On the third order structure function for rotating 3D homogeneous turbulent flow

A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation.Comment: This revised version corrects some serious flaws in the discussions after the equation (2) and the equation (13) of the earlier version. Some typos are also correcte

Doppler images of II Pegasi for 2004-2010

Aims. We study the spot activity of II Peg during the years 2004-2010 to determine long- and short-term changes in the magnetic activity. In a previous study, we detected a persistent active longitude, as well as major changes in the spot configuration occurring on a timescale of shorter than a year. The main objective of this study is to determine whether the same phenomena persist in the star during these six years of spectroscopic monitoring. Methods. The observations were collected with the high-resolution SOFIN spectrograph at the Nordic Optical Telescope. The temperature maps were calculated using a Doppler imaging code based on Tikhonov regularization. Results. We present 12 new temperature maps that show spots distributed mainly over high and intermediate latitudes. In each image, 1-3 main active regions can be identified. The activity level of the star is clearly lower than during our previous study for the years 1994-2002. In contrast to the previous observations, we detect no clear drift of the active regions with respect to the rotation of the star. Conclusions. Having shown a systematic longitudinal drift of the spot-generating mechanism during 1994-2002, the star has clearly switched to a low-activity state for 2004-2010, during which the spot locations appear more random over phase space. It could be that the star is near to a minimum of its activity cycle.Comment: Accepted for publication in Astron. and Astrophys., 8 pages, 5 figure

Adaptation to dislodgement risk on wave-swept rocky shores in the snail Littorina saxatilis

The periwinkle Littorina saxatilis has repeatedly evolved both a small, fragile and globose "wave ecotype" confined to wave-swept shores and a large, robust and elongated "crab ecotype" found in nearby crab-rich but less-exposed shores. This phenotypic divergence is assumed to reflect, in some part, local adaptation to wave exposure, but this hypothesis has received incomplete experimental testing. Here, we report a test of the prediction that the wave ecotype has a higher capacity to resist water flow than the crab ecotype. We sampled snails along a crab-wave transect and measured their resistance to dislodgement in a high-speed water flume with water speeds that match those of breaking waves in a range of relevant field conditions. Snails from the wave environment were consistently more resistant to water flow than snails from the crab environment and high resistance was positively correlated with the surface area of the foot and the area of the outer aperture contour both relative to shell size, and to the extent of lateral shell compression. In a separate experiment, we found that snails raised in still water in a common garden showed higher resistance to water flow if originating from a wave environment than from a crab environment, and this was true both at juvenile (2 weeks) and adult (10 months) developmental stages. This result suggests genetic control of a distinct "wave adapted" phenotype, likely to be maintained under strong divergent selection between the two adjacent habitats

Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc

Multiperiodicity, modulations and flip-flops in variable star light curves II. Analysis of II Peg photometry during 1979-2010

According to earlier Doppler images of the magnetically active primary giant component of the RS CVn binary II Peg, the surface of the star was dominated by one single active longitude that was clearly drifting in the rotational frame of the binary system during 1994-2002; later imaging for 2004-2010, however, showed decreased and chaotic spot activity, with no signs of the drift pattern. Here we set out to investigate from a more extensive photometric dataset whether such a drift is a persistent phenomenon, in which case it could be due to either an azimuthal dynamo wave or an indication of the binary system orbital synchronization still being incomplete. We analyse the datasets using the Carrier Fit method (hereafter CF), especially suitable for analyzing time series in which a fast clocking frequency (such as the rotation of the star) is modulated with a slower process (such as the stellar activity cycle). We combine all collected photometric data into one single data set, and analyze it with the CF method. As a result, we confirm the earlier results of the spot activity having been dominated by one primary spotted region almost through the entire data set, and the existence of a persistent, nearly linear drift. Disruptions of the linear trend and complicated phase behavior are also seen, but the period analysis reveals a rather stable periodicity with P(spot)=6.71054d plus/minus 0.00005d. After the linear trend is removed from the data, we identify several abrupt phase jumps, three of which are analyzed in more detail with the CF method. These phase jumps closely resemble what is called flip-flop event, but the new spot configurations do not, in most cases, persist for longer than a few months.Comment: 9 pages, 7 figures, submitted to Astronomy and Astrophysic

Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical and wave modes of a 3D rotating stratified fluid as a function of $\epsilon = f/N$. Working in regimes characterized by moderate Burger numbers, i.e. $Bu = 1/\epsilon^2 < 1$ or $Bu \ge 1$, our results indicate profound change in the character of vortical and wave mode interactions with respect to $Bu = 1$. As with the reference state of $\epsilon=1$, for $\epsilon < 1$ the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as $\epsilon$ decreases: we see a shift from $k^{-1}$ to $k^{-5/3}$ scaling for $k_f < k < k_d$ (where $k_f$ and $k_d$ are the forcing and dissipation scales, respectively). On the other hand, when $\epsilon > 1$ the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about $\epsilon = 1$. With regard to the vortical modes, for $\epsilon \le 1$, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a $k^{-3}$ scaling for $k_f < k < k_d$ and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all $k < k_f$. In contrast, for $\epsilon > 1$ and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem plays an energetically smaller role in the overall dynamics.Comment: 18 pages, 6 figs. (abbreviated abstract

Multiperiodicity, modulations and flip-flops in variable star light curves II. Analysis of II Pegasus photometry during 1979–2010

Aims. According to previously published Doppler images of the magnetically active primary giant component of the RS CVn binary II Peg, the surface of the star was dominated by one single active longitude that was clearly drifting in the rotational frame of the binary system during 1994-2002; later imaging for 2004–2010, however, showed decreased and chaotic spot activity, with no signs of the drift pattern. Here we set out to investigate from a more extensive photometric dataset whether this drift is a persistent phenomenon, in which case it could be caused either by an azimuthal dynamo wave or be an indication that the binary system’s orbital synchronization is still incomplete. On a differentially rotating stellar surface, spot structures preferentially on a certain latitude band could also cause such a drift, the disruption of which could arise from the change of the preferred spot latitude. Methods. We analyzed the datasets using the carrier fit (CF) method, which is especially suitable for analyzing time series in which a fast clocking frequency (such as the rotation of the star) is modulated with a slower process (such as the stellar activity cycle). Results. We combined all collected photometric data into one single data set and analyzed it with the CF method. We confirm the previously published results that the spot activity has been dominated by one primary spotted region almost through the entire data set and also confirm a persistent, nearly linear drift. Disruptions of the linear trend and complicated phase behavior are also seen, but the period analysis reveals a rather stable periodicity with Pspot = 671054 ± 000005. After removing the linear trend from the data, we identified several abrupt phase jumps, three of which are analyzed in more detail with the CF method. These phase jumps closely resemble what is called a flip-flop event, but the new spot configurations do not persist for longer than a few months in most cases. Conclusions. There is some evidence that the regular drift without phase jumps is related to the high state, while the complex phase behavior and disrupted drift pattern are related to the low state of magnetic activity. The most natural explanation of the drift is weak anti-solar (pole rotating faster than the equator) differential rotation with a coefficient k ≈ 0.002 combined with the preferred latitude of the spot structure

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200

Investigation of whisker growth from alkaline non-cyanide zinc electrodeposits

Electroplated zinc finishes have been widely used in the packaging of electronic products for many years as a result of their excellent corrosion resistance and relatively low cost. However, the spontaneous formation of whiskers on zinc electroplated components, which are capable of resulting in electrical shorting or other damaging effects, can be highly problematic for the reliability of long-life electrical and electronic equipment. This work investigated the mechanism for whisker growth from zinc electrodeposited mild steel substrates. The incubation time for whisker growth from the surface of nodules on the surface of the electrodeposit was considerably reduced compared with that from the planar deposit surface. Recrystallisation of the as-deposited columnar structure was observed at the whisker root. This result is consistent with some recent whisker growth models based on recrystallisation. There was no evidence of iron-zinc (Fe-Zn) intermetallic formation at the iron/zinc (Fe/Zn) interface or within the zinc coating beneath the whiskers