Hydraulics of floods upstream of horseshoe canyons and waterfalls

Lapôtre, M. G. A.; Lamb, Michael P.

doi:10.1002/2014jf003412

Cited by 12 publications

(42 citation statements)

References 63 publications

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“…The degree to which Q h ,2D differs from the equivalent dimensional upstream discharge was addressed by Lapotre and Lamb [] and parametrized into a nondimensional canyon‐head discharge for steady nonuniform flow, Q *, such that

Q_{h, 2 normalD} = Q * w q_{n},

where q n is the upstream discharge per unit width. The latter can be related to the upstream bed shear stress through conservation of mass and momentum.…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

“…The normalized cumulative discharge to the canyon head, Q *, is a dimensionless measure of how much the dimensional discharge into a horseshoe canyon head, Q h ,2D , is enhanced by flow focusing compared with the upstream normal flow discharge and depends on four dimensionless parameters, namely, the upstream Froude number, Fr n , the canyon‐width to flood‐width ratio,

w * = \frac{w}{W}

, where W is the flood width, the flood‐width limitation factor,

W * = \frac{((), W - w) S}{2 h_{n}}

, and the downslope backwater parameter,

l * = \frac{l S}{h_{n}}

, where l is the canyon length (Figure ) [ Lapotre and Lamb , ].…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

“…Bed shear stress at the rim of a horseshoe waterfall, τ 0,2D , can be written as

τ_{0, 2 normalD} = ρ C_{f 0, 2 normalD} {U_{0, 2 D}}^{2},

where ρ is the density of water and

C_{f 0, 2 normalD} = \frac{n^{2} g}{h_{0, 2 D}^{1 / 3}}

is the friction coefficient at the canyon rim [e.g., Stein and Julien , ]. Flow velocity at the rim, U 0,2D , can be written in terms of the upstream normal flow velocity, U n , such that equation becomes

τ_{0, 2 normalD} = ρ C_{f 0, 2 normalD} {(α_{2 D} U_{n})}^{2},

in which

α_{2 normalD} ≡ \frac{U_{0, 2 D}}{U_{n}}

is defined as the acceleration factor at the rim of a horseshoe waterfall [ Lapotre and Lamb , ]. The acceleration factor at the rim of a horseshoe waterfall, α 2D , takes into account both lateral flow focusing and drawdown of the water surface in response to the loss of hydrostatic pressure at the waterfall.…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

“…The acceleration factor at the rim of a horseshoe waterfall, α 2D , takes into account both lateral flow focusing and drawdown of the water surface in response to the loss of hydrostatic pressure at the waterfall. It can also be defined as

α_{2 normalD} ≡ α * α_{1 normalD},

where

α * = \frac{α_{2 D}}{α_{1 D}}

is the acceleration factor ratio defined in the work of Lapotre and Lamb [] that accounts for lateral flow focusing, and

α_{1 normalD} = \frac{U_{0, 1 D}}{U_{n}} = \frac{h_{n}}{h_{0, 1 D}}

, which accounts for drawdown in 1‐D along the centerline, in which U 0,1D and h 0,1D are the flow velocity and depth at the brink of a linear escarpment, respectively. The 1‐D acceleration factor, α 1D , is a function of the upstream Froude number only, with

α_{1 normalD} = \frac{1.4}{{F r}_{normaln}^{\frac{true}{2}}}

when Fr n ≤ 1 and

α_{1 normalD} = \frac{0.4 + normalF r_{n}^{2}}{normalF r_{n}^{2}}

when Fr n > 1 [ Rouse , ; Delleur et al ., ; Hager , ].…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

“…The acceleration factor ratio, α *, is a measure of the enhancement or decrease in flow acceleration at the brink of a horseshoe waterfall compared with that at a 1‐D escarpment: for a linear escarpment, α * = 1, so that α 2D = α 1D , while at the center of a canyon head, α * ≥ 1. Lapotre and Lamb [] evaluated α * at three different locations around the rim of semicircular‐headed canyons (Figure )—the head (upstream end of the canyon head,

α_{h}^{*}

), the wall (junction between the horseshoe head and the straight sidewall,

α_{w}^{*}

), and the toe (downstream end of the canyon sidewall,

α_{t}^{*}

). Analogous to the semiempirical relationships derived for Q *, Lapotre and Lamb [] developed semiempirical relationships to predict the acceleration factor ratio, α *.…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

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Canyon formation constraints on the discharge of catastrophic outburst floods of Earth and Mars

2016

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Catastrophic outburst floods carved amphitheater‐headed canyons on Earth and Mars, and the steep headwalls of these canyons suggest that some formed by upstream headwall propagation through waterfall erosion processes. Because topography evolves in concert with water flow during canyon erosion, we suggest that bedrock canyon morphology preserves hydraulic information about canyon‐forming floods. In particular, we propose that for a canyon to form with a roughly uniform width by upstream headwall retreat, erosion must occur around the canyon head, but not along the sidewalls, such that canyon width is related to flood discharge. We develop a new theory for bedrock canyon formation by megafloods based on flow convergence of large outburst floods toward a horseshoe‐shaped waterfall. The model is developed for waterfall erosion by rock toppling, a candidate erosion mechanism in well fractured rock, like columnar basalt. We apply the model to 14 terrestrial (Channeled Scablands, Washington; Snake River Plain, Idaho; and Ásbyrgi canyon, Iceland) and nine Martian (near Ares Vallis and Echus Chasma) bedrock canyons and show that predicted flood discharges are nearly 3 orders of magnitude less than previously estimated, and predicted flood durations are longer than previously estimated, from less than a day to a few months. Results also show a positive correlation between flood discharge per unit width and canyon width, which supports our hypothesis that canyon width is set in part by flood discharge. Despite lower discharges than previously estimated, the flood volumes remain large enough for individual outburst floods to have perturbed the global hydrology of Mars.

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Q_{h, 2 normalD} = Q * w q_{n},

where q n is the upstream discharge per unit width. The latter can be related to the upstream bed shear stress through conservation of mass and momentum.…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

w * = \frac{w}{W}

, where W is the flood width, the flood‐width limitation factor,

W * = \frac{((), W - w) S}{2 h_{n}}

, and the downslope backwater parameter,

l * = \frac{l S}{h_{n}}

, where l is the canyon length (Figure ) [ Lapotre and Lamb , ].…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

“…Bed shear stress at the rim of a horseshoe waterfall, τ 0,2D , can be written as

τ_{0, 2 normalD} = ρ C_{f 0, 2 normalD} {U_{0, 2 D}}^{2},

where ρ is the density of water and

C_{f 0, 2 normalD} = \frac{n^{2} g}{h_{0, 2 D}^{1 / 3}}

τ_{0, 2 normalD} = ρ C_{f 0, 2 normalD} {(α_{2 D} U_{n})}^{2},

in which

α_{2 normalD} ≡ \frac{U_{0, 2 D}}{U_{n}}

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

α_{2 normalD} ≡ α * α_{1 normalD},

where

α * = \frac{α_{2 D}}{α_{1 D}}

is the acceleration factor ratio defined in the work of Lapotre and Lamb [] that accounts for lateral flow focusing, and

α_{1 normalD} = \frac{U_{0, 1 D}}{U_{n}} = \frac{h_{n}}{h_{0, 1 D}}

α_{1 normalD} = \frac{1.4}{{F r}_{normaln}^{\frac{true}{2}}}

when Fr n ≤ 1 and

α_{1 normalD} = \frac{0.4 + normalF r_{n}^{2}}{normalF r_{n}^{2}}

when Fr n > 1 [ Rouse , ; Delleur et al ., ; Hager , ].…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

α_{h}^{*}

), the wall (junction between the horseshoe head and the straight sidewall,

α_{w}^{*}

), and the toe (downstream end of the canyon sidewall,

α_{t}^{*}

). Analogous to the semiempirical relationships derived for Q *, Lapotre and Lamb [] developed semiempirical relationships to predict the acceleration factor ratio, α *.…”

Section: Model For the Stability Of Canyons And Escarpmentsmentioning

confidence: 99%

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Canyon formation constraints on the discharge of catastrophic outburst floods of Earth and Mars

2016

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Sediment transport through self‐adjusting, bedrock‐walled waterfall plunge pools

Scheingross

Lamb

2016

JGR Earth Surface

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Many waterfalls have deep plunge pools that are often partially or fully filled with sediment.Sediment fill may control plunge-pool bedrock erosion rates, partially determine habitat availability for aquatic organisms, and affect sediment routing and debris flow initiation. Currently, there exists no mechanistic model to describe sediment transport through waterfall plunge pools. Here we develop an analytical model to predict steady-state plunge-pool depth and sediment-transport capacity by combining existing jet theory with sediment transport mechanics. Our model predicts plunge-pool sediment-transport capacity increases with increasing river discharge, flow velocity, and waterfall drop height and decreases with increasing plunge-pool depth, radius, and grain size. We tested the model using flume experiments under varying waterfall and plunge-pool geometries, flow hydraulics, and sediment size. The model and experiments show that through morphodynamic feedbacks, plunge pools aggrade to reach shallower equilibrium pool depths in response to increases in imposed sediment supply. Our theory for steady-state pool depth matches the experiments with an R 2 value of 0.8, withdiscrepancies likely due to model simplifications of the hydraulics and sediment transport. Analysis of 75 waterfalls suggests that the water depths in natural plunge pools are strongly influenced by upstream sediment supply, and our model provides a mass-conserving framework to predict sediment and water storage in waterfall plunge pools for sediment routing, habitat assessment, and bedrock erosion modeling.

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Incision of Licus Vallis, Mars, From Multiple Lake Overflow Floods

Goudge

Fassett

2018

JGR Planets

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Licus Vallis is a large valley (>350 km long, >2 km wide, and >150 m deep) that heads at the outlet breach of an ~30 km diameter impact crater. We present observations of the geomorphology and topography of this paleolake outlet valley and associated tributary valleys to constrain the history of incision of the Licus Vallis system. Licus Vallis has an abrupt increase in gradient by a factor of approximately 4 along its longitudinal profile, and a knickpoint that drops ~200 m over a reach of ~2 km approximately 12 km downstream from the valley head. We also describe a set of paired terraces within Licus Vallis, which are continuous for tens of kilometers and define an interior valley >2 km in width. We interpret the geomorphology of Licus Vallis as recording at least two discrete, major episodes of valley incision, both driven by lake overflow floods. The main portion of Licus Vallis formed by overflow flooding from a large (~103–104 km2) lake contained in an intercrater basin. Subsequently, overflow flooding from a lake within the ~30 km diameter impact crater reactivated Licus Vallis, forming a major knickpoint at the valley head and establishing the upstream section of the valley at a lower slope. Farther down the valley, this flood event incised an interior valley bounded by paired terraces. Regional tributary valleys that feed Licus Vallis also have prominent knickpoints, which have retreated farthest for downstream valleys. We conclude that these knickpoints record successive waves of incision that swept up Licus Vallis during lake overflow flooding, with erosion in the main trunk of the valley (from overflow floods) significantly outpacing erosion in the tributary valleys (from regional surface runoff). These observations of Licus Vallis illustrate how lake overflow floods may have provided an important control on the pace of landscape evolution on Mars.

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Hydraulics of floods upstream of horseshoe canyons and waterfalls

Cited by 12 publications

References 63 publications

Canyon formation constraints on the discharge of catastrophic outburst floods of Earth and Mars

Canyon formation constraints on the discharge of catastrophic outburst floods of Earth and Mars

Sediment transport through self‐adjusting, bedrock‐walled waterfall plunge pools

Incision of Licus Vallis, Mars, From Multiple Lake Overflow Floods

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