Topological constraints on scroll and spiral waves in excitable media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

On the propagation rate of the chemical waves observed during the course of CO oxidation on a Ag/Pt(110) composite surface

We have analyzed the propagation rate of the chemical waves observed during the course of CO oxidation on a Ag/Pt(I 10) composite surface that were reported in our previous papers [Surf Interface Anal. 2001, 32, 179; J. Phys. Chem. B 2002, 106, 5645]. In all cases, the propagation rate v can be adequately fitted as v = v(0) + D-0/d, in which v(0) and D-0 are constants, and d is the distance between the reaction front of the chemical wave and the boundary from which the chemical wave originates. We propose that the surface species responsible for the formation of the chemical wave comes from two paths: the adsorption of molecules in the gas phase on the surface and the migration from the adjacent surface with different catalytic activity. v(0) corresponds to the contribution from the surface species due to the adsorption, and D-0/d to that of the surface species that migrates from the adjacent surface. The rate equation clearly suggests that the observed chemical wave results from the coupling between adjacent surfaces with different catalytic activities during the course of heterogeneous catalysis. These results, together with our previous reports, provide a good fundamental understanding of spillover, an important phenomenon in heterogeneous catalysis.

Modern changes of tidal troughs among the radial sand ridges in northern Jiangsu coastal zone

Using satellite images taken on different dates, GIS analysis of aerial photos, bathymetric maps and other field survey data, tidal troughs and major sand ridges in the northern Jiangsu coastal area were contrasted. The results show that there have been three types of movement or migration of tidal trough in this area: (1) Periodic and restricted, this type of trough usually developed along the beaches with immobile gully head as a result of the artificial dams and the swing range increased from gully head to the low reaches, so they have been obviously impacted by human activity and have longer swing periods; (2) Periodic and actively, this kind of trough, which swung with a fast rate and moved periodically on sand ridges, were mainly controlled by the swings of the host tidal troughs and hydrodynamic forces upon tidal sand ridge and influenced slightly by human constructions; (3) Steadily and slowly, they are the main tidal troughs with large scale and a steady orientation in this area and have slow lateral movement. The differences in migration mode of tidal trough shift result in different rates of migration and impact upon tidal sand ridges. Lateral accumulation on current tidal trough and deposition on abandoned tidal troughs are the two types of sedimentation of the tidal sand ridges formation. The whole radial sand ridge was generally prone to division and retreat although sand ridges fluctuated by the analysis of changes in talwegs of tidal troughs and shorelines of sand ridges.

Short-term morphological changes after sand-digging during a sand sculpture activity

The morphology of the beach backshore and foreshore at Huiquan Bay, Qingdao, China, is characterized by a single intertidal sandbar system with a spring tide range of 4.59 m. The beach was measured with a laser total station of Leica TPS402. Contours of the beach were generated using data collected in March and November 2005. The survey method provided 2 mm measuring accuracy and 4-10 m horizontal spacing. The net accretion volume of the foreshore was about 11, 215 m(3) from March to November. After sand sculpture activity, the axis of the sand trough migrated onshore from about 3.5 m to 17.5 m on the foreshore beach in November. At the same time, the axis of the sandbar crest migrated onshore no more than 42.25 m on the northwest foreshore; and it migrated offshore no more than 23.75 m on the southeast foreshore. On the northwest and southeast foreshore beach, two strips of erosion areas with a thickness of 0-0.2 m appeared on the sandbar crest. Accretion occurred at the bottom of the sand trough with a thickness of similar to 0.2-0.6 m. The sandbar height decreased after sand sculpture activity, and it was no more than 0.7 m in March and 0.6 m in November. Human activities, such as sand digging on the sandbar crest during sand sculpture activity, also can disturb the beach morphology of intertidal bar systems. This phenomenon also was validated by comparison of beach morphology, the results of a color artificial tracer experiment and a sediment transportation trend prediction.

On the relationships between the radial tidal current field and the radial sand ridges in the southern Yellow Sea: a numerical simulation

The ori-in of the radial sand ridges (RSRs) in the southern Yellow Sea has been a controversial problem since they were discovered in the early 1960s. To resolve the problem, two key questions need to be answered: (1) was the radial tidal current field in the RSR area generated by the submarine topography, or (2) did it exist before the RSRs occurred? In this study, the M-2 tide and tidal currents in the RSR area were simulated with a two-dimensional tidal model using a flat bottom and a shelving slope topography, the results being then compared with the field data. It is demonstrated that the radial tidal current field in the southern Yellow Sea is independent of bottom topography, and may thus be the controlling factor generating the RSRs. The radial tidal current field probably existed before the RSRs were formed.

Temperature phase tilt in unstable baroclinic waves

A general property on the phase relation in linear baroclinic instability is proved analytically: in a potential vorticity homogenization regime, the complex geometry of the quasigeostrophic equations determines that the phase lines of temperature and pressure disturbances tilt with height in opposite directions.

A unified criterion for initiation of sediment motion and inception of sheet flow under water waves

A unified criterion is developed for initiation of non-cohesive sediment motion and inception of sheet flow under water waves over a horizontal bed of sediment based on presently available experimental data. The unified threshold criterion is of the single form, U-o = 2 pi C[1 + 5(T-R/T)(2)](-1/4), where U-o is the onset velocity of sediment motion or sheet flow, T is wave period, and C and T-R are the coefficients. It is found that for a given sediment, U-o initially increases sharply with wave period, then gradually approaches the maximum onset velocity U-o = 2 pi C and becomes independent of T when T is larger. The unified criterion can also be extended to define sediment initial motion and sheet flow under irregular waves provided the significant wave orbital velocity and period of irregular waves are introduced in this unified criterion.

Remote sensing of ocean waves by along-track interferometric synthetic aperture radar

A new wave retrieval method for the Along-Track Interferometric Synthetic Aperture Radar (AT-InSAR) phase image is presented. The new algorithm, named parametric retrieval algorithm (PRA), uses the full nonlinear mapping relations. It differs from previous retrieval algorithms in that it does not require a priori information about the sea state or the wind vector from scatterometer data. Instead, it combines the observed AT-InSAR phase spectrum and assumed wind vector to estimate the wind sea spectrum. The method has been validated using several C-band and X-band HH-polarized AT-InSAR observations collocated with spectral buoy measurements. In this paper, X-band and C-band HH-polarized AT-InSAR phase images of ocean waves are first used to study AT-InSAR wave imaging fidelity. The resulting phase spectra are quantitatively compared with forward-mapped in situ directional wave spectra collocated with the AT-InSAR observations. Subsequently, we combine the parametric retrieval algorithm (PRA) with X-band and C-band HH-polarized AT-InSAR phase images to retrieve ocean wave spectra. The results show that the ocean wavelengths, wave directions, and significant wave heights estimated from the retrieved ocean wave spectra are in agreement with the buoy measurements.

Validation of RADARSAT-2 fully polarimetric SAR measurements of ocean surface waves

C band RADARSAT-2 fully polarimetric (fine quad-polarization mode, HH+VV+HV+VH) synthetic aperture radar (SAR) images are used to validate ocean surface waves measurements using the polarimetric SAR wave retrieval algorithm, without estimating the complex hydrodynamic modulation transfer function, even under large radar incidence angles. The linearly polarized radar backscatter cross sections (RBCS) are first calculated with the copolarization (HH, VV) and cross-polarization (HV, VH) RBCS and the polarization orientation angle. Subsequently, in the azimuth direction, the vertically and linearly polarized RBCS are used to measure the wave slopes. In the range direction, we combine horizontally and vertically polarized RBCS to estimate wave slopes. Taken together, wave slope spectra can be derived using estimated wave slopes in azimuth and range directions. Wave parameters extracted from the resultant wave slope spectra are validated with colocated National Data Buoy Center (NDBC) buoy measurements (wave periods, wavelengths, wave directions, and significant wave heights) and are shown to be in good agreement.