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A review was made of power spectral methods for determining linear response of structures to random pressure fluctuations. Various simplifying assumptions are made for the purpose of obtaining useful formula for structural response. The transmission of sound through a flexible structure into an interior cavity was also treated.
Papers from private industry reporting applications of remote sensing to oil and gas exploration were presented. Digitally processed LANDSAT images were successfully employed in several geologic interpretations. A growing interest in digital image processing among the geologic user community was shown. The papers covered a wide geographic range and a wide technical and application range. Topics included: (1) oil and gas exploration, by use of radar and multisensor studies as well as by use of LANDSAT imagery or LANDSAT digital data, (2) mineral exploration, by mapping from LANDSAT and Skylab imagery and by LANDSAT digital processing, (3) geothermal energy studies with Skylab imagery, (4) environmental and engineering geology, by use of radar or LANDSAT and Skylab imagery, (5) regional mapping and interpretation, and digital and spectral methods.
The cross-spectra of temperature and ozone mass mixing ratio at 42 km and 28 km has been determined for spring (1971) and summer (1971-2) over Christchurch, New Zealand (44 S, 172 E). The sources of data are the SCR and BUV experiments on Nimbus 4. The observed covariances are compared with a model in which the temperature and ozone perturbations are forced by an upward propagating planetary wave. The agreement between the observations and the model is reasonable. It is suggested that this cross-spectral method permits an estimate of the meridional gradient of ozone mass mixing ratio from measurements of the vertical profile of ozone mass mixing ratio at one location, supported by temperature profiles from at least two locations.
An algorithm and ILLIAC computer program, developed for the simulation of homogeneous incompressible turbulence in the presence of an applied mean strain, are described. The turbulence field is represented spatially by a truncated triple Fourier series (spectral method) and followed in time using a fourth-order Runge-Kutta algorithm. These include: (1) transformation of variables suggested by Taylor's sudden-distortion theory; (2) implicit viscous diffusion by use of an integrating factor; (3) implicit pressure calculation suggested by Taylor's sudden-distortion theory, and (4) inexpensive control of aliasing by random and phased coordinate shifts.
An office size digital computer with capabilities exceeding a CDC 7600 can be constructed for less than 300 K and spectral methods offer a factor ten improvement over finite difference methods. Integration of these facts can produce two orders of magnitude reduction in cost of fluid dynamic computations and permit solution of 3-D problems which were not previously feasible.
A three dimensional study of convection in a self gravitating sphere of Boussinesq fluid with a Rayleigh number of 10 to the 10th power and a Prandtl of 1 is presented. The velocity and temperature of the fluid are computed at the largest wavelengths using spectral methods. A confirmation that the fluid is anisotropic and that the energy spectra are not smooth functions of wavelength but have a large amount of fine structure is discussed. The parameterization of the transport properties of the unresolvable inertial subrange with eddy viscosities and diffusivities is described. The time dependent fluctuations in the energy spectra and how they cascade from large to small wavelengths is examined.
Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.
The full time-dependent two dimensional Navier-Stokes equations are solved using spectral methods to achieve high spatial accuracy and high order time-splitting methods together with conformal mapping methods to allow simulation of flow over steep waves, including general turbulent Reynolds stresses. The programs are used to study the properties of laminar and turbulent flow over a flat plate and in various wavy geometries. Results are compared with both available theory and experiment. For laminar flow, good agreement is achieved. For turbulent flow, the agreement is less satisfactory and may be explained by the simplified turbulent modelling use in the calculations.
Two dimensional incompressible flow over wavy surfaces are analyzed numerically by spectral methods. Algorithms for periodic flows (Fourier modes in the periodic flow direction and Chebycheff modes in the normal direction), and inflow-outflow boundary conditions (Chebycheff modes used in both directions) are described. Results obtained using both codes are reported for laminar flows. Comparisons with known theoretical and experimental results are made.
Jordan's (1969) spectral method of leaf-area index determination from measurements of the transmitted light at the forest floor is evaluated under a wide variety of illumination conditions in the Luquillo Rain Forest of Puerto Rico, using a hand-held radiometer. Previously suggested 'correction factors' for temporal adjustment were found to degrade the data. Quantitative use of the method was found to be restricted to high sun periods. Data collected under uniformly overcast conditions were of greater stability than under clear skies, however, stability was impaired by changes in cloud thickness. Care must be taken to minimize irradiational variability and to adquately sample the spatial variability.
Spectral methods are used to solve the Navier-Stokes equations numerically for two-dimensional incompressible flow over wavy surfaces. Results obtained for high Reynolds number laminar flows and turbulent flows are compared to experiment and analytical theory. Overall, good agreement has been achieved.
The results of a numerical, three-dimensional study of convection in a self-gravitating sphere of Boussinesq fluid with a Rayleigh number of 10-billion and a Prandtl number of 1 are presented. The velocity and temperature are computed by using spectral methods in the horizontal and finite-differencing in the radial directions. An eddy viscosity and diffusivity are needed to model the subresolution flow. For Rayleigh numbers much less than 10-billion the flows do not have well-defined inertial ranges, and an eddy viscosity and diffusivity cannot be assigned in this self-consistent manner. By computing the energy spectra as well as the detailed energy budgets as a function of wavenumber, it is shown that for Rs = 10-billion there is an inertial range for the modes corresponding to spherical harmonics with l greater than 6.
Two-dimensional incompressible flow over wavy surfaces is studied numerically by spectral methods. Turbulence effects are modeled. Results for symmetric and asymmetric wave forms are presented. Effect of propagating surface waves on drag reduction is studied. Comparisons between computer simulations and experimental results are made.
A numerical scheme is presented, which employs a standard finite difference approximation for the viscous terms in high Reynolds number flows, and resorts to pseudo-spectral methods for the advection terms to greatly reduce the major source of numerical error without dramatically increasing computational cost. The spectral/finite difference (SFD) method evaluates the advection term and second-order differences to evaluate the diffusion term. The fully finite difference (FFD) method with second-order central differences on both terms is also used. The SFD method can handle strong shocks and can outperform the FFD method at moderate viscosity.
Simulations of reconnection utilizing spectral methods show that the 'reconnection zone' exhibits internal structure in the form of a current filament and a 'quadrupole' of kinetic vorticity. A qualitative model of the dynamical role of these local structures is presented. It is suggested that the effect of small scale structures near the X-point is to increase the rate of reconnection.
The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.
The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.
Results are proven concerning certain projection operators on the space of all polynomials of degree less than or equal to N with respect to a class of one-dimensional weighted Sobolev spaces. The results are useful in the theory of the approximation of partial differential equations with spectral methods.