.. _doc.sedim.ws: Settling velocities : Modelling strategy --------------------------------------------- * If you are **not using key_sedim** : 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** : a modelling strategy is proposed with a choice of some formulations. Options and parameters are given by user in :ref:`doc_variabledat` for each particulate variable (MUD, PART or NoCP). Settling velocity is defined by 2 notions : :ref:`doc_ws_free` and :ref:`doc_ws_hindered`. * Exemple of evolution and values of settling velocities issued from these different choices are presented below (:ref:`doc_ws_exple`) .. _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** : | | +----------------------------+-------------------------------------------------------+