### Abstract

The most common bedload transport calculation methods use an equation for the vector direction that is a linear function of the transverse slope. Existing theoretical formulations that account for nonlinear effects when transverse slopes are steep (such as noncohesive stream banks) are not widely used in practice, due largely to the complexity of their implementation. In this analysis, a single equation for the bedload transport rate direction is derived that accounts for the nonlinearity. The equation is cast in the same form as most linear formulations, but with the constant replaced by a function that requires the equation to be solved numerically. Negligible streamwise slopes are assumed, which allows the simplified expression; otherwise, the derivation follows past rigorous theoretical treatments that are valid for transverse slopes up to the angle of repose. A direct comparison is made between linear and nonlinear derivations that highlights the approximations inherent in the linear form. Application of the equation to two different types of past experiments illustrates the degree of error associated with evaluating bedload data involving steep transverse slopes using a traditional linear form for the vector direction.

Original language | English (US) |
---|---|

Article number | 04019028 |

Journal | Journal of Hydraulic Engineering |

Volume | 145 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2019 |

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### ASJC Scopus subject areas

- Civil and Structural Engineering
- Water Science and Technology
- Mechanical Engineering

### Cite this

**Nonlinear Bedload Transport Trajectory Angle Expressed in a Traditional Form : Derivation and Application.** / Waterman, David M.; Garcia, Marcelo Horacio.

Research output: Contribution to journal › Article

*Journal of Hydraulic Engineering*, vol. 145, no. 8, 04019028. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001619

}

TY - JOUR

T1 - Nonlinear Bedload Transport Trajectory Angle Expressed in a Traditional Form

T2 - Derivation and Application

AU - Waterman, David M.

AU - Garcia, Marcelo Horacio

PY - 2019/8/1

Y1 - 2019/8/1

N2 - The most common bedload transport calculation methods use an equation for the vector direction that is a linear function of the transverse slope. Existing theoretical formulations that account for nonlinear effects when transverse slopes are steep (such as noncohesive stream banks) are not widely used in practice, due largely to the complexity of their implementation. In this analysis, a single equation for the bedload transport rate direction is derived that accounts for the nonlinearity. The equation is cast in the same form as most linear formulations, but with the constant replaced by a function that requires the equation to be solved numerically. Negligible streamwise slopes are assumed, which allows the simplified expression; otherwise, the derivation follows past rigorous theoretical treatments that are valid for transverse slopes up to the angle of repose. A direct comparison is made between linear and nonlinear derivations that highlights the approximations inherent in the linear form. Application of the equation to two different types of past experiments illustrates the degree of error associated with evaluating bedload data involving steep transverse slopes using a traditional linear form for the vector direction.

AB - The most common bedload transport calculation methods use an equation for the vector direction that is a linear function of the transverse slope. Existing theoretical formulations that account for nonlinear effects when transverse slopes are steep (such as noncohesive stream banks) are not widely used in practice, due largely to the complexity of their implementation. In this analysis, a single equation for the bedload transport rate direction is derived that accounts for the nonlinearity. The equation is cast in the same form as most linear formulations, but with the constant replaced by a function that requires the equation to be solved numerically. Negligible streamwise slopes are assumed, which allows the simplified expression; otherwise, the derivation follows past rigorous theoretical treatments that are valid for transverse slopes up to the angle of repose. A direct comparison is made between linear and nonlinear derivations that highlights the approximations inherent in the linear form. Application of the equation to two different types of past experiments illustrates the degree of error associated with evaluating bedload data involving steep transverse slopes using a traditional linear form for the vector direction.

UR - http://www.scopus.com/inward/record.url?scp=85066927722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066927722&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)HY.1943-7900.0001619

DO - 10.1061/(ASCE)HY.1943-7900.0001619

M3 - Article

AN - SCOPUS:85066927722

VL - 145

JO - Journal of Hydraulic Engineering

JF - Journal of Hydraulic Engineering

SN - 0733-9429

IS - 8

M1 - 04019028

ER -