Presentation on theme: "ENGR 691, Fall Semester 2010-2011 Special Topic on Sedimentation Engineering Section 73 Coastal Sedimentation Yan Ding, Ph.D. Research Assistant Professor,"— Presentation transcript:
1ENGR 691, Fall Semester Special Topic on Sedimentation Engineering Section 73 Coastal SedimentationYan Ding, Ph.D.Research Assistant Professor, National Center for Computational Hydroscience and Engineering (NCCHE), The University of Mississippi, Old Chemistry 335, University, MS 38677Phone:
2OutlineIntroduction of morphodynamic processes driven by waves and currents in coasts, estuaries, and lakesInitiation of motion for combined waves and currentsBed forms in waves and in combined waves and currentsBed roughness in combined waves and currentsSediment transport in wavesSediment transport in combined waves and currentsTransport of cohesive materials in coasts and estuariesMathematical models of morphodynamic processes driven by waves and currentsIntroduction of a process-integrated modeling system (CCHE2D-Coast) in application to coastal sedimentation problems
3Near-bed Orbital Velocities Applying linear wave theory, the peak value of the orbital excursion (Aδ) and velocity (U δ) at the edge of the wave boundary layer can be expressed asH = wave heighth = water depthω = angular frequency = 2π/Tk = wave number
5Wave Boundary Layer (2) z u Uδ δw The wave boundary layer is a thin layer forming the transition layer between the bed and the upper layer of irrotational oscillatory flow (Fig.). The thickness of this layer remains thin (0.01 to 0.1 m) in short period wave (<=12s) because the flow reverses before the layer can grow in vertical direction. The boundary layer thickness δw can be defined as the minimum distance between the wall and a level where the velocity equals the peak value of the free stream velocity Uδ.Jonson (1980):Manohar (1955):ν = kinematic viscosity coefficient (m2/s)T = wave period (s)ks = effective bed roughness (m)In case of turbulent boundary layer: δw=f(T, ks)
6Wave Boundary layer (3) - Bed shear stress and bed friction Wave exerts friction forces at the bed during oscillations. The bed shear stress, which is important for wave damping and sediment entrainment, is related to the friction coefficient by :fw = friction coefficient (non-dimension), which is assumed to be constant over the wave cycleuδ = instantaneous fluid velocity of the free stream (just outside boundary layerThe time-averaged over half a wave cycle bed shear stress isThe calculations of the friction coefficient fw depend on the flow regimes of the wave boundary layer, i.e. laminar flow, smooth turbulent flow, and rough turbulent flow. See van Rijin (1993) for details.
8Initiation of Motion in Waves Critical VelocityIn oscillatory flow there is no generally accepted relationship for initiation of motion on a plane bed. Many equations have been proposed. One of the more popular equations is proposed by Komar and Miller (1975)Uδ, cr= critical peak value of orbital velocity near the bedA δ, cr = critical peak value of orbital excursion near beds = specific gravity (=ρs/ρ)
9Initiation of Motion in Waves - Critical Velocity
10Initiation of Motion in Waves - Critical Bed-Shear Stress The experimental data for initiation of motion in waves can also be expressed in terms of the Shield parameter using the time-averaged bed-shear stress, i.e.where=time-averaged over half a wave period) wave-related bed-shear stressD*=particle parameter
11Initiation of motion for waves over a plane bed based on critical bed-shear stress No motionThe Shields curve which is valid for unidirectional flow data only.The variation between the results of different investigators is mainly caused by the definition problem for initiation of motion .The Shields curve can also be applied as a criterion for initiation of motion for oscillatory flow over a plane bed. It represents a critical stage at which only a minor part (1% to 10%) of the bed surface is moving.
13ExampleThe water depth in a coastal sea with a plane bed is h = 5m. The wave period is T = 7s. The bed material parameters are d50=200μm, d90=300μm, ρs=2650kg/m3. The water temperature Te = 20oC. The kinematic viscosity coefficient ν=1.0x10-6m2/s, fluid density ρ=1025kg/m3.What is the wave height at initiation of motion?Method 1Using the figure for initiation of wave motion, the critical peak orbital velocity can be obtained: Uδ,cr = 0.23Calculate the wave length by the dispersion relationYielding L = 45.7m.Online wave calculator:Using the definition of the critical velocity, the wave height can be calculated= 0.38m
14Initiation of motion for combined current and wave
15Initiation of motion for combined current and wave The resulting time-averaged total bed-shear stress :
17Wave Breaking (1)Wave breaking limit: assume that wave crest particle velocity equals the wave celerity at the breaking point, i.e.In generalThen,Therefore, the wave breaking limit:
18Wave Breaking (2)The wave breaking limit (wave steepness) based on small amplitude wave theory:is not accurate!In deep water,According to observationsIn shallow water,too lateAs a rule of thumb,Saturated wave breaking in shallow water (McCowan 1894)
19Breaking Wave Criteria in Shallow Water Goda (1985) proposed a very useful breaking wave criteria (BWC) based on a large amount of observation data (laboratory and field data), i.e.Hb = Breaking Wave HeightL0 = Wave LengthA = Empirical Coefficient (0.12 – 0.18)= Sea Bed SlopeC(εd) = Coefficient (if = 1.0, BWC = Goda’s formula (Goda 1975);if not equal to 1.0, BWC=extended Goda’s formula (Sakai et al. 1988)
20Breaking Wave Criteria (3) In deep water, wave celerity can be written:and the particle velocity amplitude at surfaceThen,Or,Actually, Ramberg and Griffin (1987) found that the deep water breaking height is best represented bye.g.T = 10s in deep water, if breaking wave, the wave height could be 21 meter. That’s a huge wave.In Hurricane Katrina, offshore maximum wave height record in offshore of Mississippi Gulf Coast is 36 ft = 10.8m. It might not be breaking yet.Tsunami wave in deep water, in general, is not breaking wave, because tsunami wave in deep water is long wave.
22Bed forms in waves and in combined waves and currents Introduction of morphodynamic processes driven by waves and currents in coasts, estuaries, and lakesInitiation of motion for combined waves and currentsBed forms in waves and in combined waves and currentsBed roughness in combined waves and currentsSediment transport in wavesSediment transport in combined waves and currentsTransport of cohesive materials in coasts and estuariesMathematical models of morphodynamic processes driven by waves and currentsIntroduction of a process-integrated modeling system (CCHE2D-Coast) in application to coastal sedimentation problems
25Classification of Bed Forms in Unidirectional Currents
26SAND WAVES PLANE BEDANTI-DUNESDUNESClassification of Bed Forms in Unidirectional Currents (van Rijn 1984, 1989)Regimes: Lower, transition, and upperBed Form = F(T, D)Particle parameter:Excess bed-shear stress parameter:
27Shape and Dimension of Bed Forms at Lower Regime in Unidirectional Flows (1) Flat bed, lower region: Before onset of particle motionRibbons and ridges, lower regime: small scale, parallel to the main flow direction, esp. in case of fine sediments (d50<100μm), probably generated by secondary flows and near-bed turbulence burst-sweep effect, vertical scales ≈ 10d50, the width scale = 100ν/u*Ripples, lower regime: Mini ripples, 3-D ripples, lunate ripples (concave shape), linguoid ripples (convex shape), mega-ripplesMini ripples: ripple height Δr = 50 ~ 200 d50ripple length λr = 500 ~ 1000d50Mega-ripple:for 1.0≤ D*≤ and 3.0 ≤ T ≤ 10.0Particle parameterExcess bed-shear stress parameter
28Dune Characteristics after van Rijn (1982) Nondimensional dune height vs Transport Parameter T
29Dune Characteristics after van Rijn (1982) Dune steepness vs Transport Parameter T
30Shape and Dimension of Bed Forms at Lower Regime in Unidirectional Flows (2) 4. Dune, lower regimeThe dune-type bed form is a typical bed form at the lower regime. Dunes have an asymmetrical profile with a rather steep leeside and a gentle stoss side. A general feature of dune-type bed forms is a leeside flow separation, which results in strong eddy motions downstream of the dune crestThe length of dunes is strongly related to the water depth with values in the range of 3 to 15 h.Dunes can migrate to downstream, or to upstream (anti-dune)Estimations of dune shapes by van Rijn’s formulations:Where h = water depth from water surface to mean bed level (at the half the bed form height)Note that the dunes are assumed to be washed out for T ≥25.0FigBars, lower regime: the largest bed forms in the lower regimeAlternate bars, side bars (point bars & scroll bars), braid bars, and transverse bars
31Shape and Dimension of Bed Forms at transition and upper Regime in Unidirectional Flows Washed-out dunes and sand waves in the transition regimeIt is a well-known phenomenon that the bed forms generated at low regime are washed out at high velocities. Ultimately, relative long and smooth sand waves with a roughness equal to the grain roughness were generatedBased on van Rijn’s result in Fig , the transition regime will occur for T ≥ 15 . The bed forms in the transition regime which will most likely occur are washed-out dune and (symmetrical) sand waves. The dimensions of the sand waves are described by:The bed forms will fully disappear for T ≥ 25.Plane bed and sand waves, upper regimeTwo sub-regimes:Subcritical upper transport regime: T≥25.0 and Fr< 0.8, symmetrical sand wavesSupercritical upper transport regime: T≥25.0 and Fr ≥ 0.8, plane bed and/or anti-dunes. When the flow velocity further increases, finally a stage with chute and pools may be generatedfor T ≥ 15.0 and subcritical flow regime
32Examples and Problems (1) A wide open channel has a mean water depth h = 3m, a mean velocity u = 1 m/s, the bed material characteristics are d50 = 0.35mm, d90=1.0mm, sediment density ρs=2650kg/m3, ρ=1000kg/m3, kinematic viscosity ν = 1x10-6.Given that the bottom boundary layer flow regime is hydraulic rough flow, what types of bed forms are generated? What are the dimensions of the bed forms?Bed forms by van Rijn’s approach (Fig )1. Calculate the bed shear stressChezy roughness coefficient C = 18log(12h/3d90) = 73.4 m1/2/sBed shear stress τb,c = ρg(u/C)2 = 1.82 N/m22. Calculate the critical bed shear stressSpecific density = ρs /ρParticle parameter D* = ((s-1)g/ν2)1/3d50 = 8.79According to the Shields’ curve, the critical mobility parameter:θcr = 0.14D*-0.64=0.0348The critical shear stress τb,cr = (ρs-ρ)gd50 θcr =0.197N/m23. Calculate the excess bed-shear stress parameterT=(τb,c - τb,cr )/ τb,cr =8.234. Find the bed forms from Fig using the values of D* and T
33Examples and Problems (2) A wide open channel has a mean water depth h = 3m, a mean velocity u = 1 m/s, the bed material characteristics are d50 = 0.35mm, d90=1.0mm, sediment density ρs=2650kg/m3, ρ=1000kg/m3, kinematic viscosity ν = 1x10-6.Given that the bottom boundary layer flow regime is hydraulic rough flow, what types of bed forms are generated? What are the dimensions of the bed forms?4. Find the bed forms from Fig using the values of D* and TBed forms: mega-ripples and dunesBed form dimensions by van Rijn’s approach1. mega-ripplesRipple height: Δmr= 0.02h(1-exp(-0.1T))(10-T) = 0.074mRipple length: λmr = 0.5h = 1.5m2. DunesDune height: Δd= 0.11h (d50/h)0.3(1-exp(-0.5T))(25-T) = 0.37mRipple length: λd = 7.3h = 21.9m
34Homework (1)A wide open channel has a mean water depth h = 2.0m, a mean velocity u = 1.2 m/s, the bed material characteristics are d50 = 0.35mm, d90=1.0mm, sediment density ρs=2650kg/m3, ρ=1000kg/m3, kinematic viscosity ν = 1x10-6.Given that the bottom boundary layer flow regime is hydraulic rough flow, using van Rijn’s method, find the types of bed forms generated by the flow, and determine the dimensions of the bed forms.Hint: please refer to pages in van Rijn’s book (Principle s of Sediment Transport in Rivers, Estuaries and Coastal Seas) or my notes for solving the problems
35Bed Forms in Waves Classification Two typical regimes can be observed in nature:Lower regime with flat immobile bed, ripples and bars,Upper regime with flat mobile bed (i.e. sheet flow)A typical transition regime does not occurTwo parameters for classifying the regimes:Ripple regime forSheet flow regime for
36Bed form classification diagram for waves after Allen (1982)
37Bed Forms in the Coastal Zone (1) - Clifton (1976) and Shipp (1984)
39Bed Forms in the Coastal Zone (2) - Clifton (1976) and Shipp (1984) Upper shore face: linear ripples, asymmetric ripples, flat bed (sheet flow)Longshore trough: Linear ripples (λr = 0.7m, Δr = 0.15m)Landward slope of bar: cross ripple, irregular ripples and linear ripples (from top to bottom)Longshore bar crest: irregular and cross ripples for low energy conditions lunate mega-ripples (λr = 0.7m, Δr = 0.15m) for higher energy conditionsSeaward slope of bar: Cross-ripples and linear ripplesTransitional zone: linear ripples of fine sand (0.2mm), locally coarse grain deposits (0.6mm) forming linear mega-ripplesOffshore: linear ripples of fine sand (0.15 – 0.20 mm)
40Dimensions of Bed Forms (1) - Observed ripple height (a) For regular waves(b) For irregular waves
41Dimensions of Bed Forms (1) - Observed ripple length (a) For regular waves(b) For irregular waves
42Dimensions of Bed Forms (2) For non-breaking irregular waves - van Rijn’s FormulationsDimensionless ripple height:Ripple steepness:Sheet flow regimeThe upper regime with sheet flow conditions is assumed to be present for Ψ ≥ 250.0Surf –zone bars or longshore barsThese type of bars have their orientation (crests) parallel to the coastline and are formed in the surf zone near the breakline. It may be generated by net offshore-directed current in the surf zone (undertow flow).
43Examples and Questions A coastal sea has a water depth of h = 5m. Irregular waves with a peak period of Tp=7s are present. The bed material characteristics are d50 = 0.3mm, d90=0.5mm. Other coastal water parameters: ρ = 1025kg/m3, ρs=2650kg/m3, ν=1x10-6m2/sWhat is the significant wave height at the initiation of sheet flow?Significant wave height (Hs) is the average wave height (trough to crest) of the one-third largest wavesSolution:Initiation of sheet flow: Ψ ≥ 250.0and s = ρs/ρ =The wave length of the wave (Tp=7s): LS = 45.7mAnswer: A significant wave height of 1.79m (or higher) will initiate sheet flow on the sea bed.
44Homework (2)A coastal sea has a water depth of h = 5m. Irregular waves with a significant wave height Hs = 1 m and a peak period of Tp=7s are present. The bed material characteristics are d50 = 0.3mm, d90=0.5mm. Other coastal water parameters: ρ = 1025kg/m3, ρs=2650kg/m3, ν=1x10-6m2/sWhat are the ripple height and the length according to van Rijn’s method?What is the flow regime if the wave height Hs = 2m and Tp=7.0s?
45Bed Forms in Currents and waves (1) Currents in the nearshore and surf zone:Cross-shore return flow, longshore current, and tidal current when weather is clam.The cross-shore return flows refer to a general seaward flow or to a channelized narrow seaward rip current due to wave breaking. Seaward-facing mega-ripples have been commonly observed.Longshore currents refer to the current in the zone between the longshore bar and the shoreline.Complex ripples patterns are found in the areas.In the offshore zone, tidal currents may become dominant, which may be following, opposing, or oblique to the wave direction. Bed forms in tidal seas are related to the peak current velocities, water depth, sediment diameter and the availability of sediment.Tidal inlet
46Ripple Patterns in Combined Current and Wave Conditions ucuwcurrentwaveSymmetrical wave-induced ripples (2.5D)Asymmetrical current-induced ripples (3D)wave-current induced ripples (honeycomb pattern, 3D)
47Ripples created by ebb-tide Honeycomb ripplesRipples created by ebb-tide
48Others patterns Patterns on Borth Sands As the tide ebbs, it has left a scallop-shaped pattern on the sandbank.
49Bed Forms in Currents and waves (2) Four types of bed forms in combined current and wave conditions:Symmetrical wave-induced ripples with their crest almost perpendicular to the wave direction in case of weak tidal current velocitiesAsymmetrical current-induced ripples and large symmetrical sand waves with their crest perpendicular to the tidal current direction in case of a strong tidal current and weak orbital velocitiesWave-current ripples in a honeycomb pattern in case of equal strength of the current and peak orbital velocities.Longitudinal furrows, ribbons, ridges and banks with crests and troughs almost parallel to the peak tidal current directionThe bed forms generated by combined currents and waves bear some features of both hydraulic effects. Where the wave component dominates, the bed forms are similar to fully developed wave-related bed forms. As the current component gains in strength, the bed forms become more asymmetrical and larger in height and length, especially in case of an opposing current. The influence of the waves is that the bed form crest will become more rounded.
50Bed Forms in Currents and waves (3) - Classification in terms of van Rijn’s approach Based on the available data, van Rijn proposed a classification diagram for bed forms under combined waves and currents conditions. Two key nondimensional parameters are defined as follows:The current-related mobility parameter:The wave-related mobility parameter:whereCurrent-related effective bed-shear velocity:Current-related friction factor:Wave-related effective bed-shear velocity:Wave-related friction factor:= depth-averaged velocityUδ = peak orbital velocity at bed based on relative wave periodAδ = peak orbital excursion at bed based on relative period, U δ =ωA δ
52Example and ProblemA coastal sea has a water depth of h = 20m, the peak flood-current velocity is umax.flood = 0.6m/s; the peak ebb-current velocity is umax.ebb = 0.5m/s. Irregular waves perpendicular to the flood and ebb current directions are present. The significant wave height Hs=1.5m, the peak period Tp = 8s. The bed material characteristics are d50 = 0.3mm, d90 = 0.6mm. Other data are ρ = 1025kg/m3, ρs=2650kg/m3, ν=1x10-6m2/s.What type of bed forms are present in combined wave and current (flood/ebb) conditions?Wave length: L = mPeak orbital velocity:Peak orbital excursion:Wave-related friction factor:Current-related friction factor:Bed-shear velocity by wave:By flood currentBy ebb current
53Example and Problem (cont.) Mobility parameter:By waveBy flood currentBy ebb currentAnswer: Using Fig.5.5.1, van Rijn’s method, bed forms are 2D waves-ripples superimposed on 3D current ripples in honeycomb pattern. Both types may be superimposed on large-scale sand waves.
54Homework (3)A coastal sea has a water depth of h = 10m, the peak flood-current velocity is umax.flood = 1.0 m/s; the peak ebb-current velocity is umax.ebb = 1.2 m/s. Irregular waves perpendicular to the flood and ebb current directions are present. The significant wave height Hs=1.5m, the peak period Tp = 8s. The bed material characteristics are d50 = 0.3mm, d90 = 0.6mm. Other data are ρ = 1025kg/m3, ρs=2650kg/m3, ν=1x10-6m2/s.What type of bed forms are present in combined wave and current (flood/ebb) conditions?Hint: wave length will be changed to 70.93m at the 10m water depth
56Outline Bed roughness in combined waves and currents Introduction of morphodynamic processes driven by waves and currents in coasts, estuaries, and lakesInitiation of motion for combined waves and currentsBed forms in waves and in combined waves and currentsBed roughness in combined waves and currentsSediment transport in wavesSediment transport in combined waves and currentsTransport of cohesive materials in coasts and estuariesMathematical models of morphodynamic processes driven by waves and currentsIntroduction of a process-integrated modeling system (CCHE2D-Coast) in application to coastal sedimentation problems
57Bed Shear Stress and Bed Friction in Unidirectional Flows h = water depthI = energy slope= depth-averaged velocityC = Chézy coefficient (m^0.5/s)fc = friction factor of Darcy-Weisbachρ = fluid densityHydraulic rough flow regime:ks = effective bed roughness (m)Manning’s n
58Wave-Related Bed Shear Stress and Bed Friction Time-averaged over half a wave cycle bed shear stress isfw = wave-related friction coefficientUδ = peak orbital velocity near the bedRough Turbulent Flow RegimeWith fw, max = 0.03 for Aδ/ks ≤ 1.57An estimate of roughnessks = 3 d90Aδ = peak value of orbital excursion near bed
59Effective Bed Roughness Nikuradse (1932) introduced the concept of an equivalent or effective sand roughness height (ks) to simulate the roughness of arbitrary roughness elements of the bottom boundary. In case of a movable bed consisting of sediments, the effective bed roughness (ks) mainly consists of grain roughness generated by skin friction forces and of form roughness generated by pressure forces acting on the bed forms
60Fluid Pressure and Shear-stress Distribution along a Dune
61Available Methods for Determining ks Basically, two approaches can be found in the literature to estimate the bed roughness.Methods based on bed-form and grain-related parameters such as bed-form length, height, steepness and bed-material sizeMethods based on integral parameters such as mean depth, mean-velocity and bed-material size.The first method is more universal and can also be used to determine the roughness of a movable bed in non-steady conditions, provided that the bed-form characteristics are known.Based on the bed-form parameters, the bed-shear stress (τb )in an alluvial channel can be divided into:Grain-related bed-shear stress (τ’b )Form-related bed shear stress (τ”b )
62Grain RoughnessGrain roughness is the roughness of individual moving or non-moving sediment particles as present in the top layer of a natural plane movable or non-movable bed.Van Rijn (1982) analyzed about 120 sets of flume and field data with and without a mobile bed to determine the grain roughness. The grain roughness k’s was calucated by using the Chézy coefficient, which is derived from the measured water depth (h), depth-averaged velocity (u), and energy slope (I), i.e.Hydraulic rough flow regimeVan Rijn’s results: Grain roughness in the lower regime is mainly related to the largest particles of the top layer of the bedk’s,c = 2 ~ 3 d90 for non-movable plane bedk’s,c = 3 ~ 5 d90 for movable plane bedBased on the data in the upper regime (mobility parameter θ > 1, van Rijn proposes to use
64Bed-form Roughness Ripple-related roughness γs = ripple presence factor(=1.0 for ripples alone, = 0.7 for ripples superimposed on dunes or sand waveDune-related roughnessSymmetrical Sand Wave:The leeside slopes of symmetrical sand waves are relatively mild. Hence, flow separation will not occur. Therefore, the form roughness of symmetrical sand waves is assumed to be zero.
65Example and ProblemsA wide channel with a depth h = 8m has a bed covered with dunes. Ripples are superimposed on the dunes. The dune dimensions are Δd = 1.0m, λd = 50.0m. The ripple dimensions are Δr = 0.2m, λr = 3.0m. The bed material characteristics are d50 = 0.3mm, d90 = 0.5mm.What is the effective bed roughness, the Chézy-coefficient, and the Manning’s n?Solution:Grain roughness (lower regime) :=0.0015mRipple form roughness (γs = 0.7):=0.187mDune form roughness=0.303mEffective bed roughness:=0.492mChézy-coefficient:=41.3 m1/2/sManning’s n:=
66Wave-related Bed Roughness The effective wave-related bed roughness also consists of two components:In which k’s,w = wave-related grain roughness height (m)k”s,w = wave-related bed-form roughness height (m)The wave-related friction factor (fw) for rough oscillatory flow isTime-averaged over half a wave cycle bed shear stress is
67Wave-related Grain Roughness A number of empirical formulations based on experimental and field data on non-movable and movable bed. Van Rijn’s approach is introduced as follows:According to van Rijn, the effective grain roughness of a sheet flow bed is of the order of the sheet flow layer thickness or the boundary layer thickness (k’s,w ≈δw). The sheet flow layer is a high-concentration layer of bed material particles. Van Rijn (1989) proposed the following values to calculate the grain roughness:inwhichfor friction factor in transition regimeνm = kinematic viscosity of fluid-sediment mixture in near-bed region (νm ≈ 10ν)The grain roughness equations have to be solved iteratively. Typically, this approach yields a value in the range of 3 ~30 d90 for θ = 1 ~ 10.
68Wave-related Form Roughness Ripples are the dominant bed forms generated by oscillatory flows. Ripples may be present on a horizontal bed or superimposed on large sand waves. Large-scale sand waves have no friction effect on the water waves, because the water waves experience the sand waves as a gradual bottom topography. When the nesr-bed orbital excursion is larger than the ripple length, the ripples are the dominant roughness elements for the wave motion in the sea waters.Apparently, bed-form roughness depends on the bed form height and length. There are a number of empirical formulations for estimating the ripple roughness. They can be described asVan Rijn (1989) proposedγs = ripple presence factor(=1.0 for a ripple covered bed, = 0.7 for ripples superimposed on sand wave sRaudkivi (1988)
69Bed Roughness in Combined Currents and Waves The most important bed form regime created by currents and waves:Ripples in case of weak (tidal) currents and low wavesSand waves with ripples in case of (tidal) current and low wavesPlane bed with sheet flow in case of strong (tidal) currents and high waves (surf zone)Sand waves with sheet flow in case of strong (tidal) currents and high waves (outside surf zone)More complicated!No universal solutions
70Grain Roughness (k’s)in Combined Currents and Waves Grain roughness is dominant for both the wave-related and current-related friction when the bed is plane.When bed forms are present and the peak orbital excursion at the bed is smaller than the bed form length (i.e. Aδ < λ), the grain roughness is also dominant for the wave-related friction. In that case the bed forms act as topographic features for the waves.For wave motion:For current motion:Note that the calculation of the mobility parameter θ for current are different from that for wave motion
71Form Roughness (k”s)in Combined Currents and Waves When the bed is covered with ripples, the ripple roughness is dominant for the current-related friction. Ripple roughness is also dominant for the wave-related friction when the peak value of the orbital excursion at the bed is larger than the ripple length (i.e. Aδ < λr). The ripple roughness is calculated byWhen sand waves with or without (mega or mini) ripples are present, the large-scale sand waves act as topographic features for the waves motion because the sand waves have a length much larger than the orbital excursion at the bed. Thus, the wave-related friction factor is not determined by the large-scale sand wave dimensions, but by the small-scale ripples (if present) on the back of the sand waves.
72Dune on Mars ?Three pairs of before and after images from the High Resolution Imaging Science Experiment (HiRISE) camera on NASA's Mars Reconnaissance Orbiter illustrate movement of ripples on dark sand dunes in the Nili Patera region of Mars. Image Credit: NASA/JPL-Caltech/University of Arizona/International Research School of Planetary Sciences