.. _doc.MUSTANG.settling: Setlling Process ++++++++++++++++ * Settling process depend on settling velocity, which varies according to the particulate material. * a modelling strategy is proposed with a choice of some formulations for defining the settling velocity W_s for **MUD variables**. (:ref:`doc.sedim.ws`). .. _doc.sedim.flxw2s: Settling fluxes from water to sediment ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * the settling fluxes which carry particles from the bottom layer to sediment are evaluated for each variable, according to their settling velocity and the bottom shear rate ((:ref:`doc.MUSTANG.deposit`) .. _doc.sedim.ws: Settling velocities : Modelling strategy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * If you are **not using key_sedim_MUSTANG** : settling velocity is defined by 2 parameters given by user in :ref:`doc_variabledat` for each particulate variable (PART or NoCP) : * minimum value : *ws_free_min(iv)* * maximum value : *ws_free_max(iv)* * If you are **using key_sedim_MUSTANG** : a modelling strategy is proposed with a choice of some formulations. * Options and parameters are given by user in variable.dat for each particulate variable (MUD, PART or NoCP).(:ref:`definition_parasubstancesed`) * SAND variable have settling velocities W_s which depend on particle diameter. * Settling velocity of MUD is defined by 2 notions : :ref:`doc_ws_free` and :ref:`doc_ws_hindered`. * None constitutive SORBED variables have the same settling velocity as the associated constitutives particulate variable. * For the none constitutive variables which are not sorbed on constitutive particulate variable (type NoCP), settling velocity is evaluated in the same manner as MUD variables. * Exemple of evolution and values of settling velocities issued from these different choices are presented below (:ref:`doc_ws_exple`) * in MARS, for variables which have high settling velocity, vertical transport is computed using several sub time step in order to avoid instabilities. .. _definition_parasubstancesed: Definition of parameters for particulate-sediment substances in **variable.dat** ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * particulate variables are defined in :ref:`doc_variabledat` as : * GRAV or SAND or MUDS or PART : constitutive variables (kg/m3) * SORB or NoCP : non constitutive variables (X/m3) * For GRAV and SAND variables, only diameter of particles, critical stress of deposition and density of particle are given in *variable.dat* * For MUDS, PART and NoCP : settling velocity varies with time and space (:ref:`doc.sedim.ws`) and 4 lines with 11 parameters are given in *variable.dat* * 1 option for free velocity followed by 6 parameters : minimum and maximum setling velocity (m/s) and : * If ws_free_opt=0 (Ws constant) ==>> (1)=unused (2)= unused (3)=unused (4)=unused * If ws_free_opt=1 (Van Leussen) ==>> (1)=c_factor (2)=c_exponent (3)=VL_a (4)=VL_b * If ws_free_opt=2 (Winterwerp) ==>> (1)= Primary Particle Diameter (2)=aggregation factor (3)=breakup factor (4)=fractal dimension * If ws_free_opt=3 (Wolanski) ==>> (1)= c_factor (2)=c_exponent (3)=unused (4)=unused * 1 option for hindered velocity followed by 2 parameters : * If ws_hind_opt=0 (no hindered settling) ==> (1)=unused (2)=unused * If ws_hind_opt=1 (Scott) ==> (1)=phi_factor (2)=phi_exponent * If ws_hind_opt=2 and ws_free_opt=2 (Winterwerp) ==> (1)=gel concentration (kg/m3) (2)=phi_exponent * If ws_hind_opt=3 (Wolanski) ==> (1)=c_constant (2)=c_exponent * diameter of particles, critical stress of deposition and density of particle are given after * For SORB variables, user must given the name of the associated constitutive particulate variable. * **Inital concentration** in sediment is expressed as : * gravel, sand, mud and PART : fraction of total initial sediment concentration (total=1) * SORB (or NCSP) : unit/m3 of sediment * DISS : unit of m3 of interstitial water * For SAND variable only; 2 boolean are given in *variable.dat* : * *l_sand2D* which is TRUE if this sand variable is treated as 2D variable (used only if key_sand2D) * *l_outsandrouse* which is TRUE if you want to use a ROUSE profil reconstituted for output in water column (used only if ikey_sand2D and l_sand2D is TRUE for this variable) .. _doc_ws_free: Free settling velocity ~~~~~~~~~~~~~~~~~~~~~~ 4 options defined by a parameter (*ws_free_opt*) given by user in :ref:`doc_variabledat` for each particulate variable (MUD, PART or NoCP). Some parameters values are proposed below. * **Option free 0** : Constant settling velocity defined by minimum value (*ws_free_min(iv)*) and maximum value (*ws_free_max(iv)*) - aditional parameters are not used (ws_free_para(1:4) * **Option free 1** : Formulation of Van Leussen, 1994 | :math:`Ws=kC^m \frac{1+aG}{1+bG^2}` * :math:`k=0.0005` =*ws_free_para(1)* * :math:`m=1.2` =*ws_free_para(2)* * :math:`a=0.3` =*ws_free_para(3)* * :math:`b=0.09` =*ws_free_para(4)* * **Option free 2** : Formulation of Winterwerp, 1999 | :math:`D_e=D_p+ \frac{k_aC}{k_b \sqrt{G}}` | :math:`Ws=\frac{1}{18} \frac{(\rho_s-\rho)g}{\mu} D_p^{3-n_f} D_e^{n_f-1}` * :math:`D_p=4.10^{-6}` =*ws_free_para(13)* * :math:`k_a=14.6` =*ws_free_para(2)* * :math:`k_b=30000` =*ws_free_para(3)* * :math:`n_f=2` =*ws_free_para(4)* * **Option free 3** : Wolanski et al., 1989 : include Hindered settling (ws_hind_opt must be = 3 also; otherwise error and stop) | :math:`Ws=k C^m` * :math:`k=0.01` =*ws_free_para(1)* * :math:`m=2.1` =*ws_free_para(2)* * *ws_free_para(3)* and *ws_free_para(4)* not used .. _doc_ws_hindered: Hindered settling velocity ~~~~~~~~~~~~~~~~~~~~~~~~~~ 4 options defined by a parameter (*ws_hind_opt*) given by user in :ref:`doc_variabledat` for each particulate variable (MUD, PART or NoCP) * **Option hindered 0** : no hindered settling velocity * **Option hindered 1** : Formulation of Scott, 1984 | :math:`\Phi=\frac{SPM_{tot}}{cgel}` | :math:`Ws=Ws(1-\Phi)^m` * :math:`cgel=40` =*ws_hind_para(1)* * :math:`m=4.5` =*ws_hind_para(2)* * **Option hindered 2** : Winterwerp 2002 | :math:`Ws=Ws(1-\Phi_v)^m \frac{(1-\Phi)}{1+2.5\Phi_v}` | if Option *free* = 2 :math:`\Longrightarrow \Phi_v=\Phi (\frac{D_e}{D_p})^{3-n_f}` * :math:`m=1` =*ws_hind_para(2)* | if Option *free* :math:`\neq 2 \Longrightarrow \Phi_v=\frac{SPM_{tot}}{cgel}` * :math:`cgel=40` =*ws_hind_para(1)* * :math:`m=1` =*ws_hind_para(2)* * **Option hindered 3** : Wolanski et al., 1989 | :math:`Ws=frac{Ws}{(C^2+b_w^2)^{m_w}}` | if Option *free* = 3 * :math:`b_w=2` =*ws_hind_para(1)* * :math:`m_w=1.46` =*ws_hind_para(2)* | if Option *free* :math:`\neq 3` : error and stop .. _doc_ws_exple: Exemples of evolution of settling velocity according to different options ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +----------------------------+-------------------------------------------------------+ | **Option free 1** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f1h0.jpg | | and | | | **Option hindered 0** : | | +----------------------------+-------------------------------------------------------+ | **Option free 1** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f1h1.jpg | | and | | | **Option hindered 1** : | | +----------------------------+-------------------------------------------------------+ | **Option free 1** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f1h2.jpg | | and | | | **Option hindered 2** : | | +----------------------------+-------------------------------------------------------+ | **Option free 2** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f2h1.jpg | | and | | | **Option hindered 1** : | | +----------------------------+-------------------------------------------------------+ | **Option free 2** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f2h2.jpg | | and | | | **Option hindered 2** : | | +----------------------------+-------------------------------------------------------+ | **Option free 3** | .. image:: FIG/SEDIM/Ws_tracer_romaric_f3h3.jpg | | and | | | **Option hindered 3** : | | +----------------------------+-------------------------------------------------------+