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The Coastal Inlets Research Program (CIRP) is developing predictive numerical models for simulating the waves, currents, sediment transport, and morphology change at and around coastal inlets. Water motion at a coastal inlet is a combination of quasi-steady currents such as river flow, tidal current, wind-generated current, and seiching, and of oscillatory flows generated by surface waves. Waves can also create quasi-steady currents, and the waves can be breaking or non-breaking, greatly changing potential for sediment transport. These flows act in arbitrary combinations with different magnitudes and directions to mobilize and transport sediment. Reliable prediction of morphology change requires accurate predictive formulas for sediment transport rates that smoothly match in the various regimes of water motion. This report describes results of a research effort conducted to develop unified sediment transport rate predictive formulas for application in the coastal inlet environment. The formulas were calibrated with a wide range of available measurements compiled from the laboratory and field and then implemented in the CIRP's Coastal Modeling System.

Emphasis of the study was on reliable predictions over a wide range of input conditions. All relevant physical processes were incorporated to obtain greatest generality, including: (1) bed load and suspended load, (2) waves and currents, (3) breaking and non-breaking waves, (4) bottom slope, (5) initiation of motion, (6) asymmetric wave velocity, and (7) arbitrary angle between waves and current. A large database on sediment transport measurements made in the laboratory and the field was compiled to test different aspects of the formulation over the widest possible range of conditions. Other phenomena or mechanisms may also be of importance, such as the phase lag between water and sediment motion or the influence of bed forms. Modifications to the general formulation are derived to take these phenomena into account. The performance of the new transport formulation was compared to several popular existing predictive formulas, and the new formulation yielded the overall best predictions among the formulas investigated. Results of this report are thus considered to represent a significant and operational step toward a unified formulation for sediment transport at coastal inlets and the nearshore where transport of non-cohesive sediment is common.

Chapter 1 - Introduction

  • Background
  • Objectives
  • Procedure

Chapter 2 - General Sediment Transport Properties

  • Physical properties of particles
    • Granulometry
    • Porosity and friction angle
    • Settling velocity
  • Shear stresses and friction coefficients
    • Bottom boundary layer flow
    • Current-related shear stress
    • Wave related shear stress
    • Combined wave and current shear stress
  • Bed forms effects and roughness computation
    • Current ripples, dunes, and wave ripples
    • Computation of various roughnesses
    • Calculation of total roughness
  • Shields parameter and sediment transport
    • Threshold of motion and critical Shields parameter
    • Mode of sediment transport
    • Inception of sheet flow

Chapter 3 - Bed Load

  • Introduction
  • Previous studies on bed-load transport under wave and current interaction
    • Bijker formula
    • Bailard formula
    • Van Rijn formula
    • Dibajnia and Watanabe formula
    • Ribberink formula
  • Bed-load transport by currents
    • Existing formulas
    • Comparison with data
    • New formula for bed-load transport
  • Bed-load transport by waves
    • Existing formulas
    • Development of new formula
    • Comparison with experimental data
  • Bed-load transport by waves and currents
    • Development of new formula
    • Comparison with experimental data
    • Comparison with existing formulas for waves and current
  • Phase-lag effects on sediment transport in sheet flow
    • Introduction
    • Simple conceptual model
    • Dibajnia and Watanabe formula
    • Modification of Camenen and Larson formula for phase lag
    • Experimental data
    • Calibration of conceptual model
    • Influence of median grain size
    • Influence of wave orbital velocity
    • Influence of wave period
    • Comparison with all data
    • Concluding remarks on phase-lag effects

Chapter 4 - Suspended Load

  • Introduction
  • Equilibrium profile for suspended sediment
    • Mass conservation equation
    • Schmidt number
    • Sediment diffusivity and concentration profiles
  • Sediment diffusivity due to steady current
    • Experimental data
    • Shape of concentration profile
    • Estimation of Schmidt number
  • Sediment diffusivity due to nonbreaking waves
    • Theoretical profiles
    • Estimation of sediment diffusivity profiles for oscillatory flows
    • Starting point for suspension load
    • Shape of concentration profile
    • Relationships for mean sediment diffusivity due to waves
    • New formula for mean sediment diffusivity due to waves
    • Interaction between waves and current
  • Effect of breaking waves on sediment diffusivity
    • Extension of sediment diffusion expression
    • Experimental data with breaking waves
    • Energy dissipation due to breaking waves
    • Influence of Irribaren parameter and u*w/Ws on sediment diffusivity
  • Reference concentration
    • Effect of current
    • Effect of waves
    • Wave-current interaction
    • Cases with breaking waves
  • Suspended load transport
    • Existing formulas for suspended load under wave-current interaction
    • A simple formula
    • Experimental data
    • Validation of hypothesis
    • Comparison with experimental data in case of current only
    • Comparison with experimental data for waves-current interaction
  • Suspended sediment transport for rippled beds
    • Effects of ripples on suspended load
    • Simple conceptual model for phase-lag effects on suspended load
    • Modification of formula for asymmetric waves
    • Observations of phase-lag effects on suspended load over ripples
    • Empirical formulas for and
    • Sensitivity analysis for different formulas
    • Concluding remarks on phase-lag effects

Chapter 5 - Unified Sediment Transport Formula for Coastal Inlet Applications

  • Summary of total load formula
    • Bed-load transport
    • Suspended load transport
    • Velocity profiles for varying slope
  • Application to coastal inlet studies
    • Validation for longshore sediment transport
    • Validation of cross-shore sediment transport
    • Comments on morphological evolution using total load formulas

Chapter 6 - Conclusions



The Coastal Inlets Research Program (CIRP) is developing predictive numerical models for simulating the waves, currents, sediment transport, and morphology change at coastal inlets. Water motion at a coastal inlet can synoptically range through quasi-steady currents as in river flow, tide, wind, and seiching; oscillatory flow as under surface waves, which can create quasi-steady wave-induced currents; breaking and nonbreaking waves; and arbitrary combinations of these flows acting with different magnitudes and at different directions. Reliable prediction of morphology change requires accurate predictive formulas for sediment transport rates that will smoothly match in the aforementioned regimes of water motion and change according to the driving forces and water depth. This report describes a research effort conducted with the aim of developing unified sediment transport rate formulas for application in the coastal inlet environment. These formulas, calibrated with a wide range of available measurements compiled from the laboratory and field, have been implemented in CIRP's Coastal Modeling System.

CIRP is administered at the U.S. Army Engineer Research and Development Center (ERDC), Coastal and Hydraulics Laboratory (CHL) under the Navigation Systems Program for Headquarters, U.S. Army Corps of Engineers (HQUSACE). James E. Walker is HQUSACE Navigation Business Line Manager overseeing CIRP. James E. Clausner, CHL, is the Technical Director for the Navigation Systems Program. Dr. Nicholas C. Kraus, Senior Scientists Group (SSG), CHL, is the CIRP Program Manager.

The mission of CIRP is to conduct applied research to improve USACE capability to manage federally maintained inlets, which are present on all coasts of the United States, including the Atlantic Ocean, Gulf of Mexico, Pacific Ocean, Great Lakes, and U.S. territories. CIRP objectives are to advance knowledge and provide quantitative predictive tools to (a) make management of Federal coastal inlet navigation projects, principally the design, maintenance, and operation of channels and jetties, more effective and reduce the cost of dredging, and (b) preserve the adjacent beaches and estuary in a systems approach that treats the inlet, beaches, and estuary as sediment-sharing components. To achieve these objectives, CIRP is organized in work units conducting research and development in hydrodynamic, sediment transport and morphology change modeling; navigation channels and adjacent beaches; navigation channels and estuaries; inlet structures and scour; laboratory and field investigations; and technology transfer.

This report was prepared under contract with CIRP by Dr. Magnus Larson, Department of Water Resources Engineering, Lund University, Sweden, and by Dr. Benoît Camenen, presently at Cemagref Lyon, France, and formerly a post-doctoral researcher at Lund University, Sweden, and at the Disaster Prevention Research Institute, Kyoto University, Japan. J. Holley Messing, Coastal Engineering Branch, Navigation Division, CHL, typed the equations and format-edited this report. Dr. Kraus oversaw technical elements of this project during the 3 years of required research and development. Thomas W. Richardson was Director, CHL, and Dr. William D. Martin, Deputy Director, CHL, during the study and preparation of this report.

COL Richard B. Jenkins was Commander and Executive Director. Dr. James R. Houston was Director of ERDC.