A Lagrangian for water waves

A Lagrangian for strongly nonlinear unsteady water waves (including overturning waves) is obtained. It is shown that the system of quadratic equations for the Stokes coefficients, which determine the shape of a steady wave (discovered by Longuet-Higgins 100 years after Stokes derived his system of cubic equations) directly follows from the canonical system of Lagrange equations. Applications to the investigation of the stability of water waves and to the construction of numerical schemes are pointed out

The suppression of short waves by a train of long waves

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived

Strong ExB shear flows in the pedestal region in H-mode plasma

We report the first experimental observation of stationary zonal flows in the pedestal region of the H-mode plasma in the H-1 toroidal heliac. Strong peaks in E_r shear mark the top and foot of the density pedestal. Strong m=n=0 low-frequency (f < 0.6 kHz) zonal flows are observed in regions of increased E_r, suggesting substantial contribution of zonal flows to the spatial modulation of E_r radial profiles. Radial localization of zonal flows is correlated with a region of zero magnetic shear and low-order (7/5) rational surfaces.Comment: 4 pages, 5 figure

Triple cascade behaviour in QG and drift turbulence and generation of zonal jets

We study quasigeostrophic (QG) and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus on the zonostrophy, an extra invariant in the CHM model, and on its role in the formation of zonal jets. We use a generalized Fjørtoft argument for the energy, enstrophy, and zonostrophy and show that they cascade anisotropically into nonintersecting sectors in k space with the energy cascading towards large zonal scales. Using direct numerical simulations of the CHM equation, we show that zonostrophy is well conserved, and the three invariants cascade as predicted by the Fjørtoft argument

Tau Polarization in Λb→Xcτνˉ \Lambda_b \to X_c \tau \bar{\nu} and B→XcτνˉB \to X_c \tau \bar{\nu}

We discuss the longitudinal and transverse $\tau$-polarization in inclusive decays of hadrons containing $b$-quarks. The calculation is performed by means of an OPE in HQET. Some mathematical difficulties in calculating transverse polarizations are explained. Numerical results are presented for longitudinal and for transverse polarizations, both in and perpendicular to the decay plane.Comment: LATEX, 20 pages, 5 Postscript figure

Measurements of Nanoscale Domain Wall Flexing in a Ferromagnetic Thin Film

We use the high spatial sensitivity of the anomalous Hall effect in the ferromagnetic semiconductor Ga1-xMnxAs, combined with the magneto-optical Kerr effect, to probe the nanoscale elastic flexing behavior of a single magnetic domain wall in a ferromagnetic thin film. Our technique allows position sensitive characterization of the pinning site density, which we estimate to be around 10^14 cm^{-3}. Analysis of single site depinning events and their temperature dependence yields estimates of pinning site forces (10 pN range) as well as the thermal deactivation energy. Finally, our data hints at a much higher intrinsic domain wall mobility for flexing than previously observed in optically-probed micron scale measurements

Self-organization in turbulence as a route to order in plasma and fluids

Transitions from turbulence to order are studied experimentally in thin fluid layers and magnetically confined toroidal plasma. It is shown that turbulence self-organizes through the mechanism of spectral condensation. The spectral redistribution of the turbulent energy leads to the reduction in the turbulence level, generation of coherent flow, reduction in the particle diffusion and increase in the system's energy. The higher order state is sustained via the nonlocal spectral coupling of the linearly unstable spectral range to the large-scale mean flow. The similarity of self-organization in two-dimensional fluids and low-to-high confinement transitions in plasma suggests the universality of the mechanism.Comment: 5 pages, 4 figure

The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets

We consider an adiabatic-type (approximate) invariant that was earlier obtained for the quasi-geostrophic equation and the shallow water system; it is an extra invariant, in addition to the standard ones (energy, enstrophy, momentum), and it is based on the Rossby waves. The presence of this invariant implies the energy transfer from small-scale eddies to large-scale zonal jets. We show that this extra invariant can be extended to the dynamics of a three-dimensional (3-D) fluid layer on the beta plane. Combined with the investigation of other researchers, this 3-D extension implies enhanced generation of zonal jets. For a general physical system, the presence of an extra invariant (in addition to the energy–momentum and wave action) is extremely rare. We summarize the unique conservation properties of geophysical fluid dynamics (with the beta effect) that allow for the existence of the extra invariant, and argue that its presence in various geophysical systems is a strong indication that the formation of zonal jets is indeed related to the extra invariant. Also, we develop a new, more direct, way to establish extra invariants (without using cubic corrections). For this, we introduce the small denominator lemma