Tsunami run-up and draw-down motions on a uniformly sloping beach are evaluated based on fully nonlinear shallow-water wave theory. The nonlinear equations of mass conservation and linear momentum are first transformed to a single linear hyperbolic equation. To solve the problem with arbitrary initial conditions, we apply the Fourier–Bessel transform, and inversion of the transform leads to the Green function representation. The solutions in the physical time and space domains are then obtained by numerical integration. With this semi-analytic solution technique, several examples of tsunami run-up and draw-down motions are presented. In particular, detailed shoreline motion, velocity field, and inundation depth on the shore are closely examined. It was found that the maximum flow velocity occurs at the moving shoreline and the maximum momentum flux occurs in the vicinity of the extreme draw-down location. The direction of both the maximum flow velocity and the maximum momentum flux depend on the initial waveform: it is in the inshore direction when the initial waveform is predominantly depression and in the offshore direction when the initial waves have a dominant elevation characteristic.

Two major marine surveys off northern Papua New Guinea (PNG) earlier this year now suggest, when survivors' reports are taken into account, that last summer's disastrous tsunami there was caused by a sediment slump 25 km offshore. The slump was probably the result of seabed shaking from an earthquake. Not only was a sediment slump, or submarine landslide, responsible for the tsunami, according to the data, but the magnitude and wave‐height distribution of the tsunami along the coast were the result of focusing by local seabed morphology. The conclusions are based on new off‐shore bathymetry, remote operated vehicle (ROV) dive investigations, the time delay between the source earthquake and when the tsunami struck, computer simulation models, and earthquake aftershock distribution. The most critical evidence is in survivors' accounts of the timing of the tsunami relative to the initially felt earthquake and aftershock [see Davies, 1998a].

Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is not in the form of a Korteweg–de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression. Evolution of stem-wave amplification is in good agreement with the Kadomtsev–Petviashvili (KP) theory. The asymptotic characteristics and behaviours are also in agreement with the theory of Miles (J. Fluid Mech., vol. 79, 1977b, p. 171) except those in the neighbourhood of the transition between the Mach reflection and the regular reflection. The predicted maximum fourfold amplification of the stem wave is not realized in the laboratory environment. On the other hand, the laboratory observations are in excellent agreement with the previous numerical results of the higher-order model of Tanaka (J. Fluid Mech., vol. 248, 1993, p. 637). The present laboratory study is the first to sensibly analyse validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking near the wall results in the substantial increase in wave height and slope away from the wall.

The deep population history of East Asia remains poorly understood due to a lack of ancient DNA data and sparse sampling of present-day people. We report genome-wide data from 191 individuals from Mongolia, northern China, Taiwan, the Amur River Basin and Japan dating to 6000 BCE – 1000 CE, many from contexts never previously analyzed with ancient DNA. We also report 383 present-day individuals from 46 groups mostly from the Tibetan Plateau and southern China. We document how 6000-3600 BCE people of Mongolia and the Amur River Basin were from populations that expanded over Northeast Asia, likely dispersing the ancestors of Mongolic and Tungusic languages. In a time transect of 89 Mongolians, we reveal how Yamnaya steppe pastoralist spread from the west by 3300-2900 BCE in association with the Afanasievo culture, although we also document a boy buried in an Afanasievo barrow with ancestry entirely from local Mongolian hunter-gatherers, representing a unique case of someone of entirely non-Yamnaya ancestry interred in this way. The second spread of Yamnaya-derived ancestry came via groups that harbored about a third of their ancestry from European farmers, which nearly completely displaced unmixed Yamnaya-related lineages in Mongolia in the second millennium BCE, but did not replace Afanasievo lineages in western China where Afanasievo ancestry persisted, plausibly acting as the source of the early-splitting Tocharian branch of Indo-European languages. Analyzing 20 Yellow River Basin farmers dating to ∼3000 BCE, we document a population that was a plausible vector for the spread of Sino-Tibetan languages both to the Tibetan Plateau and to the central plain where they mixed with southern agriculturalists to form the ancestors of Han Chinese. We show that the individuals in a time transect of 52 ancient Taiwan individuals spanning at least 1400 BCE to 600 CE were consistent with being nearly direct descendants of Yangtze Valley first farmers who likely spread Austronesian, Tai-Kadai and Austroasiatic languages across Southeast and South Asia and mixing with the people they encountered, contributing to a four-fold reduction of genetic differentiation during the emergence of complex societies. We finally report data from Jomon hunter-gatherers from Japan who harbored one of the earliest splitting branches of East Eurasian variation, and show an affinity among Jomon, Amur River Basin, ancient Taiwan, and Austronesian-speakers, as expected for ancestry if they all had contributions from a Late Pleistocene coastal route migration to East Asia.

Abstract-The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field that can represent either a 2D compressible flow or the projection of a 3D compressible or incompressible flow onto a 2D manifold. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue manifold and eigenvector manifold. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Moreover, we extend eigenvectors continuously into the complex domains which we refer to as pseudoeigenvectors. We make use of evenly spaced tensor lines following pseudoeigenvectors to illustrate the local linearization of tensors everywhere inside complex domains simultaneously. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide a physical interpretation of our tensor-driven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data.