Expand spin term definition on Theory page

Show both tensor form and vorticity magnitude equivalence
F_spin = +ρ₀ΣRᵢⱼ² = +ρ₀/2|ω'|², with ω' components explicit.
Clarifies why positive forcing → low p' (dynamic pipe effect).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

python/updraft_forcing/app.py

@@ -582,15 +582,22 @@ def _theory_content():
             html.Div([
                 html.Div("Nonlinear spin", className="theory-term-title"),
                 _eq(
-                    r"\begin{aligned}"
-                    r"F_{\mathrm{spin}} &= +\rho_0 \sum_{i,j} R_{ij}^2 \\"
-                    r"R_{ij} &= \tfrac{1}{2}\!\left(\frac{\partial u_i'}{\partial x_j}"
+                    r"F_{\mathrm{spin}} = +\rho_0 \sum_{i,j} R_{ij}^2"
+                    r" = +\frac{\rho_0}{2}\,|\boldsymbol{\omega}'|^2"
+                ),
+                _eq(
+                    r"R_{ij} = \tfrac{1}{2}\!\left("
+                    r"\frac{\partial u_i'}{\partial x_j}"
                     r"- \frac{\partial u_j'}{\partial x_i}\right)"
-                    r"\end{aligned}"
+                ),
+                _eq(
+                    r"|\boldsymbol{\omega}'|^2 = \zeta_x^2 + \zeta_y^2 + \zeta_z^2"
                 ),
                 _p(
-                    r"Rotation-rate tensor squared. Always produces low $p'$ — "
-                    r"the dynamic pipe effect. Drives upward acceleration inside "
+                    r"Rotation-rate tensor squared, equal to $\tfrac{1}{2}|\boldsymbol{\omega}'|^2$. "
+                    r"Positive definite, so $F_{\mathrm{spin}} > 0$ everywhere. "
+                    r"Positive forcing in $\nabla^2 p' = F$ yields **low** $p'$ "
+                    r"— the dynamic pipe effect. Drives upward acceleration inside "
                     r"a rotating mesocyclone."
                 ),
             ], className="theory-term"),