Consistent with the observed t to the -n decay laws for isotropic homogeneous turbulence and the form of the longitudinal correlation function f(r, t) for small r, the Hopf Phi equation is shown to be satisfied approximately by an asymptotic power series in t to the -n. This solution features a self-similar universal equilibrium functional which manifests Kolmogoroff-type scaling.

Rosen, G.↗

NASA NTRS1981

Grid-generated isotropic homogeneous turbulence at high Reynolds numbers

Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.

Rosen, G.↗

NASA NTRS1981

Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence

An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.

Rosen, G.↗

NASA NTRS1980

Broadness, decay, and correlation functions of isotropic homogeneous turbulence

General theoretical relationships consistent with experiments are obtained for isotropic homogeneous incompressible-fluid turbulence governed by the Navier-Stokes flow equation. A key quantity that structures the turbulence is the 'broadness' B of the probability measure over velocity fields. Both the decay law and the longitudinal correlation function for small r appear as simple functions of this quasiconstant parameter B.

Rosen, G.↗

NASA NTRS1980

Semi-classical Reissner-Nordstrom model for the structure of charged leptons

The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.

Rosen, G.↗

NASA NTRS1980

Restricted invariance of the Navier-Stokes equation

It is well known that the classical Navier-Stokes equation for three-dimensional incompressible viscous flow is invariant under Galilean transformations. In the present paper, it is shown that, although the general invariance group is no larger than Galilean-scale dilitation, the Navier-Stokes equation for incompressible viscous flow admits time-dependent rotational invariance for solutions of special types.

Rosen, G.↗

NASA NTRS1980

Space-time metrical fluctuations induced by cosmic turbulence

For a stochastic stress-energy tensor associated with cosmic turbulence, it is observed that Einstein's equations imply fluctuations in the space-time metric tensor. Such metrical fluctuations are shown to engender modified values for the average effective proper density and total pressure and thus to alter the solutions to the Friedman equations.

Rosen, G.↗

NASA NTRS1980

A remarkable operator version of the Navier-Stokes equation

The Navier-Stokes equation is transformed into a closed nonlinear equation for the convected curl operator. It is shown how Lie algebraic methods can be employed to solve the obtained double-commutator equation. The proposed operator equation provides a way to the further development of the Navier-Stokes fluid flow theory.

Rosen, G.↗

NASA NTRS1979

Are large concentration of atomic H storable in tritium-impregnated solid in H2 below 0.10 K

The storage and release of atomic hydrogen produced by the beta decay of tritium contained in a crystalline solid H2 matrix at concentrations greater than 2% and temperatures below 0.80 K are investigated. The temperature of a sample chamber containing tritium-impregnated H2 and placed in the mixing chamber of a dilution refrigerator was measured as the chamber was heated and cooled in order to determine the rates of energy storage and release. It is found that for samples containing 1.2 wt.% tritium, after storage at 0.054 K for 40 h, an increase in sample temperature to a trigger point of 0.17 K leads to an energy release due to the destabilization of atomic H in H2 as predicted by the phenomenological rate process theory. For a tritium weight fraction of 2.5%, energy releases were triggered at 0.54 and 0.82 K after storage at 0.080 K, indicating the trapping of H atoms at the sites of T2 and HT molecules in the sample. The application of a 15 kG magnetic field is shown to increase the storage capacity of T2 traps while reducing that of HT traps, and to lower the trigger temperatures of both. Results suggest that the direct conversion of nuclear energy to chemical energy may become technically feasible in the future.

Rosen, G.↗

NASA NTRS1979

Solutional method for the energies of a parameter-dependent system

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Rosen, G.↗

NASA NTRS1978

Approximate solutions to the Navier-Stokes initial value problem

A Galerkin-Ritz procedure for any arbitrary system of field equations is shown to follow generically from 'two-functional' variational conditions. The initial-value problem for boundary-free incompressible Navier-Stokes flow is solved analytically in the two-parameter-function approximation.

Rosen, G.↗

NASA NTRS1978

Requisite temperatures for the stabilization of atomic H in solid H2

If an atomic hydrogen/molecular hydrogen propellant containing at least 15% free H atoms by weight may be used, values for the theoretical specific impulse near and above 750 s may be predicted. The tritium-impregnation concept has been applied to manufacturing such an H/H2 propellant, and a phenomenological rate process theory has been derived for the matrix-isolation storage and equilibrium stability of atomic H produced at such ultralow temperatures in tritium-impregnated H2. It is suggested that an energy storage efficiency greater than 0.30 may be obtained at temperatures below 100 mK. So that the storage of atomic H is stable with respect to arbitrary small perturbations, the surface temperature must be less than a critical value dependent on sample volume, tritium weight fraction, and energy storage efficiency. A derivation of the formula for this critical surface temperature is presented, noting that the energy storage efficiency is to be fixed by experiment.

Rosen, G.↗