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## Physics

                  | -> CONstant [cd]                       |
|                                        |
|    CHARNock [beta] [height]            |
|                                        |
|    LINear [a1] [a2] [b] [wlow] [whigh] |
|                                        |   | REL  [alpha]
WIND [vel] [dir] <     WU                                   > <
|                                        |   | RELW [crest]
|    GARRatt                             |
|                                        |
|    SMIthbanke                          |
|                                        |
|    FIT                                 |


With this optional command the user can specify wind speed, direction and wind drag. Wind speed and direction are assumed constant. If this command is not used, SWASH will not account for wind effect.

This command is usually meant for large-scale wind driven circulation, tides and storm surges. Inclusion of wind effects may also be beneficial to buoyancy driven flows in coastal seas, estuaries and lakes. However, this option may also be useful for applications concerning wind effects on wave transformation in coastal waters, ports and harbours.

In SWASH seven different wind drag formulation are available, i.e., constant, linear on wind speed, Charnock, Wu, Garratt, Smith and Banke and the second order polynomial fit. The Charnock drag formulation is based on an implicit relationship between the wind and the roughness, while the other formulations, those of Wu, Garratt and Smith and Banke, express a linear relationship between the drag and the wind speed.

Recent observations indicate that these linear parameterizations overestimate the drag coefficient at high wind speeds (U10 > 20 m/s, say). Based on many authoritative studies it appears that the drag coefficient increases almost linearly with wind speed up to approximately 20 m/s, then levels off and decreases again at about 35 m/s to rather low values at 60 m/s wind speed. We fitted a 2nd order polynomial to the data obtained from these studies, and this fit is given by

Cd = (0.55 + 2.97 -1.49) x 10-3

where = U10/Uref, and the reference wind speed Uref = 31.5 m/s is the speed at which the drag attains its maximum value in this expression. These drag values are lower than in the expression of Wu (1982) by 10% - 30% for high wind speeds (15 U10 30 m/s) and over 30% for hurricane wind speeds (U10 > 30 m/s).

Usually, the wind stress depends on the drag and the wind speed at a height of 10 m, U10. However, it might be obvious that the influence of wind stress will reduce if the water is flowing in the same direction and it will decrease when the water flow and wind are in opposite directions. This may lead to a smaller wind setup on very shallow areas. Hence, the wind stress may be dependent on the wind velocity relative to the water, i.e. U10 - u, instead of the wind velocity as such. Here, u is either the depth-averaged flow velocity in the depth-averaged mode or the surface flow velocity in the multi-layered mode. Experiments have shown that the eigenfrequencies damp out much faster when this alternative is employed.

The considered wind is at 10 m above the surface. However, it might be better to consider the wind at the surface in order to relate this wind to the flow velocity. A factor ( 0 < 1) is introduced that take into account the difference between the wind velocity at 10 m height and the wind velocity at the surface, Us =  U10. With the use of in this formulation the influence of the flow velocity becomes even stronger. However, the exact value of is yet unknown; further research on this parameter is needed. Therefore, this parameter is optionally and should be used with care.

Wave growth due to wind in shallow areas is included in the model. It is based on a parameterization of the momentum flux transferred from wind to surface waves similar to the well-known sheltering mechanism of Jeffreys (1925) as described in Chen et al. (J. Waterwy, Port, Coastal, Ocean Engng., 130, 312-321, 2004). The wind stress is expressed by

=  Cd | U10 - c| (U10 - c)

where is the air density and c is the wave celerity. Hence, the wind velocity is taken relative to the wave celerity. The wind stress may vary over a wave length with a larger wind drag on the wave crest than that in the trough (Chen et al., 2004). This effect is implemented in the model by applying the wind stress on the wave crest only.

The default option is a constant wind drag coefficient, while the wind stress is related to the wind velocity at 10 m height only.

 [vel] wind velocity at 10 m height (in m/s). [dir] wind direction at 10 m height (in degrees; Cartesian or Nautical convention, see command SET). CONSTANT this option indicates that a constant drag coefficient will be adopted. [cd] dimensionless coefficient. Default: [cd] = 0.002 CHARNOCK indicates that the Charnock drag formulation will be adopted. [beta] dimensionless Charnock coefficient. Default: [beta] = 0.032 [height] height (in m) above the free surface where the wind speed has been measured. Default: [height] = 10. LINEAR indicates that the wind drag depends linearly on wind speed. For this, both lower and upper bounds of the wind speed, [wlow], [whigh], and two coefficients, [a1], [b], need to be specified as follows: cd = 0.001 ( [a1] + [b] U10), with cd the drag coefficient and U10 the wind speed in between [wlow] and [whigh]. [a1] coefficient in the above linear function. [a2] not used. [b] coefficient in the above linear function. [wlow] lower bound of wind speed. [whigh] upper bound of wind speed. WU indicates that the drag formulation of Wu will be adopted. GARRATT indicates that the drag formulation of Garratt will be adopted. SMITHBANKE indicates that the drag formulation of Smith and Banke will be adopted. FIT drag coefficient is based on the 2nd order polynomial fit. RELATIVE indicates that the wind stress depends on the wind velocity relative to the water. [alpha] parameter to relate the wind velocity at 10 m height to wind velocity at surface. Note: 0 < [alpha] 1. Default: [alpha] = 1. RELWAVE indicates that the wind stress depends on the wind velocity relative to the wave celerity. This option enables to include wind effects on the nearshore wave transformation. [crest] free parameter representing a ratio of the forced crest height to maximum surface elevation. Use of this parameter implies that the wind stress is only applied on wave crests of which the surface elevation is larger than the given fraction [crest] of the maximum elevation with respect to the datum level. Note: 0 [crest] 1. Default: [crest] = 0.4

The quantities [vel] and [dir] are required if this command is used except when the command READINP WIND is specified.

           |    CONstant [cf]
|
|    CHEZy [cf]
|
| -> MANNing [cf]
FRICtion  <
|    COLEbrook [h]
|
|            | -> SMOOTH
|    LOGlaw <
|    ROUGHness [h]


With this optional command the user can activate bottom friction. If this command is not used, SWASH will not account for bottom friction.

For typically depth-averaged calculations, four different bottom friction values are available, i.e., constant, Chezy, Manning and Colebrook-White values. Note that the Colebrook-White friction value equals the Nikuradse roughness height. Although they are associated with depth-averaged flow velocities, they may be applied in the multi-layered mode as well. However, some inaccuracies may occur in the vertical structure of the velocity, in particular when the depth-averaged velocity is zero. Alternatively, the logarithmic wall law may be applied. In this case, a distinction is made between smooth and rough beds. For rough beds, the user must apply a Nikuradse roughness height.

The aforementioned friction formulations are usually derived for quasi-steady flow condition (e.g. flow in a river). However, numerical experiments have indicated that the Manning formula provides a good representation of wave dynamics in the surf zone, and even better to that returned by other friction formulations.

The default option is: MANNING with a constant friction coefficient.

                            | -> CONstant [visc]
|
| -> Horizontal <     SMAGorinsky [cs]
|                |
|                |    MIXing [lm]
VISCosity <
|
|    Vertical  KEPS [cfk] [cfe]


With this optional command the user can activate turbulent mixing. If this command is not used, SWASH will not account for turbulent mixing.

In SWASH both the horizontal and vertical eddy viscosities can be specified.

Three different horizontal eddy viscosity models are available, i.e., a constant viscosity, the Smagorinsky model and the Prandtl mixing length hypothesis. Vertical mixing can be modelled by using the standard k - model, with k the turbulent kinetic energy per unit mass and the dissipation rate of turbulent kinetic energy per unit mass (Launder and Spalding, 1974).

Within the vegetation canopy, it is assumed that all energy of the mean flow is converted to turbulent energy due to the plant drag. This process is modelled by means of the vegetation-induced turbulence production terms in the k - model. They are accompanied with two empirical constants [cfk] and [cfe] associated with k and , respectively. We have selected the values as suggested by Shimizu and Tsujimoto (1994), i.e. [cfk] = 0.07 and [cfe] = 0.16 (see also Defina and Bixio, 2005).

The default option is a constant horizontal eddy viscosity.

 HORIZONTAL indicates that the horizontal mixing will be activated. CONSTANT this option indicates that a constant horizontal eddy viscosity will be adopted. [visc] constant viscosity value (in m2/s). SMAGORIN indicates that the Smagorinsky model will be employed. [cs] Smagorinsky constant. Default: [cs] = 0.2 MIXING indicates that the Prandtl mixing length hypothesis will be used. [lm] mixing length (in meters). VERTICAL indicates that the vertical mixing will be activated. KEPS indicates that the standard k - model will be used. [cfk] vegetative drag-related constant for turbulent kinetic energy. Default: [cfk] = 0.07 Note that this constant is only relevant when vegetation is included (see command VEGE). [cfe] vegetative drag-related constant for dissipation rate. Default: [cfe] = 0.16 Note that this constant is only relevant when vegetation is included (see command VEGE).

POROsity [size] [height] [alpha0] [beta0] [wper]


This command indicates the use of porosity layers inside the computational domain to simulate full/partial reflection and transmission through porous structures such as breakwaters, quays and jetties. Also the interaction between waves and porous coastal structures can be simulated in this way. The mean flow through porous medium is described by the volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations. The laminar and turbulent frictional forces in porous medium is modelled by means of the empirical formula's of Van Gent (1995). In the case of an oscillatory wave motion the turbulent loss will enhance, which depends on the Keulegan-Carpenter number.

See commands INPGRID POROSITY and READINP POROSITY in order to define porosity layers. If neither of this command nor the command READINP POROSITY is used, SWASH will not account for wave interactions with porous structures.

 [size] characteristic grain size of porous structure(s) (in m). Note that [size] is allowed to vary over the computational region; in that case use the commands INPGRID PSIZE and READINP PSIZE to define and read the grain sizes of different porous structures. The value of [size] in this command is then not required (it will be ignored). [height] structure height (relative to the bottom in meters). Both submerged and emerged porous structures can be defined in this way. An emerged structure is the default. Default: [height] = 99999. Note that [height] is allowed to vary over the computational region; in that case use the commands INPGRID HSTRUC and READINP HSTRUC to define and read the structure heights of different structures. The value of [height] in this command is then not required (it will be ignored). [alpha0] dimensionless constant for laminar friction loss (surface friction). Default: [alpha0] = 200. [beta0] dimensionless constant for turbulent friction loss (form drag). Default: [beta0] = 1.1 [wper] characteristic wave period (either mean of peak period in s). In case of wave interaction with porous structures this parameter is required.

VEGEtation  < [height] [diamtr] [nstems] [drag] >  INERtia [cm]


With this optional command the user can activate wave damping induced by aquatic vegetation. If this command is not used, SWASH will not account for vegetation effects.

The vegetation (rigid plants) can be divided over a number of vertical segments and so, the possibility to vary the vegetation vertically is included. Each vertical segment represents some characteristics of the plants. These variables as indicated below can be repeated as many vertical segments to be chosen.

The vegetation effect is due to the drag force on a fixed body in an oscillatory flow which can be determined using the well-known Morison equation. Apart from the drag force, inertia force can be included optionally, which is specified by means of the virtual mass coefficient. Note that this coefficient is uniform over the plant.

 [height] the plant height per vertical segment (in m). [diamtr] the diameter of each plant stand per vertical segment (in m). [nstems] the number of plant stands per square meter for each segment. Note that [nstems] is allowed to vary over the computational region to account for the zonation of vegetation. In that case use the commands INPGRID NPLANTS and READINP NPLANTS to define and read the vegetation density. The (vertically varying) value of [nstems] in this command will be multiplied with this horizontally varying plant density. Default: [nstems] = 1 [drag] the drag coefficient per vertical segment. INERTIA indicates that the inertia force will be included. [cm] virtual or added mass coefficient (i.e. 1 less than the inertia coefficient).

                          | -> Sec |    | -> NONCohesive [size]            |
TRANSPort [diff] [retur] <     MIn  >  <                                    > &
|    HR  |    | COHesive [tauce] [taucd] [erate] |
|    DAy |

| -> Yes  |
[fall] [snum] [ak]  DENSity <           >
| No      |

ANTICreep  None | STAndard | SVK


With this optional command the user can specify some relevant parameters in case of transport of constituent. These parameters are only relevant when transport of salinity, temperature, or suspended sediment load is included.

Inclusion of transport of constituent is indicated by the commands INPTRANS SALINITY and READTRANS SALINITY in case of salinity, or the commands INPTRANS TEMPERATURE and READTRANS TEMPERATURE in case of temperature, or the commands INPTRANS SEDIMENT and READTRANS SEDIMENT in case of suspended sediment load. Using these commands, both the initial and stationary boundary conditions for constituent are thus specified. If none of these commands is used, SWASH will not account for transport of any of these constituents.

The first parameter that may be specified in this command is the horizontal eddy diffusivity. A uniform eddy diffusivity value may be chosen that can be used as a calibration parameter to account for all forms of unresolved horizontal mixing. This parameter may be chosen independently from the eddy viscosity (see command VISCOSITY HOR). The eddy diffusivity depends on the flow and the grid size used in the simulation. A typical small-scale model with grid sizes of tens of meters or less, the eddy diffusivity typically ranges from 1 to 10 m2/s. For a large-scale (tidal) areas with grid sizes of at least hundreds of meters, the parameter is typically in the range of 10 to 100 m2/s. Alternatively, when not specified, the eddy diffusivity is related to the eddy viscosity that is determined by either the Smagorinsky model or the Prandtl mixing length model. Otherwise it is zero.

Note that in 3D simulations the vertical eddy diffusivity is automatically included and is related to the vertical mixing (see command VISCOSITY VERT).

The second parameter in this command is the return time for unsteady salt intrusion in a tidal flow. A boundary condition at the seaward side is required. This is usually the ambient or background concentration of salt sea water. However, at the transition between sea and river, alternating conditions hold regarding inflow of salt sea water during flood tide and outflow of fresh river water during ebb tide. Immediately after low water, the salinity of the inflowing water will not be equal to the salinity of the sea water. It will take some time before this happens at the boundary. This time lag is the return time for salinity from its value at the outflow depending on conditions in the interior of model domain relative to its background value specified at the inflow, see Figure 4.2.

This memory effect is characterised by the so-called Thatcher-Harleman condition that specifies an appropriate time lag. The return time depends on the tidal flow conditions outside the estuary.

Either noncohesive suspended sediment (sand) or cohesive suspended sediment (mud or clay) transport can be considered. We assume a single sediment class. Bed load is not taken into account. In case of noncohesive suspended load transport, median sediment diameter can be specified. In this respect, a pickup function is employed to model the upward sediment flux in which the amount of noncohesive sediment (sand) is eroded from the bed surface into the flow. The following pickup function is used (Van Rijn, 1984):

- = 0.00033 ,         >

with c the (volumetric) sediment concentration, the vertical eddy viscosity (see command VISCOSITY VERT), the Schmidt number for sediment, the Shields parameter related to the bed shear stress, = 0.05 the critical Shields parameter, s = 2.65 the sediment specific gravity (see command SET [rhosed]), d50 the median sediment diameter, and the kinematic viscosity of water. Sediment deposition is determined by the downward flux related to the settling velocity ws. If this fall velocity is not specified by the user, then the fall velocity will be calculated by SWASH depending on the particle size (Rubey, 1933):

ws = -

Note that if the sediment diameter is not specified by the user, then no mass exchange between the bed and the flow will be taken into account.

For cohesive sediment the mass exchange of suspended load between the bed and the flow are calculated with the well-known Partheniades-Krone formulations, which include the erosion and deposition fluxes:

- = Se - Sd

The sediment flux for erosion is given by

Se = E - 1 ,        if    >

where E is the entrainment rate for erosion flux, is the critical bed shear stress for erosion and is the actual bed shear stress. The sediment flux for deposition is given by

Sd = cb ws1 -  ,        if    <

where cb is the (volumetric) sediment concentration near the bed and is the critical bed shear stress for sedimentation. Here, the critical bed shear stresses for erosion, , and sedimentation, , the sediment erosion rate E and the fall velocity ws must be specified by the user.

It is assumed that the interaction between sediment and turbulent flow is mainly governed by sediment-induced buoyancy effects. In this respect, the standard k - model and the logarithmic wall law near the bed surface must be applied. This wall law is used to calculate the bed shear stress , which in turn serves as one of the parameters for the mass exchange between the bed and the flow. For sand transport the roughness height may depend on the sediment diameter (if the user wants so) and is determined as 5.5 d50.

Because of the assumption of the upward sediment flux being equal to the pickup rate, the Schmidt number for sediment becomes a free parameter. Experiences have shown that sediment diffusivity is rather sensitive to this parameter. The sediment diffusivity is usually larger than the eddy viscosity, and so < 1.

The turbidity flow is usually considered as a mixture of water and sediment with a mixture density, i.e. the effect of sediment on the density of (salt) water is included. However, in some cases it may be desirable not to include this effect. In this case the density of water remains unchanged, while the sediment transport is only influenced by the flow and (turbulent) dispersion. Also, there is no sedimentation and erosion near the bed. Hence, sediment can be considered here as a passive tracer.

SWASH makes use of the terrain-following coordinates of which the advantages are a better representation of bottom topography and a better resolution in shallow areas. A disadvantage is the transformation of the transport equation due to the geometrical properties of the curved z-planes, so that the curvature terms are involved, which may complicate the computation. However, when these curvature terms are neglected, this may lead to a false generation of vertical mixing. This effect, known as the artificial creeping, becomes evident when the bottom slope is relatively large in regions of strong stable stratification. Hence, in such as case, inclusion of the curvature terms, known as the anti-creepage terms, may reduce significantly the artificial creeping. The standard method is based on the actual transformation. An alternative is the method of Stelling and Van Kester (1994), which computes the horizontal diffusion along strictly horizontal planes.

 [diff] constant horizontal eddy diffusivity (in m2/s). [retur] return time, the unit is indicated in the next option: SEC unit seconds MIN unit minutes HR unit hours DAY unit days NONCOHES indicates that noncohesive suspended load transport (sand) will be activated. This is the default. [size] median sediment diameter (in m). Note that if [size] is not specified, no sedimentation and erosion will be taken place at the bed. COHESIVE indicates that cohesive suspended load transport (mud) will be activated. [tauce] critical bed shear stress for erosion (in N/m2). [taucd] critical bed shear stress for deposition (in N/m2). [erate] entrainment rate for erosion (in kg/m2/s). [fall] fall velocity (in mm/s). In case of cohesive sediment transport this parameter is required. For sand transport, [fall] may not be given by the user, which it will then be calculated based on the sediment diameter. [snum] Schmidt number for sediment. Default: [snum] = 0.7 [ak] empirical constant to reduce the Von Karman constant and thereby the bed shear stress in sediment-laden bottom boundary layer. Adams and Weatherly (1981) suggest [ak] = 5.5. DENSITY this option indicates whether to include the density effect of suspended sediment in the fluid mixture or not. YES indicates that the mixture density will be computed. This is the default. NO indicates that the density of water will not be changed by the presence of sediment in the water column. ANTICREEP this option indicates whether to include the anti-creepage terms or not. NONE indicates that the anti-creepage terms will not be included. This is the default. STANDARD indicates that the anti-creepage terms as derived from the local transformation will be employed. SVK indicates that the Stelling and Van Kester method will be adopted.

BREaking [alpha] [beta]


With this optional command the user can control wave breaking in the case of relatively coarse resolution in the vertical. If this command is not used, SWASH will not account for this control. Note that SWASH will account for energy dissipation due to wave breaking anyhow!

By considering the similarity between breaking waves and bores or moving hydraulic jumps, energy dissipation due to wave breaking is inherently accounted for. However, when a few vertical layers are to be employed, the amount of this energy dissipation may be underestimated due to the inaccuracy with which the phase velocity at the front face of the breaking wave is approximated. To initiate the wave breaking process correctly, steep bore-like wave fronts need to be tracked and this can be controlled by the vertical speed of the free surface. When this exceeds a fraction of the shallow water celerity, as follows,

>

the non-hydrostatic pressure in corresponding grid points is then neglected and remains so at the front face of the breaker. The parameter > 0 represents the maximum local surface steepness and determines the onset of the breaking process. A threshold value of = 0.6 is advised. (This corresponds to a local front slope of 25o.) This single value is not subject to calibration and seems to work well for all the test cases we have considered, both regular and irregular waves.

To represent persistence of wave breaking (even if < ), we also label a grid point for hydrostatic computation if a neighbouring grid point has been labelled for hydrostatic computation and the local steepness is still high enough, i.e.,

>

with < . In all other grid points, the computations are non-hydrostatic.

This approach combined with a proper momentum conservation leads to a correct amount of energy dissipation on the front face of the breaking wave. Moreover, nonlinear wave properties such as asymmetry and skewness are preserved as well.

Note that by taking a sufficient number of vertical layers (10 or so) the phase velocity at the breaking front will be computed accurately enough and hence, this option should not be activated.

 [alpha] threshold parameter at which to initiate wave breaking. Note: [alpha] > 0. Default: [alpha] = 0.6 [beta] threshold parameter at which to stop wave breaking. Note: 0 < [beta] < [alpha]. Default: [beta] = 0.3

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The SWASH team 2017-04-06