Effect of favorable pressure gradient on transitional spot formation rate

The calculation of the transitional boundary layer requires estimates of the extent of the transition zone, which in turn depends on the rate at which turbulent spots are formed. This rate has been found to scale with local boundary layer thickness and viscosity, and the resulting nondimensional group (called crumble) is a function of the pressure gradient, among other parameters. Available experimental data are analyzed to show that the crumble increases slowly with increasing favorable pressure gradients, being about four times as large as in constant-pressure flow when the Thwaites pressure gradient parameter at the effective origin of the resulting turbulent boundary layer is 0.1 and when transition is driven by free-stream turbulence.

Latitudinal gradient in aerosol properties over the Indian and Southern Oceans during the austral summer

Extensive measurements of columnar aerosol optical depth (AOD), composite (M-T) and black carbon aerosol mass (M-B) concentrations were made over the tropical Indian and Southern Oceans as a part of the Pilot Expedition to the Southern Ocean during the boreal winter. The AOD, M-T and M-B show large latitudinal gradient towards south up to ITCZ. Beyond ITCZ, up to 56 degrees S, AOD and M-B show very low and steady values. However M-T shows large variations in the Southern Ocean due to the enhanced production of sea salt aerosols associated with high sea surface winds. The short wave aerosol radiative forcing at the surface over north of equator is in the range - 10 to -23 W m(-2), whereas that over the Southern Ocean was in the range -4 to -5 W m(-2). The corresponding atmospheric forcing was in the range of 6-13 W m(-2) and 0.8-1.4 W m(-2). This large north south change in the aerosol radiative forcing has important implications to the meridional circulation and hence to climate.

Studies on Unsteady Pressure Fields in the Region of Separating and Reattaching Flows

Experimental studies on the measurement of pressure fields in the region of separating and reattaching flows behind several two-dimensional fore-bodies and one axisymmetric body are reported. In particular, extensive measurements of mean pressure, surface pressure fluctuation, and pressure fluctuation within the flow were made for a series of two-dimensional fore-body shapes consisting of triangular nose with varying included angle. The measurements from different bodies are compared and one of the important findings is that the maximum values of rms pressure fluctuation levels in the shear layer approaching reattachment are almost equal to the maximum value of the surface fluctuation levels.

Nonsimilar boundary layers for non-Darcy mixed convection flow about a horizontal surface in a saturated porous medium

The nonsimilar non-Darcy mixed convection flow about a heated horizontal surface in a saturated porous medium has been studied when the surface temperature is a power function of distance (Tw = T∞ ± Axλ). The analysis is performed for the cases of parallel and stagnation flows with favourable induced pressure gradient. The partial differential equations governing the flow have been solved numerically using the Keller box method. The heat transfer is enhanced due to the buoyancy parameter and wall temperature, but the non-Darcy parameter reduces it. For non-Darcy flow, the similarity solution exists only for the case of parallel flow.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.

Biorthogonal series method for Oseen type flows

A biorthogonal series method is developed to solve Oseen type flow problems. The theory leads to a new set of eigenfunctions for a specific class of linear non-selfadjoint operators containing the biharmonic one. These eigenfunctions differ from those given earlier in the literature for the biharmonic operator. The method is applied to the problem of thermocapillary flow in a cylindrical liquid bridge of finite length with axial through flow. Flow and temperature distributions are obtained at leading order of an expansion for small surface tension Reynolds number and Prandtl number. Another related problem considered is that of cylindrical cavity flow. Solutions for both cases are presented in terms of biorthogonal series. The effect of axial through flow on velocity and temperature fields is discussed by numerical evaluation of the truncated analytical series. The presence of axial through flow not only convectively shifts the vortices induced by surface forces in the direction of the through flow, but also moves their centers toward the outer cylindrical boundary. This process can lead to significantly asymmetric flow structures.

Gradient solid-electrolyte for use with dissimilar gas electrodes

The EMF of a solid-state cell, incorporating a composite solid-electrolyte with gradual variation in composition, and dissimilar gas electrodes, has been studied as a function of temperature and partial pressures at the electrodes. The cell with the configuration: Pt, CO2' + O2' parallel-to Na2CO3\Na(SO4)x(CO3)1-x\Na2SO4 parallel-to SO3'' + SO2'' + O2'', Pt x=0 x=1 was investigated in the temperature range 973 to 1079 K. The solid-electrolyte surface exposed to SO3 + SO2 + O2 gas mixture was doped-Na2SO4, whereas the CO2 + O2 gas mixture was in contact with pure Na2CO3. The composition of the solid solution between the carbonate and sulfate, with hexagonal structure, was varied gradually between the boundary values. It has been found that the EMF of the cell is close to that calculated from thermodynamic data, assuming unit transport number for Na+ ions. The gradient in the concentration of sulfate and carbonate ions in the electrolyte does not give rise to a significant diffusion potential.

Thermodynamic Study of Mixed Anionic Solid Solutions Using Gradient Solid Electrolytes System K2CO3 - K2SO4

The thermodynamic properties of K2CO3 -KSO, solid solutions with hexagonal structure have been measured using a solid-state cell, incorporating a composite solid electrolyte with step-changes in composition. The cell with the configuration Pt, CO2' + O2' || K2CO3 | K2(CO3)x(SO4)1-x || CO2'' + O2'' + Pt X =1 X=X was investigated in the temperature range of 925 to 1165 K. The composite gradient solid electrolyte consisted of pure K2CO3 at one extremity and the solid solution under study at the other. The Nernstian response of the cell to changes in partial pressures of CO2 and O2 at the electrodes and temperature was demonstrated. The activity of K2CO3 in the solid solution was measured by three techniques. All three methods gave identical results, indicating unit transport number for K+ ions and negligible diffusion potential due to concentration gradients of carbonate and sulfate ions. The activity of K2CO3 exhibits positive deviation from Raoult's law. The excess Gibbs energy of mixing of the solid solution can be represented using a subregular solution model DELTAG(E) = X(1 - X)[5030X + 4715(1 - X)] J mol-1 By combining this information with the phase diagram, mixing properties of the liquid phase were obtained.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Accelerated gradient based diffuse optical tomographic image reconstruction

Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.