@@ -374,7 +374,7 @@ The momentum equation of the sea-ice model is
374374 :label: eq_momseaice
375375
376376 m \frac {D\mathbf {u}}{Dt} = -mf\mathbf {k}\times \mathbf {u} +
377- \mathbf {\tau }_{air} + \mathbf \tau }_{ocean}
377+ \mathbf {\tau }_{air} + \mathbf { \tau }_{ocean}
378378 - m \nabla {\phi (0 )} + \mathbf {F},
379379
380380 where :math: `m=m_{i}+m_{s}` is the ice and snow mass per unit area;
@@ -448,9 +448,9 @@ depends on both thickness :math:`h` and compactness (concentration)
448448:math: `c`:
449449
450450.. math ::
451+ :label: eq_icestrength
451452
452453 P_{\max } = P^{*}c\, h\,\exp \{-C^{*}\cdot (1 -c)\},
453- \label {eq:icestrength}
454454
455455 with the constants :math: `P^{*}` (run-time parameter ``SEAICE_strength ``) and
456456:math: `C^{*}=20 `. The nonlinear bulk and shear viscosities :math: `\eta `
@@ -487,8 +487,8 @@ Defining the CPP-flag ``SEAICE_ZETA_SMOOTHREG`` in ``SEAICE_OPTIONS.h`` before c
487487bounding :math: `\zeta ` by a smooth (differentiable) expression:
488488
489489.. math ::
490+ :label: eq_zetaregsmooth
490491
491- \label {eq:zetaregsmooth}
492492 \begin {split}
493493 \zeta &= \zeta _{\max }\tanh \left (\frac {P}{2 \,\min (\Delta ,\Delta _{\min })
494494 \,\zeta _{\max }}\right )\\
@@ -693,17 +693,22 @@ shearing strain rates, :math:`D_T =
693693the equations :eq: `eq_evpequation ` can be written as:
694694
695695.. math ::
696+ :label: eq_evpstresstensor1
696697
697- \begin {aligned}
698- \label {eq:evpstresstensor1 }
699698 \frac {\partial \sigma _{1 }}{\partial {t}} + \frac {\sigma _{1 }}{2 T} +
700- \frac {P}{2 T} &= \frac {P}{2 T\Delta } D_D \\
701- \label {eq:evpstresstensor2 }
699+ \frac {P}{2 T} &= \frac {P}{2 T\Delta } D_D
700+
701+ .. math ::
702+ :label: eq_evpstresstensor2
703+
702704 \frac {\partial \sigma _{2 }}{\partial {t}} + \frac {\sigma _{2 } e^{2 }}{2 T}
703- &= \frac {P}{2 T\Delta } D_T \\
704- \label {eq:evpstresstensor12 }
705+ &= \frac {P}{2 T\Delta } D_T
706+
707+ .. math ::
708+ :label: eq_evpstresstensor12
709+
705710 \frac {\partial \sigma _{12 }}{\partial {t}} + \frac {\sigma _{12 } e^{2 }}{2 T}
706- &= \frac {P}{4 T\Delta } D_S \end {aligned}
711+ &= \frac {P}{4 T\Delta } D_S
707712
708713 Here, the elastic parameter :math: `E` is redefined in terms of a damping
709714timescale :math: `T` for elastic waves
@@ -751,17 +756,19 @@ terminology of , the evolution equations of stress :math:`\sigma_{ij}`
751756and momentum :math: `\mathbf {u}` can be written as:
752757
753758.. math ::
759+ :label: eq_evpstarsigma
754760
755- \begin {aligned}
756- \label {eq:evpstarsigma}
757761 \sigma _{ij}^{p+1 }&=\sigma _{ij}^p+\frac {1 }{\alpha }
758762 \Big (\sigma _{ij}(\mathbf {u}^p)-\sigma _{ij}^p\Big ),
759- \phantom {\int }\\
760- \label {eq:evpstarmom}
763+ \phantom {\int }
764+
765+ .. math ::
766+ :label: eq_evpstarmom
767+
761768 \mathbf {u}^{p+1 }&=\mathbf {u}^p+\frac {1 }{\beta }
762769 \Big (\frac {\Delta t}{m}\nabla \cdot {\bf \sigma }^{p+1 }+
763770 \frac {\Delta t}{m}\mathbf {R}^{p}+\mathbf {u}_n
764- -\mathbf {u}^p\Big ).\end {aligned}
771+ -\mathbf {u}^p\Big ).
765772
766773:math: `\mathbf {R}` contains all terms in the momentum equations except
767774for the rheology terms and the time derivative; :math: `\alpha ` and
@@ -782,8 +789,8 @@ Another variant is the aEVP scheme :cite:`kimmritz16`, where the value
782789of :math: `\alpha ` is set dynamically based on the stability criterion
783790
784791.. math ::
792+ :label: eq_aevpalpha
785793
786- \label {eq:aevpalpha}
787794 \alpha = \beta = \max \left ( \tilde {c}\pi \sqrt {c \frac {\zeta }{A_{c}}
788795 \frac {\Delta {t}}{\max (m,10 ^{-4 }\text {\, kg})}},\alpha _{\min } \right )
789796
@@ -805,8 +812,8 @@ Truncated ellipse method (TEM) for yield curve
805812In the so-called truncated ellipse method the shear viscosity :math: `\eta ` is capped to suppress any tensile stress:
806813
807814.. math ::
815+ :label: eq_etatem
808816
809- \label {eq:etatem}
810817 \eta = \min \left (\frac {\zeta }{e^2 },
811818 \frac {\frac {P}{2 }-\zeta (\dot {\epsilon }_{11 }+\dot {\epsilon }_{22 })}
812819 {\sqrt {\max (\Delta _{\min }^{2 },(\dot {\epsilon }_{11 }-\dot {\epsilon }_{22 })^2
@@ -1085,8 +1092,8 @@ concentration :math:`c` and effective snow thickness
10851092(:math: `c\cdot {h}_{s}`) are advected by ice velocities:
10861093
10871094.. math ::
1095+ :label: eq_advection
10881096
1089- \label {eq:advection}
10901097 \frac {\partial {X}}{\partial {t}} = - \nabla\cdot \left ({{\vec {\mathbf {u}}}}\, X\right ) +
10911098 \Gamma _{X} + D_{X}
10921099
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