The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

In this paper, a hydrologic/hydrodynamic modeling of the Amazon River basin iscpresented using the MGB-IPH model with a validation using remotely sensed observations. Moreover, the sources of model errors by means of the validation and sensitivity tests are investigated, and the physical functioning of the Amazon basin is also explored. The MGBIPH is a physically based model resolving all land hydrological processes and here using a full 1-D river hydrodynamic module with a simple floodplain storage model. Riverfloodplain geometry parameters were extracted from the SRTM digital elevation model, and the model was forced using satellite-derived rainfall from TRMM3B42. Model results agree with observed in situ daily river discharges and water levels and with three complementary satellite-based products: (1) water levels derived from ENVISAT altimetry data; (2) a global data set of monthly inundation extent; and (3) monthly terrestrial water storage (TWS) anomalies derived from the Gravity Recovery and Climate Experimental mission. However, the model is sensitive to precipitation forcing and river-floodplain parameters. Most of the errors occur in westerly regions, possibly due to the poor quality of TRMM 3B42 rainfall data set in these mountainous and/or poorly monitored areas. In addition, uncertainty in river-floodplain geometry causes errors in simulated water levels and inundation extent, suggesting the need for improvement of parameter estimation methods. Finally, analyses of Amazon hydrological processes demonstrate that surface waters govern most of the Amazon TWS changes (56%), followed by soil water (27%) and ground water (8%). Moreover, floodplains play a major role in stream flow routing, although backwater effects are also important to delay and attenuate flood waves.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/wrcr.20067

Large‐scale hydrologic and hydrodynamic modeling of the Amazon River basin

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ 2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.

/pdf/turbulent-fluctuations-above-the-buffer-layer-of-wall-41ka7kmfdt.pdf

Turbulent fluctuations above the buffer layer of wall-bounded flows

Wave attenuation by flexible, idealized salt marsh vegetation

The current knowledge about some particular kinds of coherent structures in the logarithmic and outer layers of wall-bounded turbulent flows is briefly reviewed. It is shown that a lot has been learned about their geometry, flow properties and temporal behaviour. It is also shown that, although the wall-attached structures carry the largest fraction of most flow properties, they are only extreme cases of smaller wall-detached eddies, and that the latter connect with the more classical behaviour of homogeneous turbulence away from walls. Nevertheless, it is argued that little is known about the dynamical origin of these structures, and that a concerned effort is required to quantitatively identify which one (or ones) of the plausible available dynamical models is a better representation of the observed behaviour.

Coherent Structures in Wall-Bounded Turbulence

On 29 September 2009, a strong earthquake took place south of the Samoa Islands in the southcentral Pacific. It triggered a local tsunami, which caused considerable damage and 189 fatalities on the Samoa Islands and in the northern Tonga archipelago. We present here the results of a tsunami survey conducted by an International Tsunami Survey Team in the Samoa Islands on 4-10 October 2009 and in northern Tonga on 25–27 November 2009.

### The Earthquake of 29 September 2009: Geographical Background

The earthquake occurred at 17:48:10 GMT (local time 06:48 on the 29th in Samoa; on the 30th in Tonga), with a source located at 15.51°S and 172.03°W and a focal depth estimated at 18 km by the U.S. Geological Survey (USGS). The epicenter is thus 200 km south of the Samoa Islands and 350 km NNE of the principal groups of Tonga (Figure 1). Note however, the presence of a small island, Niuatoputapu, only 200 km WSW of the epicenter.

The Samoa Islands comprise the territory of American Samoa, which regroups the island of Tutuila (142 km2; capital: Pago Pago), and the islets of Ofu, Olosega, Ta'u, Rose, and Swains, and the independent country of Samoa (formerly Western Samoa), comprised of the islands of Upolu (1,125 km2; capital: Apia), Savai'i (1,708 km2), and a few islets including Manono. The island of Niuatoputapu, the nearby islet of Tafahi, and the more distant island of Niuafo'ou belong to the Kingdom of Tonga.

### Plate Tectonics Background

The Samoa Islands are located 200 km north of the bend in the boundary of the Pacific plate marking the termination of the Kermadec-Tonga subduction zone. The convergent boundary expressing the subduction of the Pacific plate under the Australian one gives way to a strike-slip regime along a transform fault running north of the Fiji Islands, and linked across a spreading center in …

Field Survey of the Samoa Tsunami of 29 September 2009

Coupling of hydrologic and hydraulic models for the Illinois River Basin

We study the effects of emergent coastal forests on the propagation of long surface waves of small amplitude. The forest is idealized by an array of vertical cylinders. Simple models are employed to represent bed friction and to simulate turbulence generated by flow through the tree trunks. A multi-scale (homogenization) analysis similar to that for seepage flows is carried out to deduce the effective equations on the macro-scale. The effective coefficients are calculated by numerically solving the micro-scale problem in a unit cell surrounding one or several cylinders. Analytical and numerical solutions for wave attenuation on the macro-scale for different bathymetries and coastal forest configurations are presented. For a transient incident wave, analytical results are discussed for the damping of a leading tsunami. For comparison series of laboratory data for periodic and transient incident waves are also presented. Good agreement is found even though some of the measured waves are short or nonlinear.

/pdf/long-waves-through-emergent-coastal-vegetation-vao9oydtzh.pdf

Long waves through emergent coastal vegetation

[1] Using the records of free surface fluctuations at several locations during the 2011 Japan Tohoku tsunami, we first show that the leading tsunami waves in both near-field and far-field regions are small amplitude long waves. These leading waves are very different from solitary waves. We then focus on investigating the evolution and runup of non-breaking long waves on a plane beach, which is connected to a constant depth region. For this purpose, we develop a Lagrangian numerical model to solve the nonlinear shallow water equations. The Lagrangian approach tracks the moving shoreline directly without invoking any additional approximation. We also adopt and extend the analytical solutions by Synolakis (1987) and Madsen and Schaffer (2010) for runup and rundown of cnoidal waves and a train of multiple solitary waves. The analytical solutions for cnoidal waves compare well with the existing experimental data and the direct numerical results when wave amplitudes are small. However, large discrepancies appear when the incident amplitudes are finite. We also examine the relationship between the maximum runup height and the leading wave form. It is concluded that for a single wave the accelerating phase of the incident wave controls the maximum runup height. Finally, using the analytical solutions for the approximated wave forms of the leading tsunamis recorded at Iwate South station from the 2011 Tohoku Japan tsunami, we estimate the runup height.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2012JC007994

On the runup of long waves on a plane beach

Using the Boussinesq approximation, a set of depth-integrated wave equations for long-wave propagation over a mud bed is derived. The wave motions above the mud bed are assumed to be irrotational and the mud bed is modelled as a highly viscous fluid. The pressure and velocity are required to be continuous across the water-mud interface. The resulting governing equations are differential-integral equations in terms of the depth-integrated horizontal velocity and the free-surface displacement. The effects of the mud bed appear in the continuity equation in the form of a time integral of weighted divergence of the depth-averaged velocity. Damping rates for periodic waves and solitary waves are calculated. For the solitary wave case, the velocity profiles in the water column and the mud bed at different phases are discussed. The effects of the viscous boundary layer above the mud-water interface are also examined.

I-Chi Chan

Papers

Field Survey of the Samoa Tsunami of 29 September 2009

Coupling of hydrologic and hydraulic models for the Illinois River Basin

Long waves through emergent coastal vegetation

On the runup of long waves on a plane beach

On long-wave propagation over a fluid-mud seabed