function, which is bilinear in the Reynolds stress anisotropy and the unit direction vector of the magnetic field. The tensor function coefficients are second-order in the scalar dimensionality parameter. A phenomenological transport equation for the dimensionality parameter is proposed. The model is closed using the pressure–strain model of Sarkar, Speziale and Gatski and a magnetic destruction term in the standard dissipation equation. The purely magnetic linear problem contains no undetermined constants, while the complete model contains two constants. Model predictions for the case of decaying turbulence show very good agreement with direct numerical simulations. © 1998 American Institute of Physics.

Notes: The expansion into eigenfunctions of a general disturbance in a viscous flow is possible only when both the discrete and continuous modes of the Orr–Sommerfeld equation are employed. Proper implementation of the boundary conditions and a method for computation of the continuous modes are developed. The unique phenomenon known as shear sheltering is discussed and illustrated. It is shown that the penetration depth of disturbances into the boundary layer has a dependence on frequency and Reynolds number similar to that of a Stokes layer. A simple model that captures this dependence is developed. © 1998 American Institute of Physics.

Notes: The principle of minimum Fisher information (MFI) and the theory of random Gaussian fields are used to work out the joint distribution function of the density and velocity in homogeneous, isotropic, stationary, nearly incompressible turbulence, in the case where the velocity and pressure are correlated. The appropriate Fisher variables seem to be the mass flux, the density, and the generalized heat function (enthalpy) or pressure head. It is shown that simple constraints on the minimization may be chosen to give a good fit to the pressure distribution function found in recent direct numerical simulations and experiments, where the PDF is exponential for negative p and roughly exp[−(p/p0)3/2]p−1/2 for positive p. In this case, the fit is an improvement on a past MFI calculation, in which the correlations between p and u were not accounted for. In addition, the form of the conditional average 〈p|u〉 as found from direct numerical simulations is taken into consideration. The theory of random Gaussian velocity fields predicts 〈p|u〉=〈p|0〉−βu2, where u2≡u⋅u and β≤1/8 is a constant. In conjunction with this theory, MFI predicts a specific dependence of the conditional average 〈ux2|p〉 on p, where ux is a typical velocity component. The conditional PDF P(ux|p) is slightly non-Gaussian, but P(ux) is Gaussian. The relation 2〈u2δp〉2=〈u2〉[〈u2(δp)2〉−〈u2〉〈(δp)2〉] is predicted. © 1998 American Institute of Physics.

Notes: Transient disturbance growth in parallel two-phase flow is studied. When the disturbance growth is measured in terms of the kinetic energy norm, which is commonly used for single-phase flow, the disturbance growth function does not converge as the number of eigenmodes used in the computation increases. A solution to this problem is presented in the form of a norm that also includes the potential energy of the disturbed interface. This solution is used to examine the two-phase flow experiment by Kao and Park. © 1998 American Institute of Physics.

Notes: Consistency conditions for the prediction of turbulent flows in a rotating frame are examined. It is shown that the dissipation rate should vanish along with the eddy viscosity in the limit of rapid rotations. The latter result is also true when the eddy viscosity is anisotropic and formally follows from the explicit algebraic stress approximation as well as from a phenomenological treatment. The former result has been built into the modeled dissipation rate equation of recent turbulence models where the second result has been violated. In fact, some of these models have the eddy viscosity going to infinity while the dissipation rate vanishes, leading to an inconsistency. For consistency, both of these conditions must be satisfied. The implications of these results for turbulence modeling are thoroughly discussed. © 1998 American Institute of Physics.

Notes: The dynamics of an interface between two incompressible, inviscid, irrotational, and immiscible liquids with densities ρ1 and ρ2 under the influence of a time-dependent gravitational field g(t) is investigated. A Hamiltonian formulation of the system is adopted leading to a perturbative expansion of the equations of motion for the canonical variables. Equations, accurate up to third order in the perturbation amplitude are derived. They are able to describe the initial stage of instability "saturation." The latter equations are integrated iteratively for two standard limiting cases: constant gravity (classical Rayleigh–Taylor instability), g(t)≡g0, and impulsive Richtmyer–Meshkov loading, g(t)=v0δ(t−t0). The comparative growth of various two-dimensional structures and rectangular and hexagonal cells is evaluated. Surface tension effects are considered. © 1998 American Institute of Physics.

Notes: The feasibility of controlling flow patterns of Rayleigh–Bénard convection in a fluid layer confined in a circular cylinder heated from below and cooled from above (the Rayleigh–Bénard problem) is investigated numerically. It is demonstrated that, through the use of feedback control, it is possible to stabilize the no-motion (conductive) state, thereby postponing the transition from a no-motion state to cellular convection. The control system utilizes multiple sensors and actuators. The actuators consist of individually controlled heaters positioned on the bottom surface of the cylinder. The sensors are installed at the fluid's midheight. The sensors monitor the deviation of the fluid's temperatures from preset desired values and direct the actuators to act in such a way so as to eliminate these deviations. The numerical predictions are critically compared with experimental observations. © 1998 American Institute of Physics.

Notes: In this paper the generation and evolution of an edge-wave packet are studied experimentally and numerically. In the laboratory an edge-wave packet is first generated on a sloping beach by a hinge-type wave-maker. Both the free surface displacement and velocity field are measured along several on-offshore cross sections. Numerical results are also obtained by solving the linear shallow-water wave equations and are compared with experimental data. Numerically predicted wave evolution characteristics are in good agreement with those shown by laboratory data. Analyses of the wave amplitude density spectra of both numerical solutions and experimental data show that wave packets are indeed trapped in the nearshore region and consist of a mixture of Stokes and higher-mode edge waves. Furthermore, the Stokes mode dominates in the low frequency range. Two additional wave-maker designs, i.e., the piston-type and the reverse hinge-type, are investigated numerically. Away from the wave-maker the wave forms (time histories) of the wave packets are insensitive to the details of wave-maker movements. The effects of beach slope on the evolution of wave packets are investigated. The behavior of the velocity field and the attenuation rates of runup amplitudes are also discussed. © 1998 American Institute of Physics.

Notes: The interaction of a near-critical axisymmetric incompressible swirling flow in a straight pipe with small inlet azimuthal vorticity perturbations is studied. Certain flow conditions that may reflect the physical situation are prescribed along the pipe inlet and outlet. It is first demonstrated that under these conditions a regular-expansion solution in terms of the small azimuthal vorticity perturbations has a singular behavior around the critical swirl. This singularity infers that large-amplitude disturbances may be induced by the small perturbations when the incoming flow to the pipe has a swirl level around the critical swirl. In order to understand the nature of flows in this swirl range, a small-disturbance analysis is developed. It shows that under the prescribed inlet/outlet conditions, a small but finite inlet azimuthal vorticity perturbation breaks the transcritical bifurcation of solutions of the Euler equations at the critical swirl into two branches of perturbed solutions. When the azimuthal vorticity perturbations are positive these branches show a regular behavior. However, when they are negative, the perturbed branches fold at limit points near the critical swirl, with a finite gap between the two branches, and no near-columnar equilibrium state can exist for an incoming flow with swirl close to the critical level. The flow must develop large disturbances in this swirl range. Beyond this range, two equilibrium states may exist under the same inlet/outlet conditions. When the negative inlet vorticity perturbations become larger in their size, this special behavior uniformly changes into a branch of single equilibrium state for each incoming swirl. The relevance of the results to the appearance of the axisymmetric vortex breakdown in a pipe and the control of this phenomenon using inlet vorticity perturbations is also discussed. The results suggest that, in general, positive inlet azimuthal vorticity perturbations may be used to delay vortex breakdown to higher swirl levels whereas negative perturbations induce the appearance of vortex breakdown at levels below the critical swirl. © 1998 American Institute of Physics.

Notes: Static pressure fluctuations measured in the atmospheric surface layer over a grass covered forest clearing are studied in the context of Townsend's 1961 hypothesis regarding the effect of the outer region on the inner region. It is shown that large-scale pressure features are actively straining the inertial-scale pressure fluctuations, thus invalidating the direct extension of Kolmogorov's 1941 hypothesis to the spectral scaling of pressure within the inertial subrange. A parameter describing the large scale pressure fluctuations is added to the set of variables responsible for inertial-range pressure differences and dimensional analysis is employed to derive an improved scaling law for pressure spectra which more closely matches these and previous experimental results. An examination of the Poisson equation for pressure is conducted and found to support the dimensional and experimental results. © 1998 American Institute of Physics.