We study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles π:M→B\documentclass[12pt]{minimal}
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\begin{document}$$\pi {:}\, M\rightarrow B$$\end{document} in the adiabatic limit. This limit consists in considering a family Gε\documentclass[12pt]{minimal}
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\begin{document}$$G_\varepsilon $$\end{document} of Riemannian metrics that are close to Riemannian submersions, for which the ratio of the diameter of the fibres to that of the base is given by ε≪1\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon \ll 1$$\end{document}. We assume M\documentclass[12pt]{minimal}
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\begin{document}$$M$$\end{document} to be compact and allow for fibres F\documentclass[12pt]{minimal}
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\begin{document}$$F$$\end{document} with boundary, under the condition that the ground state eigenvalue of the Dirichlet Laplacian on Fx\documentclass[12pt]{minimal}
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\begin{document}$$F_x$$\end{document} is independent of the base point. We prove for dim(B)≤3\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm {dim}(B) \le 3$$\end{document} that the nodal set of the Dirichlet eigenfunction φ\documentclass[12pt]{minimal}
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\begin{document}$$\varphi $$\end{document} converges to the pre-image under π\documentclass[12pt]{minimal}
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\begin{document}$$\pi $$\end{document} of the nodal set of a function ψ\documentclass[12pt]{minimal}
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\begin{document}$$\psi $$\end{document} on B\documentclass[12pt]{minimal}
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\begin{document}$$B$$\end{document} that is determined as the solution to an effective equation. In particular, this implies that the nodal set meets the boundary for ε\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon $$\end{document} small enough and shows that many known results on this question obtained for some types of domains, also hold on a large class of manifolds with boundary. For the special case of a closed manifold M\documentclass[12pt]{minimal}
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\begin{document}$$M$$\end{document} fibred over the circle B=S1\documentclass[12pt]{minimal}
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\begin{document}$$B=S^1$$\end{document}, we obtain finer estimates and prove that every connected component of the nodal set of φ\documentclass[12pt]{minimal}
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\begin{document}$$\varphi $$\end{document} is smoothly isotopic to the typical fibre of π:M→S1\documentclass[12pt]{minimal}
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\begin{document}$$\pi {:}\, M\rightarrow S^1$$\end{document}.
