Engineering topics

Wolff, Charles L.

Publications and source records attributed to Wolff, Charles L..

At least 19 records

NASA NTRS2018

Solar Irradiance Variability, Influenced by r Modes

A spectrum of the four-decade solar irradiance record has a prominent cluster of power for periodicities near 1 yr. Correlating irradiance with a bandpass filter showed that periodicity values were not constant, but varied sinusoidally with each cycle lasting 14 ± 1 yr. The large modulation amplitude makes solar frequencies ≥1 yr(exp −1) hard to detect at the solar surface. After removing the modulation, a Lomb–Scargle spectrum exposed two true periodicities: 1.006 and 0.920 yr. They are interpreted as the synodic rotation periods of r modes of lowest angular degree (ℓ = 1). The first propagates in the stable interior and the second in the convective envelope perturbed by its several flow fields. The rotational beat period of the two modes is about 10.9 yr. This is close to the average length of a solar cycle and possibly controls this average. The 1.006 yr periodicity dominates most of the filtered irradiance record but an abrupt change to about 0.8 yr occurs in mid-2010. Also found was evidence for higher-degree r modes (ℓ = 2 to 8) and a curious sawtooth modulation with a recurrence period of 2.6 yr.

Wolff, Charles L.↗

NASA NTRS2008

Identification of g-Modes in a Sun with Mixed Core

The elusive g-mode oscillations mainly operate deep inside the Sun where the nuclear fires burn. They can modify the Sun's output on a cadence of months and years when coupled into groups. Scientists have failed to detect their oscillation periods because they were looking for periods much too short. This paper shows that if g-modes slowly mix the central 16% of the Sun on a million year time scale or less, then g-mode periods become two and a half times longer. These longer periods are identified in existing data from the orbiting GOLF and SOH0 experiments. This opens the door to measuring the Sun's central regions with g-modes just as helioseismology has used sound waves to probe its outer half.

Wolff, Charles L.↗

NASA NTRS2008

Evidence for Intersections of Coupled g-Mode Sets as a Source of High Frequency Oscillations in Sunspot Occurrence

We show that sunspots tend to appear at longitudes where coupled sets of g-mode oscillations are depositing the most energy. Since the g-mode sets rotate at predictable rates slower than the Sun, the same predictability should eventually apply to the location and strength of sunspots and other solar activity. When fully developed, this model would provide long term safety warnings for astronauts. In this paper, the rotation rates and initial longitudes of eleven g-mode sets are tested against observations. The paper concludes that the time series of sunspot numbers for the last century has oscillatory components with the same frequencies and temporal phases as the eleven g-mode sets.

Juckett, David A.↗

NASA NTRS2007

Coupled Groups of g-Modes in a Sun with Mixed Core

Groups of linear g-modes can sum to create long-lived nonlinear oscillations in small "hot volumes" very deep in the Sun that help drive the modes. In these volumes (dimensions -10 Mm), the time average rate of He-3 burning doubles as temperature fluctuations exceed 10% and rises by an order of magnitude for fluctuations of 25%. To be consistent with locally large motions, we impose a mixed shell on an otherwise standard solar model before computing g-mode solutions. Mixing in the assumed shell r = (0.10+/-0.03) R(sub sun) is rapid (<<10(exp 6) yr) with slower mixing somewhat beyond. If l is the principal spherical harmonic index, a set of g-modes for any single l less than or equal to 15 with five consecutive radial harmonics can be excited with nearly linear thermal amplitudes, A(sub T) less than or equal to 0.053, throughout the star and a fractional temperature fluctuation in its hot volume of (Delta)T/T less than or equal to 0.18. These thresholds for excitation will become smaller when sets for several values of l are computed simultaneously. There is some evidence for the rotation of g-mode sets in the long solar activity record and g-mode upward wave flux has been suggested to explain the 1.3 yr reversing flows tentatively detected below the Sun's convective envelope (CE). The large local amplitudes needed for excitation implies that g-modes may transport a non-negligible fraction of the solar luminosity, yet their near linear amplitudes outside the hot volume suggests amplitudes over most of the solar surface that would be barely detectable for l > 3. A formalism is presented for summing the g-modes and estimating growth rates under the approximation that modes are strictly linear except in a hot volume which holds only a few percent of mode kinetic energy. Finally over the range 2 less than or equal to l less than or equal to 30, we summed all zonal harmonics, m, for a given l and computed the relative angular orientations that would release the most nuclear energy. This should be close to the physically preferred angular state of such a family and a few examples were displayed.

Wolff, Charles L.↗

NASA NTRS2007

Soliton Properties of Coupled g-Mode Oscillations

Several features typical of solitons are also exhibited by stellar g-modes when coupled into "sets" that have unique rotation rates relative to the star. Enhanced nuclear burning due to weakly nonlinear amplitudes in a small portion of the stellar core holds each set together against dispersion. As the nonlinear regions of each set rotate past each other they have a complex interaction (shown in a video), yet emerge from this with their original wave forms. Other similarities with solitons we mentioned, including the physical origin of a phase shift. in longitude due to the interaction. These similarities suggest that a fully nonlinear derivation of g-mode sets may be able to show that their large amplitude regions approach true solitons.

Wolff, Charles L.↗

NASA NTRS2006

QBO as Potential Amplifier of Solar Cycle Influence

The solar cycle (SC) effect in the lower atmosphere has been linked observationally to the quasi-biennial oscillation (QBO) of the zonal circulation. Salby and Callaghan (2000) in particular analyzed the QBO covering more than 40 years and found that it contains a large SC signature at 20 km. We discuss a 3D study in which we simulate the QBO under the influence of the SC. For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary with height: 0.2% (surface), 2% (50 km), 20% (100 km and above). This model produces in the lower stratosphere a relatively large modulation of the QBO, which appears to come from the SC and qualitatively agrees with the observations. The modulation of the QBO, with constant phase relative to the SC, is shown to persist at least for 50 years, and it is induced by a SC modulated annual oscillation that is hemispherically symmetric and confined to low latitudes.

Mayr, Hans G.↗

NASA NTRS2004

Zonal Flows Below the Sun's Convection: Analytic Approximation

We have derived a simple analytic solution showing how the Sun's global oscillations (g-modes) can drive east-west flows at low latitude deep inside the Sun. This flow is analogous to the Quasi Biennial Oscillation in the Earth s upper atmosphere. It has an observed period of 1.3 years in the solar case but its cause was not known until we published an explanation in a Letter to the Editor a few months ago. Now we give full details of the model and show how it can be used to limit the range of g-modes that can be actively driving the reversing flows. A nonlinear feedback feature of the model is that the flow itself creates the turbulent dissipation that extracts momentum from the g-modes that, in turn, drives the flow.

Wolff, Charles L.↗

NASA NTRS2003

Reversing Flows and Heat Spike: Caused by Solar g-Modes?

The Quasi Biennial Oscillation in the Earth s upper atmosphere has an analog deep inside the Sun. As on Earth, the flow is east or west, it is at low latitude, and it reverses direction in a roughly periodic manner. The period in the solar case is 1.3 years. It was detected using solar oscillations similar to the way earthquakes are used to study the Earth's interior. But its cause was not known. We showed that global oscillations (g-modes) can supply enough angular momentum to drive zonal flows with the observed reversal period. This required a calculation of wave dissipation rates inside each flow and in the turbulent layer that separates any two flows of opposite sign. Heat that this process leaves behind causes a thermal spike inside the Sun at the same depth. This may explain an anomaly in observed sound speed that has had no sure explanation.

Mayr, Hans G.↗

NASA NTRS2002

A Solar Model with g-Modes

Good evidence is assembled showing that the Suit's core arid surface vary on time scales from a month to a decade arid that a number of scales are similar. The most plausible source for numerous long time scales and periodicities is long-lived global oscillations. This suggests g-modes (oscillations restored mainly by buoyancy) because they particularly affect the core and base of the convective envelope, which then indirectly modulates the surface. Also, standing g-modes have rotational properties that match many observed periodicities. But the standard solar model (SSM) has a static core and excites few if any g-modes. making new interior structures worth exploring. The model outlined here assumes two well mixed shells near 0.18 and 0.68 R, (13 = solar radius) where sound speed data shows sharp deviations from the SSM. Mixing is sustained by flows driven by the oscillations. The shells form a cavity that excludes g-modes from their main damping region below 0.1 R, assisting their net excitation and increasing their oscillation periods by at least a factor of two and probably much more. In terms of the solar luminosity L, the modes transport up through the cavity a power approx. 0.004 L as a lower limit and 0.11 L as all upper limit. The modes dissipate energy in the outer shell and cool the inner shell, asymmetrically in each case, and this stimulates occasional convective events whose response time is typically 0.8 years longer near the inner shell. Such events cool the core and reduce neutrino flux while heating the envelope and increasing solar activity. This gives a physical basis for a well mixed Sun with low neutrino flux and basis for the observed anticorrelation and lag of neutrino behind surface activity.

Wolff, Charles L.↗

NASA NTRS2002

Detection of Rotational Sequences for Global Oscillation Modes inside the Sun

A very simple mathematical sequence is detected in a half century of thermal radio flux from the Sun. Since the only known physical cause of the sequence is global oscillations trapped in the nonconvecting solar interior, g-modes and probably r-modes are active. If so, their rotation frequencies are detected and some previously reported difference frequencies are confirmed with high confidence. All angular harmonics for 2 less than or = l less than or = 7 are detected as well as some others up to the limit l less than or = 14 resolvable by the observations (a Fourier spectrum of the 10.7 cm flux time series). The mean sidereal rotation of the nonconvecting interior is 428.2 nHz as averaged by g-modes and 429.8 nHz by the r-modes, indicating that g-mode energy is a bit more centrally concentrated. Helioseismology measures such rotation rates near 0.36R (R = solar radius), so the global modes would have about half their kinetic energy above and below that level. This, and the known log(r) energy dependence of most modes implies that these oscillations are significantly reflected near 0.18R, the same level at which sound speed measurements display a maximum departure from theoretical models.

Wolff, Charles L.↗

NASA NTRS2001

Model of Wave Driven Flow Oscillation for Solar Cycle

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Mayr, Hans G.↗

NASA NTRS2000

Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle

In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.

Mayr, Hans G.↗

NASA NTRS1998

A Search for r-Modes from 1825 to the Present

Global oscillations (r-modes) of the Sun's outer convective envelope with periods approximately 1 month and longer have been detected in several short data strings of several years duration. To test whether r-modes might persist beyond one 11 year cycle, the daily sunspot numbers from 1825 to the present were analyzed. Good evidence, but confidence level less than 3sigma, was found for most of the 14 r-modes with spherical harmonic index lambda less than or equal to 5 that can exist in the presence of solar differential rotation. The characteristic rotation rate of almost every such r-mode was detected, displaced systematically from its expected value by only 0.15%. If this probable detection is real, then most low harmonic r-modes have lifetimes exceeding one century and the rotation of the Sun's outer layers varies by less than 0.05%, except possibly at solar minimum.

Wolff, Charles L.↗

NASA NTRS1993

Equidistribution of energy and other quantities in oscillating systems

Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation.

Wolff, Charles L.↗

NASA NTRS1992

'Intermittent' solar periodicities

The signal from a stable periodicity can seem to be intermittent when it is partially masked by an unmodelled window function or when the data set is too short to resolve closely spaced periodicities. By taking this into account, short-lived periodicities in solar data can be reinterpreted as evidence for continuously periodic behavior. The periodic sources are located in the solar interior and caused by global oscillation modes. The convective envelope acts as the window for these sources. Recent reports of seven periodicities from 100 to 1000 days are compared with this model. Precise long-term values for the periodicities are predicted and they agree closely with observations. Some elements are suggested that might explain the well-documented 155-day periodicity. Conventional filtering methods to suppress effects of the 11-year cycle are criticized as inadequate.

Wolff, Charles L.↗

NASA NTRS1990

Solar Irradiance Observed from PVO and Inferred Solar Rotation

Solar irradiance in the extreme ultraviolet flux (EUV) has been monitored for 11 years by the Pioneer Venus Orbiter (PVO). Since the experiment moves around the Sun with the orbital rate of Venus rather than that of Earth, the measurement gives us a second viewing location from which to begin unravelling which irradiance variations are intrinsic to the Sun, and which are merely rotational modulations whose periods depend on the motion of the observer. Researchers confirm an earlier detection, made with only 8.6 years of data, that the EUV irradiance is modulated by rotation rates of two families of global oscillation modes. One family is assumed to be r-modes occupying the convective envelope and sharing its rotation, while the other family (g-modes) lies in the radiative interior which as a slower rotation. Measured power in r-modes of low angular harmonic number indicates that the Sun's envelope rotated about 0.7 percent faster near the last solar maximum (1979 thru 1982) than it did during the next rise to maximum (1986 to 1989). No change was seen in the g-mode family of lines, as would be expected from the much greater rotational inertia of the radiative interior.

Wolff, Charles L.↗

NASA NTRS1989

Periodic solar EUV flux monitored near Venus

A detector sharing the orbital rate of Venus has a unique perspective on solar periodicities. Fourier analysis of the 8.6 year record of solar EUV output gathered by the Langmuir probe on Pioneer Venus Orbiter shows the influences of global oscillation modes located in the convective envelope and in the radiative interior. Seven of the eight lowest angular harmonic r-mode familes are detected by their rotation rates which differ almost unmeasurably from ideal theoretical values. This determines a mean sidereal rotation rate for the envelope of 457.9 + or - 2.0 nHz which corresponds to a period of 25.3 days. Many frequencies are aliased at + or - 106 nHz by modulation from the lowest angular harmonic r-mode in the envelope.

Wolff, Charles L.↗

NASA NTRS1987

Solar irradiance change and special longitudes due to r-modes

Sluggish global oscillations, having a periodicity of months and trapped in the sun's convection zone, modulate the amount of energy reaching earth and seem to impose some large-scale order on the distribution of solar surface features. These recently recognized oscillations (r-modes) increase the predictability of solar changes and may improve understanding of rotation and variability in other stars. Most of the 13 periodicities ranging from 13 to 85 days that are caused by r-modes can be detected in Nimbus 7 observations of solar irradiance during 3 years at solar maximum. These modes may also bear on the classical question of persistent longitudes of high solar activity.

Wolff, Charles L.↗