Norihiro Izumi

Purely erosional cyclic and solitary steps created by flow over a cohesive bed

An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

Linear stability analysis of channel inception: downstream-driven theory

A linear stability analysis of incipient channellization on hillslopes is performed using the shallow-water equations and a description of the erosion of a cohesive bed. The base state consists of a laterally uniform Froude-subcritical sheet flow down a smooth, downward-concave hillslope profile. The downstream boundary condition consists of the imposition of a Froude number of unity. The process of channellization is thus driven from the downstream end. The flow and bed profiles describe a base state that migrates at constant, slow speed in the upstream direction due to bed erosion. Transverse perturbations corresponding to a succession of parallel incipient channels are introduced. It is found that these perturbations grow in time, so describing incipient channellization, only when the characteristic spacing between incipient channels is on the order of 6–100 times the Froude-critical depth divided by the resistance coefficient. The characteristic wavelength associated with maximum perturbation growth rate is found to scale as 10 times the Froude-critical depth divided by the resistance coefficient. Evaluating the friction coefficient as on the order of 0.01, an estimate of incipient channel spacing on the order of 1000 times the Froude-critical depth is obtained. The analysis reveals that downstream-driven channellization becomes more difficult as (a) the critical shear stress required to erode the bed becomes so large that it approaches the Froude-critical shear stress reached at the downstream boundary and (b) the Froude number of the subcritical equilibrium flow attained far upstream approaches unity. Alternative mechanisms must be invoked to explain channellization on slopes high enough to maintain Froude-supercritical sheet flow.

Tsunami-generated turbidity current of the 2011 Tohoku-Oki earthquake

We show the first real-time record of a turbidity current associated with a great earthquake, the Mw 9.0, 2011 Tohoku-Oki event offshore Japan. Turbidity current deposits (turbidites) have been used to estimate earthquake recurrence intervals from geologic records. Until now, however, there has been no direct evidence for large-scale earthquakes in subduction plate margins. After the 2011 Tohoku-Oki earthquake and tsunami, an anomalous event on the seafloor consistent with a turbidity current was recorded by ocean-bottom pressure recorders and seismometers deployed off Sendai, Japan. Freshly emplaced turbidites were collected from a wide area of seafloor off the Tohoku coastal region. We analyzed these measurements and sedimentary records to determine conditions of the modern tsunamigenic turbidity current. We anticipate our discovery to be a starting point for more detailed characterization of modern tsunamigenic turbidites, and for the identification of tsunamigenic turbidites in geologic records.

Interaction among alluvial cover, bed roughness, and incision rate in purely bedrock and alluvial‐bedrock channel

A major control on bedrock incision is the interaction between alluvial cover and erosive mobile grains. The extent of alluvial cover is typically predicted as a function of relative sediment flux (sediment supply rate over bed load transport capacity, qbs/qbc), yet little is known about how the bed roughness affects the alluvial cover. We performed field experiments with various flow discharges, sediment supply rates, grain sizes, and bed surface topographies. We then developed physically based models for estimating the threshold of sediment movement and the extent of alluvial cover, so as to include the effect of roughness change. The results for the threshold of sediment movement and the extent of alluvial cover obtained from our models show reasonable agreement with the results of the field experiments. We explored the sensitivity of the models to variations in sediment supply and bedrock relative roughness (bedrock hydraulic roughness height over grain size, ksb/d). The results suggest the following: (1) a larger relative roughness yields a greater dimensionless critical shear stress required for initial sediment motion; (2) at a given sediment supply rate, the extent of alluvial cover is larger when the relative roughness is larger; (3) when the sediment supply rate and the relative roughness are small, throughput bed load moves over (and can abrade) a purely bedrock channel with no alluvial cover; and (4) the critical value of sediment supply rate below which throughput bed load transport occurs increases with decreasing relative roughness. The experimental results and analysis provide a framework for treating the (a) incisional morphodynamics of purely bedrock rivers by throughput bed load with no alluvial cover, (b) incisional/alluvial morphodynamics of mixed bedrock-alluvial rivers, and (c) purely alluvial morphodynamics, as well as the transition between these states.

Numerical simulation of effects of sediment supply on bedrock channel morphology

AbstractNatural bedrock rivers exhibit diverse erosional morphologies. Although the formation of alternate bars on bedrock has been noted in previous studies, the influence of these alternate bars on bedrock erosion has not been clarified. In this study, the authors propose a model for bedrock-alluvial channels that reproduces both bar formation and erosional morphology. In addition, the authors report on numerical simulations to evaluate the influence of sediment supply on the state of the bed at and over the bedrock surface. The numerical results illustrate the formation of different morphologies for different supply rates. When the sediment supply rate is close to transport capacity, mixed alluvial-bedrock alternate bars form. These bars are analogous to purely alluvial alternate bars. A meandering thread of alluvial material migrates downstream over a uniformly eroding bedrock surface. When the sediment supply rate is well below capacity, however, multiple incisional troughs (grooves) form on the bedr...

Linear Stability Analysis of Open-Channel Shear Flow Generated by Vegetation

A linear stability analysis of flow in an open-channel partially covered with vegetation was performed. The differential drag between vegetated zones and adjacent nonvegetated zones is known to induce a lateral gradient of the streamwise velocity. The velocity gradient may result in flow instability in the shear layer around the edge of the vegetated zone causing the generation of discrete horizontal vortices. We assume that the base state flow field before the occurrence of instability is characterized by turbulencewith a smaller length scale than the flow depth, which is mainly generated by the bottom friction. By introducing perturbations to the flow depth as well as the stream- wise and transverse velocities in the base state, the conditions required for perturbations to grow in time were studied over a wide range of (1) Froude number, (2) normalized nonvegetated zone width, and three other dimensionless parameters that represent the relative effect of (3) bed friction, (4) vegetation drag, and (5) subdepth eddy viscosity. All parameters were found to have positive and negative growth rates of perturbations within their respective evaluated ranges. The characteristic vortex shedding frequencies associated with the maximum growth rate was compared with those observed in experiments. Although the analysis that employs a base state set without the large scale lateral motions was shown to be capable of predicting the order of magnitude of the frequencies, there is a systematic discrepancy between the predicted and observed frequencies, which may be due to the limitation of linear stability analysis. DOI: 10.1061/(ASCE)HY.1943-7900 .0000822.

On the nonlinear development of shear layers in partially vegetated channels

A predictive theory is developed to investigate the nonlinear instability regime of perturbed shear layers in open-channel flows with lateral vegetation. The turbulence is characterized by two distinct scales: a sub-depth turbulence which is associated with the bed shear stress and a large-scale turbulence associated with the large horizontal eddies which develop in the shear layer. The sub-depth turbulence is modeled by assuming a logarithmic vertical distribution of the velocity. Meanwhile, an analogous model for the large-scale turbulence requires the estimation of the transverse velocity profile in the nonlinear state because the growth of the large-scale disturbances expands the shear layer and modifies the velocity distribution across the channel. The nonlinear growth of the disturbances is limited, however, because solid boundaries in the channel play stabilizing mechanisms which lock the amplitude of the large-scale disturbances into a finite-equilibrium state, for which a corresponding transverse velocity profile is determined. A weakly nonlinear stability analysis is performed and the results are validated using experimental data from previous works.

Incisional cyclic steps of permanent form in mixed bedrock-alluvial rivers

Most bedrock river channels have a relatively thin, discontinuous cover of alluvium and are thus termed mixed bedrock-alluvial channels. Such channels often show a series of steps formed at relatively regular intervals. This bed form is the bedrock equivalent of cyclic steps formed on beds composed of cohesive soil in gullies. In this paper, we perform a full nonlinear analysis for the case of cyclic steps in mixed bedrock-alluvial channels to explain the formation of these steps. We employ the shallow water equations in conjunction with equations describing the process of bedrock incision. As a model of bedrock incision, we employ the recently introduced Macro-Roughness Saltation Abrasion Alluviation model, which allows direct interaction between alluvial and bedrock morphodynamics. The analysis is greatly simplified by making the quasi-steady assumption that alluvial processes occur much faster than bedrock erosional processes. From our analysis, we obtain the conditions for the formation of cyclic steps in bedrock, as well as the longitudinal profiles of bed elevation, water surface elevation, and areal fraction of alluvial cover. It is found from the analysis that when the sediment supply is small relative to the transport capacity, cyclic steps form only on slopes with very high gradients. The analysis indicates that the shape of a step formed on bedrock is characterized by a relatively short upstream portion with an adverse slope and a long, almost planar downstream portion with a constant slope.

Cyclic steps on ice

Boundary waves often form at the interface between ice and fluid flowing adjacent to it, such as ripples under river ice covers, and steps on the bed of supraglacial meltwater channels. They may also be formed by wind, such as the megadunes on the Antarctic ice sheet. Spiral troughs on the polar ice caps of Mars have been interpreted to be cyclic steps formed by katabatic wind blowing over ice. Cyclic steps are relatives of upstream-migrating antidunes. Cyclic step formation on ice is not only a mechanical but also a thermodynamic process. There have been very few studies on the formation of either cyclic steps or upstream-migrating antidunes on ice. In this study, we performed flume experiments to reproduce cyclic steps on ice by flowing water, and found that trains of steps form when the Froude number is larger than unity. The features of those steps allow them to be identified as ice-bed analogs of cyclic steps in alluvial and bedrock rivers. We performed a linear stability analysis and obtained a physical explanation of the formation of upstream-migrating antidunes, i.e., precursors of cyclic steps. We compared the results of experiments with the predictions of the analysis and found the observed steps fall in the range where the analysis predicts interfacial instability. We also found that short antidune-like undulations formed as a precursor to the appearance of well-defined steps. This fact suggests that such antidune-like undulations correspond to the instability predicted by the analysis and are precursors of cyclic steps.

Initiation of Channel Head Bifurcation by Overland Flow

Channel head bifurcation is a key factor for generating complexity of channel networks. Here, we investigate incipient channel head bifurcation using linear stability analysis. Channel heads are simplified as circular hollows, toward which surface sheet flow accelerates in the radial direction. Sinusoidal perturbations in the angular direction with different angular wavenumbers k are imposed on the bed, and their growth rates Ω~ are computed. Because the channel head radius R~c is extending over time, the base state (circular hollow in the absence of perturbations) also evolves continuously. With the use of the momentary stability concept, the evolving base state is defined as momentarily unstable to the imposed perturbation if the disturbance is growing faster than the evolution of the base state. It was found that in the range of sufficiently small R~c, bifurcation cannot be initiated. As R~c increases, bifurcation starts to be possible with k≈ 3–5. A higher k implies bifurcation with a narrower channel junction angle (θ = 2π/k). The average junction angle of the Colorado High Plains for the smallest drainage area is about 85∘ with a standard deviation of 35∘ [Solyom and Tucker, 2007]. Our predicted angles (75∘-120∘ ) agree qualitatively with the observed angles. Finally, we propose a simple criterion to compute the threshold R~c for the onset of bifurcation.