Jeffrey Robert Chasnov

Simulation of the Kolmogorov inertial subrange using an improved subgrid model

A subgrid model is developed and applied to a large‐eddy simulation of the Kolmogorov inertial subrange. Currently popular subgrid models are derived from models of the turbulent energy equation, resulting in a significant loss of information as a consequence of the statistical averaging performed in going from the Navier–Stokes equation to the energy equation. The subgrid model developed here is based directly on a model of the Navier–Stokes equation. The improved subgrid model contains two terms: an eddy viscosity and a stochastic force. These terms are computed from the EDQNM stochastic model representation of the momentum equation, and from a fully resolved direct numerical simulation. Use of the subgrid model in a forced large‐eddy simulation results in an energy spectrum that exhibits a clear k−5/3 power‐law subrange with an approximate value Ko=2.1 of the Kolmogorov constant.

Large-Eddy Simulations: Theory and Applications

Over twenty years have passed since the first large eddy simulation (Les) results by Deardorff (1970) were published. During this period, this technique has matured considerably: the underlying theory has been advanced, new models have been developed and tested, more efficient numerical schemes have been used. The progress in computer power and memory has made possible the application of Les to a variety of flows, compressible and incompressible, including heat transfer, stratification, passive scalars and chemical reactions.

The species, sex, and stage specificity of a Caenorhabditis sex pheromone

Four species in the ELEGANS group of subgenus the Caenorhabditis are distinguished by two very different mating systems: androdioecy in C. elegans and Caenorhabditis briggsae with males and self-fertilizing hermaphrodites and dioecy in Caenorhabditis remanei and Caenorhabditis sp. strain CB5161 with males and females. Using chemotaxis assays, we demonstrate that females secrete a potent sex pheromone that attracts males from a distance, whereas hermaphrodites do not. The female sex pheromone is not species-specific, with males of all four species attracted to both the C. remanei and Caenorhabditis sp. female sex pheromones. The pheromone is, however, sex-specific, with only females secreting the pheromone and attracting only males. Furthermore, the sex pheromone is stage-specific, with female secretion and male detection of the pheromone beginning near adulthood. Females lose their attractiveness immediately after mating but regain it several hours after mating ceases. Finally, the female somatic gonad is required for sex-pheromone production, and the male-specific cephalic neurons (CEM) are required for male response.

On the decay of two‐dimensional homogeneous turbulence

Direct numerical simulations of decaying two‐dimensional turbulence in a fluid of large extent are performed primarily to ascertain the asymptotic decay laws of the energy and enstrophy. It is determined that a critical Reynolds number Rc exists such that for initial Reynolds numbers with R(0) Rc the flow field evolves with increasing Reynolds number. Exactly at R(0)=Rc, the turbulence evolves with constant Reynolds number and the energy decays as t−1 and the enstrophy as t−2. A t−2 decay law for the enstrophy was originally predicted by Batchelor for large Reynolds numbers [Phys. Fluids Suppl. II, 12, 233 (1969)]. Numerical simulations are then performed for a wide range of initial Reynolds numbers with R(0)>Rc to study whether a universal power‐law decay for the energy and enstrophy exist as t→∞. Different scaling laws are observed for R(0) moderately larger than Rc. When R(0) becomes sufficiently large so that the energy remains essentially co...

SIMILARITY STATES OF PASSIVE SCALAR TRANSPORT IN ISOTROPIC TURBULENCE

By simple analytical and large‐eddy simulations, the time evolution of the kinetic energy and scalar variance in decaying isotropic turbulence transporting passive scalars are determined. The evolution of a passive scalar field with and without a uniform mean gradient is considered. First, similarity states of the flow during the final period of decay are discussed. Exact analytical solutions may be obtained, and these depend only on the form of the energy and scalar‐variance spectra at low wave numbers, and the molecular transport coefficients. The solutions for a passive scalar field with mean‐scalar gradient are of special interest, and we find that the scalar variance may grow or decay asymptotically in the final period, depending on the initial velocity distribution. Second, similarity states of the flow at high Reynolds and Peclet numbers are considered. Here it is assumed that the solutions also depend on the low‐wave‐number spectral coefficients, but not on the molecular transport coefficients. Th...

Homogeneous buoyancy-generated turbulence

We consider the statistically homogeneous motion that is generated by buoyancy forces after the creation of homogeneous random fluctuations in the density of infinite fluid at an initial instant. The mean density is uniform, and density fluctuations are smoothed by molecular diffusion. This turbulent flow system has interesting properties, and shows how self-generated motion contributes to the rate of mixing of an ‘active’ scalar contaminant. If nonlinear terms in the governing equations are negligible, there is an exact solution which shows that the history of the motion depends crucially on the form of the buoyancy spectrum near zero wavenumber magnitude (κ). According to this solution the Reynolds number of the motion increases indefinitely, so the linear equations do not remain valid. There are indications of similar behaviour when the nonlinear terms are retained. The value of the three-dimensional buoyancy spectrum function at κ = 0 is shown to be independent of time, and this points to the existence of a similarity state of turbulence with decreasing mean-square velocity but increasing Reynolds number at large times. We have made a numerical simulation of the flow field and have obtained the mean-square velocity and density fluctuations and the associated spectra as functions of time for various initial conditions. An estimate of the time required for the mean-square density fluctuation to fall to a specified small value is found. The expected similarity state at large times is confirmed by the numerical simulation, and there are indications of a second similarity state which develops asymptotically when the buoyancy spectrum is zero at κ = 0. The analytical and numerical results together give a comprehensive description of the birth, life and lingering death of buoyancy-generated turbulence.

The decay of axisymmetric homogeneous turbulence

The decay of a homogeneous turbulence generated by an axisymmetric distribution of random impulsive forces acting at the initial instant is studied by means of large‐eddy simulations. The impulsive forces may be either parallel or perpendicular to the symmetry axis. For impulsive forces, which result in a k4 low wave number energy spectrum of the turbulence, it is determined that the flow approaches isotropy on all scales of motion at long times, provided the Reynolds number is large. However, for the type of impulsive forces originally proposed by Saffman [J. Fluid Mech. 27, 581 (1967)], in which a k2 low wave number energy spectrum is produced, the turbulence approaches isotropy only at the smallest scales, and remains significantly anisotropic at the largest and energy‐containing scales. Nevertheless, a similarity state of the flow field establishes itself asymptotically, in which the kinetic energy per unit mass of the turbulence decays as t−6/5.

A model for fully developed turbulence

A model for stationary, fully developed turbulence is presented. The physical model used to describe the nonlinear interactions provides an equation for the turbulent spectral energy function F(k) as a function of the time scale for the energy fed into the system, n−1s. The model makes quantitative predictions that are compared with the following available data of a different nature. (a) For turbulent convection, in the case of a constant superadiabatic gradient and for σ≪1 (σ≡Prandtl number), the convective flux is computed and compared with the result of the mixing length theory (MLT). For the case of a variable superadiabatic gradient, and for arbitrary σ, as in the case of laboratory convection, the Nusselt number N versus Rayleigh number R relation is found to be N=AσR1/3 as recently determined experimentally. The computed Aσ deviates 3% and 8% from recent laboratory data at high R for σ=6.6 and σ=2000. (b) The K–e and Smagorinsky relations. Four alternative expressions for the turbulent (eddy) visco...

Computation of the Loitsianski integral in decaying isotropic turbulence

The time evolution of the Loitsianski integral at high‐Reynolds numbers is determined by computing an ensemble average of a large number of independent large‐eddy simulations of decaying isotropic turbulence. It is found that the Loitsianski integral becomes proportional to tγ at large times and that γ ≊0.25. The present simulations illustrate the efficient use of massively parallel computers for simulating large ensembles of turbulent flows.

The evolution from females to hermaphrodites results in a sexual conflict over mating in androdioecious nematode worms and clam shrimp.

The nematode worm Caenorhabditis elegans and the clam shrimp Eulimnadia texana are two well‐studied androdioecious species consisting mostly of self‐fertilizing hermaphrodites and few males. To understand how androdioecy can evolve, a simple two‐step mathematical model of the evolutionary pathway from a male–female species to a selfing‐hermaphrodite species is constructed. First, the frequency of mutant females capable of facultative self‐fertilization increases if the benefits of reproductive assurance exceed the cost. Second, hermaphrodites become obligate self‐fertilizers if the fitness of selfed offspring exceeds one‐half the fitness of outcrossed offspring. Genetic considerations specific to C. elegans and E. texana show that males may endure as descendants of the ancestral male–female species. These models combined with an extensive literature review suggest a sexual conflict over mating in these androdioecious species: selection favours hermaphrodites that self and males that outcross. The strength of selection on hermaphrodites and males differs, however. Males that fail to outcross suffer a genetic death. Hermaphrodites may never encounter a rare male, and those that do and outcross only bear less fecund offspring. This asymmetric sexual conflict results in an evolutionary stand‐off: rare, but persistent males occasionally fertilize common, but reluctant hermaphrodites. A consequence of this stand‐off may be an increase in the longevity of the androdioecious mating system.