Rouse Number: Sediment Suspension Balance
The Rouse number (P = ws / (κ u*)) compares gravitational settling velocity ws of sediment particles with the turbulent mixing intensity represented by shear velocity u* scaled by the von Kármán constant κ (≈0.4). It predicts whether particles remain in suspension, travel as bedload, or deposit. Low Rouse numbers (< 0.8) signify nearly uniform suspensions; high values (> 2.5) indicate predominantly bedload transport. This article formalises the metric, reviews its history, elaborates conceptual tools, and explores engineering and environmental uses.
Combine this overview with the Reynolds number article to characterise turbulence regimes, and use the drain pipe slope calculator when translating Rouse analyses into practical slope selections.
Definition and Governing Relationships
Balance of settling and diffusion
The Rouse number emerges from the steady-state advection-diffusion equation describing vertical sediment concentration profiles. Turbulent diffusion proportional to κ u* z balances gravitational settling ws C, yielding the classic exponential concentration profile C(z) = Ca [(z - a)/(h - z)]P, where h is flow depth, a is reference height, and P is the Rouse number. Thus, P encapsulates how turbulence suspends particles against gravity.
Dependence on particle size and fluid properties
Settling velocity ws depends on particle diameter, density contrast, and fluid viscosity. Fine silts have ws on the order of millimetres per second, while coarse sand settles at centimetres per second. Shear velocity u* relates to bed shear stress τ0 via u* = √(τ0/ρ), linking Rouse number to boundary shear.
Thresholds for transport modes
Empirical guidelines classify P < 0.8 as wash load, 0.8 ≤ P ≤ 2.5 as suspended load with vertical gradients, and P > 2.5 as bedload. Designers apply these thresholds when evaluating dredging needs or channel maintenance schedules.
Historical Development
Hans Rouse and 1930s hydraulics
Hans Rouse introduced the parameter in 1937 while analysing suspended sediment data from laboratory flumes. His work at the University of Iowa synthesised empirical profiles and theoretical turbulence concepts, providing a compact predictor of sediment transport mode.
Postwar field applications
Mid-twentieth-century river engineers adopted the Rouse number to design navigation channels on the Mississippi and Columbia Rivers. It guided dredging intervals and training structure placement by indicating when sediments would remain aloft versus settle into shoals.
Modern environmental monitoring
Contemporary researchers integrate Rouse number calculations with acoustic Doppler profiler data and satellite turbidity products to monitor coastal erosion, reservoir siltation, and habitat conditions. Numerical models embed P in sediment transport routines within morphodynamic simulations.
Applications and Importance
Channel design and maintenance
Engineers compute Rouse numbers to select channel slopes and bed materials that balance navigability with sediment transport. By coupling P with the slope between two points calculator, designers translate survey data into hydraulically efficient alignments.
Environmental assessment
Aquatic habitat managers monitor Rouse numbers to ensure turbidity stays within ecological thresholds. Low P values may threaten filter feeders, while high values can starve downstream wetlands of sediment. Integrating runoff estimates from the stormwater runoff calculator helps quantify sediment supply.
Dredging and mining operations
Dredge contractors track Rouse numbers to optimise cutterhead depth and slurry concentration. Tailings engineers use the metric to keep particles suspended in pipelines, avoiding deposition that could clog infrastructure.