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Fix entrainment documentation (#897)
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* update docu entrainment

* update

* add thickness info to write release
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awirb authored Aug 23, 2023
1 parent 9d0ef65 commit 84e420d
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Showing 3 changed files with 16 additions and 7 deletions.
3 changes: 3 additions & 0 deletions avaframe/ana3AIMEC/aimecTools.py
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Expand Up @@ -947,6 +947,9 @@ def computeRunOut(cfgSetup, rasterTransfo, resAnalysisDF, transformedRasters, si
resAnalysisDF.loc[simRowHash, 'lRunout'] = lcoord[index]
resAnalysisDF.loc[simRowHash, 'xRunout'] = gridx[cLower, index]
resAnalysisDF.loc[simRowHash, 'yRunout'] = gridy[cLower, index]
resAnalysisDF.loc[simRowHash, 'deltaSXY'] = scoord[cLower] - scoord[cUpper]
resAnalysisDF.loc[simRowHash, 'zRelease'] = transformedDEMRasters[cUpper, n]
resAnalysisDF.loc[simRowHash, 'zRunout'] = transformedDEMRasters[cLower, n]
resAnalysisDF.loc[simRowHash, 'sMeanRunout'] = scoord[cLowerm]
resAnalysisDF.loc[simRowHash, 'xMeanRunout'] = x[cLowerm]
resAnalysisDF.loc[simRowHash, 'yMeanRunout'] = y[cLowerm]
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3 changes: 2 additions & 1 deletion avaframe/in3Utils/getReleaseArea.py
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Expand Up @@ -172,7 +172,8 @@ def writeReleaseArea(xyPoints, demType, cfgR, outDir):
w.poly([[xy[3], xy[2], xy[1], xy[0]]])
w.field('ID', 'C', '40')
w.field('Name', 'C', '40')
w.record('1', 'Rel_Example')
w.field('thickness', 'N', decimal=4)
w.record('1', 'Rel_Example', relH)
w.close()


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17 changes: 11 additions & 6 deletions docs/theoryCom1DFA.rst
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Expand Up @@ -142,24 +142,24 @@ Entrainment:
"""""""""""""

The snow entrainment is either due to plowing at the front of the avalanche or to erosion
at the bottom. The entrainment rate at the front :math:`q^{\text{plo}}` can be expressed as a function of the
at the bottom. The entrainment rate at the front :math:`\dot{q}^{\text{plo}}` can be expressed as a function of the
properties of the entrained snow (density :math:`\rho_{\text{ent}}` and
snow thickness :math:`h_{\text{ent}}`), the velocity of the avalanche at the
front :math:`\overline{\mathbf{u}}` and length :math:`w_f` of the front (measured perpendicularly
to the flow velocity :math:`\overline{\mathbf{u}}`). It obviously only happens on the front of
the avalanche:

.. math::
\oint\limits_{\partial V(t)} q^{\text{plo}}\,\mathrm{d}A = \int\limits_{l_{\text{front}}}\int_b^s q^{\text{plo}}\,
\oint\limits_{\partial V(t)} \dot{q}^{\text{plo}}\,\mathrm{d}A = \int\limits_{l_{\text{front}}}\int_b^s \dot{q}^{\text{plo}}\,
\mathrm{d}{l}\,\mathrm{d}{z} = \rho_{\text{ent}}\,w_f\,h_{\text{ent}}\,\left\Vert \overline{\mathbf{u}}\right\Vert
:label: ploughing
The entrainment rate at the bottom :math:`q^{\text{ero}}` can be expressed as a function of the
The entrainment rate at the bottom :math:`\dot{q}^{\text{ero}}` can be expressed as a function of the
bottom area :math:`A_b` of the control volume, the velocity of the avalanche :math:`\overline{\mathbf{u}}`,
the bottom shear stress :math:`\tau^{(b)}` and the specific erosion energy :math:`e_b`:

.. math::
\oint\limits_{\partial V(t)} q^{\text{ero}}\,\mathrm{d}A = \int\limits_{A_b} q^{\text{ero}}\,
\oint\limits_{\partial V(t)} \dot{q}^{\text{ero}}\,\mathrm{d}A = \int\limits_{A_b} \dot{q}^{\text{ero}}\,
\mathrm{d}A = A_b\,\frac{\tau^{(b)}}{e_b}\,\left\Vert \overline{\mathbf{u}}\right\Vert
:label: erosion
Expand All @@ -179,8 +179,13 @@ breaking energy per fracture surface unit :math:`e_s`
:math:`e_d` (:math:`J.kg^{-1}`) and the entrained snow thickness
(:cite:`Sa2007,SaFeFr2008,FiFrGaSo2013`):

.. math:: F_i^{\text{ent}} = -w_f\,(e_s+\,q^{\text{ent}}\,e_d)

.. math::
F_i^{\text{ent}} = -w_f\,(e_s+\,q^{\text{ent}}\,e_d),
:label: entrainmentForce
where :math:`q^{\text{ent}}` refers to the entrainable mass per surface area (:math:`kg.m^{-2}`)
defined by :math:`q^{\text{ent}}: =\rho^{\text{ent}} h^{\text{ent}}` which depending on whether entrainment is due to ploughing
or erision, is derived using the integral of :math:`\dot{q}^{\text{plo}}`, or respectively :math:`\dot{q}^{\text{ero}}`, over time.

Resistance:
"""""""""""""
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