Cyclic steps and roll waves in shallow water flow over an erodible bed

@article{Balmforth2012CyclicSA,
  title={Cyclic steps and roll waves in shallow water flow over an erodible bed},
  author={Neil J. Balmforth and Ali Vakil},
  journal={Journal of Fluid Mechanics},
  year={2012},
  volume={695},
  pages={35 - 62}
}
Abstract The St Venant equations in conjunction with a phenomenological law for erosion are used to explore the nonlinear dynamics of cyclic steps – linearly unstable bedform patterns which emerge when uniform flow over an erodible bed becomes supercritical. The instability saturates by blocking the overlying flow and creating hydraulic jumps just downstream of the steepest part of the steps. Near onset, steadily migrating, nonlinear step patterns are constructed and shown to suffer a short… 
From standing to breaking antidunes, a Hopf bifurcation.
Antidunes are bed morphologies often observed in steep slope mountain flows but also in small streams flowing on a sand beach. Linear stability analysis of the shallow water equations (SWE), when
Sorting and bed waves in unidirectional shallow-water flows
The stability of a uniform flow above an erodible bed composed of a bimodal mixture of sediments is investigated by means of linear analysis. Results show that, for any given set of the flow and
A shallow-water theory of river bedforms in supercritical conditions
A supercritical free-surface turbulent stream flowing over an erodible bottom can generate a characteristic pattern of upstream migrating bedforms known as antidunes. This morphological instability,
Linear stability of shallow morphodynamic flows
Abstract It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary
Stability, resonance and role of turbulent stresses in 1D alluvial flows
  • M. Colombini
  • Environmental Science
    Environmental Fluid Mechanics
  • 2022
Linear stability analysis is used to investigate the behavior of small perturbations of a uniform flow in a straight channel with an erodible bed composed by a unisize sediment. A shallow-water flow
Morphodynamics and depositional signature of low‐aggradation cyclic steps: New insights from a depth‐resolved numerical model
Bedforms related to Froude‐supercritical flow, such as cyclic steps, are increasingly frequently observed in contemporary fluvial and marine sedimentary systems. However, the number of observations
Morphodynamics and sedimentary structures of bedforms under supercritical‐flow conditions: New insights from flume experiments
Supercritical‐flow phenomena are fairly common in modern sedimentary environments, yet their recognition and analysis remain difficult in the stratigraphic record. This fact is commonly ascribed to
...
...

References

SHOWING 1-10 OF 23 REFERENCES
Dynamics of roll waves
Shallow-water equations with bottom drag and viscosity are used to study the dynamics of roll waves. First, we explore the effect of bottom topography on linear stability of turbulent flow over
Transportational cyclic steps created by flow over an erodible bed. Part 1. Experiments
Froude-supercritical flow over a flat, erodible bed with copious transport of sediment in suspension appears to be fundamentally unstable. Under a broad range of conditions the flow and bed co-evolve
Numerical simulations of transportational cyclic steps
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
On roll waves down an open inclined channel
  • D. Needham, J. Merkin
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1984
Flow down an open inclined channel is considered. Dressler (Communs pure appl. Math. 2, 149-194 (1949),) using the equations of the shallow water theory augmented by the Chezy formula for drag, has
Hyperconcentrated Sand‐Water Mixture Flows over Erodible Bed
Field surveys and experiments in a tilting flume on hyperconcentrated sand‐water mixture (SWM) flows were conducted. At slopes slightly smaller than the equilibrium slope, a rapid development of sand
Nonlinear evolution of small disturbances into roll waves in an inclined open channel
This paper concerns the asymptotic behaviour (for the limiting case of small amplitudes) of small disturbances as they evolve in time to produce the quasi-steady pattern of roll waves first discussed
Coupling or decoupling bed and flow dynamics: Fast and slow sediment waves at high Froude numbers
The effect of coupling or decoupling bed and flow dynamics is analyzed in the framework of a linear analysis of the stability of a uniform, rotational, two-dimensional flow in an infinitely wide
Finite-amplitude river dunes
The linear and weakly nonlinear stability of a uniform flow in an infinitely wide open channel with erodible bottom is studied. Under suitable conditions the flow is found to be unstable, leading to
...
...