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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Nearly steady flows in GONG prototype data

Doppler velocity images obtained with the GONG prototype instrument were analyzed to measure the nearly steady photospheric flows. The data consists of 88 images each of velocity, intensity, and modulation obtained at 20:00 UT on 88 days from July 1992 to February 1994. Each velocity image was temporally filtered to remove the p-mode oscillations, masked to exclude active regions, and then analyzed using spherical harmonics and orthogonal functions as described by Hathaway (1992). The spectral coefficients show very consistent results for the entire time interval with some evidence of year-to-year variations. The rotation profile agrees well with previous results and exhibits a north-south asymmetry that reverses sign during the 20 month interval. The residual rotation velocities exhibit structures with amplitudes of approximately 5 m/s that may be related to torsional oscillations. The meridional circulation is directed from the equator toward the poles with a peak velocity in the photosphere of approximately 50 m/s. The higher order components are very weak but indicate a divergent flow from the mid-latitudes (opposite that found for the June 1989 data). The convective limb shift is well fit by a 3rd order polynomial. The convection spectrum has a prominent peak at spherical harmonic degrees of l approximately 150 with very little signal in the low degree modes. Analysis of this signal shows that there is no evidence for giant cell convection at the level of approximately 10 m/s for all modes up to l = 32.

Hathaway, David H.↗
NASA NTRS1996

Ionospheric convection during different phases of magnetospheric substorms

Observations of ionospheric convection flows at a range of local times during the various phases of the substorm cycle are reported on with the aim of investigating the convection behavior during a range of times and phases. The ionospheric flow observations are from the EISCAT and DMSP satellites. The substorm phases are identified from energetic particle measurements from geosynchronous satellites. The growth phase convection indicates an initial expansion of the polar cap. There is an unexplained poleward motion of the flow reversal boundary (FRB). It is concluded that this motion does not necessarily provide a true representation of the balance between reconnection at the dayside and in the tail. The expansion phase flows do not show any evidence for tail reconnection until late in the phase. The convection during the recovery phase is indicative of tail reconnection as there is evidence that there is only a lobe cell driving convection on the dayside.

Lester, M.↗
NASA NTRS1995

Four large-scale field-aligned current systmes in the dayside high-latitude region

A system of four current sheets of large-scale field-aligned currents (FACs) was discovered in the data set of simultaneous Viking and Defense Meteorological Satellire Program-F7 (DMSP-F7) crossing of the dayside high-latitude region. This paper reports four examples of this system that were observed in the prenoon sector. The flow polarities of FACs are upward, downward, upward, and downward, from equatorward to poleward. The lowest-latitude upward current is flowing mostly in the central plasma sheet (CPS) precipitation region, often overlapping with the boundary plasma sheet (BPS) at its poleward edge, andis interpreted as a region 2 current. The pair of downward and upward FACs in the middle of te structure are collocated with structured electron precipitation. The precipitation of high-energy (greater than 1 keV) electrons is more intense in the lower-latitude downward current sheet. The highest-latitude downward flowing current sheet is located in a weak, low-energy particle precipitation region, suggesting that this current is flowing on open field lines. Simulaneous observations in the postnoon local time sector reveal the standard three-sheet structure of FACs, sometimes described as region 2, region 1, and mantle (referred to the midday region O) currents. A high correlation was found between the occurrence of the four FAC sheet structure and negative interplanetary magnetic field (IMF) B(sub Y). We discuss the FAC structurein terms of three types of convection cells: the merging, viscous, andlobe cells. During strongly negative IMF B(sub Y), two convection reversals exist in the prenoon sector; one is inside the viscous cell, and the other is between the viscous cell and the lobe cell. This structure of convection flow is supported by the Viking electric field and auroral UV image data. Based on the convection pattern, the four FAC sheet structure is interpreted as the latitude overlap of midday and morning FAC systems. We suggest that the for-current sheet structure is common in a certain prenoon localtime sector during strongly negative IMF B(sub Y).

Ohtani, S.↗
NASA NTRS2016

Aerosol Meteorology of the Maritime Continent for the 2012 7SEAS Southwest Monsoon Intensive Study - Part 1: Regional-scale Phenomena

The largest 7 Southeast Asian Studies (7SEAS) operation period within the Maritime Continent (MC) occurred in the August-September 2012 biomass burning season. Included was an enhanced deployment of Aerosol Robotic Network (AERONET) sun photometers, multiple lidars, and field measurements to observe transported smoke and pollution as it left the MC and entered the southwest monsoon trough. Here we describe the nature of the overall 2012 southwest monsoon (SWM) and biomass burning season to give context to the 2012 deployment. The MC in 2012 was in a slightly warm El Nino Southern Oscillation (ENSO) phase and with spatially typical burning activity. However, overall fire counts for 2012 were 10 lower than the Reid et al. (2012) baseline, with regions of significant departures from this norm, ranging from southern Sumatra (+30) to southern Kalimantan (42). Fire activity and monsoonal flows for the dominant burning regions were modulated by a series of intraseasonal oscillation events (e.g., Madden-Julian Oscillation, or MJO, and boreal summer intraseasonal oscillation, or BSISO). As is typical, fire activity systematically progressed eastward over time, starting with central Sumatran fire activity in June related to a moderately strong MJO event which brought drier air from the Indian Ocean aloft and enhanced monsoonal flow. Further burning in Sumatra and Kalimantan Borneo occurred in a series of significant events from early August to a peak in the first week of October, ending when the monsoon started to migrate back to its wintertime northeastern flow conditions in mid-October. Significant monsoonal enhancements and flow reversals collinear with tropical cyclone (TC) activity and easterly waves were also observed. Islands of the eastern MC, including Sulawesi, Java, and Timor, showed less sensitivity to monsoonal variation, with slowly increasing fire activity that also peaked in early October but lingered into November. Interestingly, even though fire counts were middling, resultant AERONET 500nm aerosol optical thickness (AOT) from fire activity was high, with maximums of 3.6 and 5.6 in the Sumatra and Kalimantan source regions at the end of the burning season and an average of approximately 1. AOTs could also be high at receptor sites, with a mean and maximum of 0.57 and 1.24 in Singapore and 0.61 and 0.8 in Kuching Sarawak. Ultimately, outside of the extreme 2015 El Nino event, average AERONET AOT values were higher than any other time since sites were established. Thus, while satellite fire data, models, and AERONET all qualitatively agree on the nature of smoke production and transport, the MC's complex environment resulted in clear differences in quantitative interpretation of these datasets.

Reid, Jeffrey S.↗
NASA NTRS1977

Numerical solutions of Navier-Stokes equations for the structure of a trailing vortex

The structure and decay of a trailing vortex were analyzed during the numerical solutions of the full Navier-Stokes equations. Unsteady forms of the governing equations were recast in terms of circulation, vorticity, and stream function as dependent variables, and a second upwind finite difference scheme was used to integrate them with prescribed initial and boundary conditions. The boundary conditions at the outer edge and at the outflow section of the trailing vortex were considered. Different models of the flow were postulated, and solutions were obtained describing the development of the flow as integration proceeds in time. A parametric study was undertaken with a view to understanding the various phenomena that may possibly occur in the trailing vortex. Using the Hoffman and Joubert law of circulation at the inflow section, the results of this investigation were compared with experimental data for a Convair 990 wind model and a rectangular wing. With an exponentially decaying law of circulation at the inflow section and an adverse pressure gradient at the outer edge of the trailing vortex, solutions depict vortex bursting through the sudden expansion of the core and/or through the stagnation and consequent reversal of the flow on the axis. It was found that this bursting takes place at lower values of the swirl ratio as the Reynolds number increases.

Jain, A. C.↗
NASA NTRS1951

Viscous Effects on Impact Probes in a Subsonic Rarified Gas Flow

The problem of time response of pressure gaging systems used with low density flows has been discussed in Ref ]4, and the effect of outgassing on pressure magnitudes was indicated in the same reference. Briefly, gases or vapors adhering to the internal walls of the pressure gaging system behave like gas sources and produce a pressure rise in the gage system which has no relation to the external flow. The effect can also occur in the reverse direction, with "in-gassing" or the action of an effective sink in the gage system as gases entering through the probe orifice are adsorbed to the walls. For given surface conditions, the magnitude of the pressure error to be expected due to out-gassing depends on the dimensions of the probe system. In the present tests, it was desirable to use the smallest possible probe to yield the lowest possible Reynolds number. The lower limit on size was fixed by outgassing effects, evaluated by the following procedure. 2.0 PROCEDURE The pumping system was adjusted to give a pressure, measured at the reservoir, of 9 microns Hg with no flow into the wind tunnel. The upstream metering valve was then opened and the air flow rate adjusted to give a pressure of 100 microns in the reservoir under steady flow conditions, The pressure read by one of the impact tubes, inserted into the flow, was measured. The upstream metering valve was then closed rapid)y, and the reservoir pressure, p0, and the impact probe pressure, Pj, were measured simultaneously at definite time intervals. Another probe was inserted into the flow and the procedure repeated, until the pressure-time data had been obtained for each probe investigated. The results for a series of tests Involving probe Nos.l, 2 and 3 are shown on HYD 2616 300 RESULTS From HYD 2616, It is clear that the smallest probe (No.3) requires the longest time to reach equilibrium. After a sufficient time has elapsed (about 180 seconds), this probe read the same, within the accuracy of measurement, as the other two, When a similar experiment was performed utilizing a probe which was one-half the size of probe No.2, it indicated a pressure, after 180 seconds, which was almost 10 microns Hg higher than the other probes. Accordingly, only probe Nos. 1, 2, 3 and 4 were employed in the experiments, and a time of at least 180 seconds was allowed to elapse between a change of setting and the reading of the instruments0

Kane, E. D.↗
NASA NTRS1998

Shear-Sensitive Liquid Crystal Coating Method: Surface-Inclination Effects on Shear Vector Measurements

The shear-sensitive liquid crystal coating (SSLCC) method is an image-based technique for both visualizing dynamic surface-flow phenomena, such as transition and separation, and for measuring the continuous shear-stress vector distribution acting on an aerodynamic surface. Under proper lighting and viewing conditions (discussed below), the coating changes color in response to an applied aerodynamic shear. This color-change response is continuous and reversible, with a response time of milliseconds, and is a function of both the shear magnitude and the shear vector orientation relative to the observer. The liquid crystal phase of matter is a weakly-ordered, viscous, non-Newtonian fluid state that exists between the nonuniform liquid phase and the ordered solid phase of certain organic compounds. Cholesteric liquid crystal compounds possess a helical molecular arrangement that selectively scatters white light, incident along the helical axis, as a three-dimensional spectrum. This property is linked to the helical pitch length, which is within the range of wavelengths in the visible spectrum. The pitch length, and hence the wavelength of the scattered light, is influenced by shear stress normal to the helical axis. This unique optical property produces a measurable color change in response to an applied shearing force. The full-surface shear stress vector measurement method, developed at NASA-Ames, is schematically illustrated. As with the visualization method, the coated test surface is illuminated from the normal direction with white light and the camera is positioned at an above-plane view angle of approximately 30 deg. Experiments have been initiated at NASA Ames to begin the process of quantifying surface-inclination (surface-curvature) effects on shear vector measurement accuracy. In preliminary experiments, surface-inclination angles theta(sub x), theta(sub y) of 0, +/-5, +/-10, and +/-15 deg were employed. In this arrangement, white-light illumination was positioned normal to the untilted test surface, and the camera above-plane view angle was set at 30 deg relative to the untilted test surface. As can be seen, vector-aligned lambda(sub d) values showed no dependence on theta(sub x) or theta(sub y) for absolute values of these tilt angles is less than or equal to 15 deg. Acquisition and analyses of full-surface color images are presently underway to definitively document the insensitivity limits of the shear vector measurement methodology to surface-slope variations.

Reda, Daniel C.↗
NASA NTRS1993

Double shock pairs in the solar wind

A numerical study of the evolution of a velocity enhancement disturbance in the solar wind is presented in terms of a 1D isentropic MHD flow model. It is shown that the disturbance steepens and evolves into a double shock pair while propagating outward away from the sun. The double shock pair consists of a reverse fast shock, a reverse slow shock, a forward slow shock, and a forward fast shock in order of distance away from the sun. The formation time of the double shock pair is nearly inversely proportional to the average velocity gradient of the disturbance. When the double shock pair is fully developed, the strength of the fast shocks is essentially determined by the disturbance amplitude, while the slow shocks behave differently. Their strength increases first with the disturbance amplitude but starts to decrease once the disturbance amplitude exceeds a certain value.

Hu, Y. Q.↗
NASA NTRS1981

The role of zonally asymmetric heating in the vertical and temporal structure of the global scale flow fields during FGGE SOP-1

By examining the vertical structure of the low order spherical harmonics of the divergence and vorticity fields, the relative contribution of tropical and monsoonal circulations upon the global wind fields was estimated. This indicates that the overall flow over North America and the Pacific between January and February is quite distinct both in the lower and upper troposphere. In these longitudes there is a stronger tropical overturning and subtropical jet stream in January than February. The divergent flow reversed between 850 and 200 mb. Poleward rotational flow at upper levels is associated with an equatorward rotational flow at low levels. This suggests that the monsoon and other tropical circulations project more amplitude upon low order (global scale) representations of the flow than do the typical midlatitude circulations and that their structures show conspicuous changes on a time scale of a week or less.

Paegle, J.↗
NASA NTRS1992

Excitation of slosh waves associated with low frequency impulsive reverse gravity acceleration of geyser initiation

The objective of the cryogenic fluid management of the spacecraft propulsion system is to develop the technology necessary for acquisition or positioning of liquid and vapor within a tank in reduced gravity to enable liquid outflow or vapor venting. The requirement to settle or to position liquid fuel over the outlet end of the spacecraft propellant tank prior to main engine restart poses a microgravity fluid behavior problem. The purpose of the present study is to investigate the stability of the most efficient technique for propellant resettling through the minimization of propellant usage and weight penalties. In this study slosh wave excitation induced by the resettling flow field activated by 0.1 Hz low frequency, impulsive reverse gravity acceleration, during reorientation with the initiation of geyser for liquid fill levels of 30, 50, 65, 70 and 80 percent, have been studied. Characteristics of slosh waves with various frequencies excited are discussed. Slosh wave excitation shift the fluid mass distribution in the container which impose time dependent variations in spacecraft moment of inertia. This information is important for the spacecraft control during the course of liquid reorientation.

Hung, R. J.↗
NASA NTRS1972

Model development of supersonic trough wind with shocks.

The time-dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed field line results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its 'frozen-in' plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal, but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates, the direction of the shock motion can be reversed so that the supersonic region will expand along the field line toward the state characterizing the supersonic polar wind.

Grebowsky, J. M.↗
NASA NTRS1972

Breakdown phenomena in reverse biased silicon solar cells.

Solar cell reverse current-voltage characteristics have been found to vary widely and to be generally unstable. At reverse voltages greater than approximately 20 V and at cell power dissipations of more than 4 W, the probability of permanent breakdown, resulting in cell short-circuit failure, was found to increase with increasing voltage and exposure time. Shorted cells showed evidence of cell contact material and silicon melting in very localized areas with lava-like flow patterns and channels bridging the p and n contacts.

Rauschenbach, H. S.↗
NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗
NASA NTRS2012

Photogrammetric and Global Positioning System Measurements of Active Pahoehoe Lava Lobe Emplacement on Kilauea, Hawaii

Basalt is the most common rock type on the surface of terrestrial bodies throughout the solar system and -- by total volume and areal coverage -- pahoehoe flows are the most abundant form of basaltic lava in subaerial and submarine environments on Earth. A detailed understanding of pahoehoe emplacement processes is necessary for developing accurate models of flow field development, assessing hazards associated with active lava flows, and interpreting the significance of lava flow morphology on Earth and other planetary bodies. Here, we examine the active emplacement of pahoehoe lobes along the margins of the Hook Flow from Pu'u 'O'o on Kilauea, Hawaii. Topographic data were acquired between 21 and 23 February 2006 using stereo-imaging and differential global positing system (DGPS) measurements. During this time, the average discharge rate for the Hook Flow was 0.01-0.05 cubic m/s. Using stereogrammetric point clouds and interpolated digital terrain models (DTMs), active flow fronts were digitized at 1 minute intervals. These areal spreading maps show that the lava lobe grew by a series of breakouts tha t broadly fit into two categories: narrow (0.2-0.6 m-wide) toes that grew preferentially down-slope, and broad (1.4-3.5 m-wide) breakouts that formed along the sides of the lobe, nearly perpendicular to the down-flow axis. These lobes inflated to half of their final thickness within approx 5 minutes, with a rate of inflation that generally deceased with time. Through a combination of down-slope and cross-slope breakouts, lobes developed a parabolic cross-sectional shape within tens of minutes. We also observed that while the average local discharge rate for the lobe was generally constant at 0.0064 +/- 0.0019 cubic m/s, there was a 2 to 6 fold increase in the areal coverage rate every 4.1 +/- 0.6 minutes. We attribute this periodicity to the time required for the dynamic pressurization of the liquid core of the lava lobe to exceed the cooling-induced strength of the lobe margins. Using DGPS-derived DTMs of the topography before and after pahoehoe lobe emplacement, we observed that the lava typically concentrated within existing topographic lows, with the lobe reaching a maximum thickness of approx 1.2 m above the lowest points of the initial topography and above reverse-facing slopes. Lobe margins were typically controlled by high-standing topography, with the zone directly adjacent to the final flow margin having average relief that is approx 4 cm higher than the lava-inundated region. This suggests that irregularities approx 25% of the height of the smallest breakout elements (i.e., toes) can exert a strong control on the paths of low-discharge pahoehoe lobes, with stagnated toes forming confining margins that allow interior portions of flow to topographically invert the landscape by inflation.

Hamilton, Christopher W.↗
NASA NTRS1990

Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model

A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast.

Cao, Jichang↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS2002

Satellite-Based Assessment of Sediment Transport, Distribution and Resuspension Associated with the Atchafalaya River Discharge Plume

Tbe Atchafalaya River discharges over 80 x 10(exp 6) tons of sediment annually onto the broad shallow continental shelf of central and western Louisiana. Satellite imagery from the NOAA AVHRR and Terra MODIS are used in this paper to quantify suspended sediment concentrations and to assess sediment transport processes along the Louisiana shelf under varying conditions of river discharge and wind forcing. The image data reveal the maim sources of sediment, direction of transport amd regional extent of wind-wave resuspension. The prevailing easterly winds transport much of the suspended sediments westward toward the Chernier Plain in a well-defined mud stream. Westerly flow rates of 25-50 cm/s (21-43 km per day) have been measured, yielding a transit time of about 1.5-2.5 days from the mouth of Atchafalaya Bay to the Chernier Plain. Progradation rates along the Chernier Plain coast reach 50 m per year. The westward-flowing Atchafalaya "mud stream" is rapidly disrupted by westerly winds and northerly winds, which accompany frequent winter storms and less frequent tropical storms or hurricanes. During these events, the coastal current reverses and sediments are rapidly transported out of Atchafalaya Bay and offshore where substantial sedimentary deposits can also be found. Offshore sediment fluxes during storm events, in combination with wind-wave resuspension, can result in surface sediment "plumes" extending 70 km offshore and 150 km alongshore. Field measurements of suspended sediment concentrations, current and wind velocities, and directions are used to assess sediment transport processes on the shelf. These combined processes are extending the pro-delta deposits of the Atchafalaya-Wax Lake delta complex far onto the continental shelf and supplying sediments for a renewal era of progradation along tbe downdrift Chernier Plain coast.

Walker, Nan↗
NASA NTRS2003

Turbulent Plane Wakes Subjected to Successive Strains

Six direct numerical simulations of turbulent time-evolving strained plane wakes have been examined to investigate the response of a wake to successive irrotational plane strains of opposite sign. The orientation of the applied strain field has been selected so that the flow is the time-developing analogue of a spatially developing wake evolving in the presence of either a favourable or an adverse streamwise pressure gradient. The magnitude of the applied strain rate a is constant in time t until the total strain e(sup at) reaches about four. At this point, a new simulation is begun with the sign of the applied strain being reversed (the original simulation is continued as well). When the total strain is reduced back to its original value of one, yet another simulation is begun with the sign of the strain being reversed again back to its original sign. This process is done for both initially "favourable" and initially "adverse" strains, providing simulations for each of these strain types from three different initial conditions. The evolution of the wake mean velocity deficit and width is found to be very similar for all the adversely strained cases, with both measures rapidly achieving exponential growth at the rate associated with the cross-stream expansive strain e(sup at). In the "favourably" strained cases, the wake widths approach a constant and the velocity deficits ultimately decay rapidly as e(sup -2at). Although all three of these cases do exhibit the same asymptotic exponential behaviour, the time required to achieve this is longer for the cases that have been previously adversely strained (by at approx. equals 1). These simulations confirm the generality of the conclusions drawn in Rogers (2002) regarding the response of plane wakes to strain. The evolution of strained wakes is not consistent with the predictions of classical self-similar analysis; a more general equilibrium similarity solution is required to describe the results. At least for the cases considered here, the wake Reynolds number and the ratio of the turbulent kinetic energy to the square of the wake mean velocity deficit are determined nearly entirely by the total strain. For these measures the order in which the strains are applied does not matter and the changes brought about by the strain are nearly reversible. The wake mean velocity deficit and width, on the other hand, differ by about a factor of three when the total strain returns to one, depending on whether the wake was first "favourably" or "adversely" strained. The strain history is important for predicting the evolution of these quantities.

Rogers, Michael M.↗