We present a short, self-contained technical note on a norm-preserving dissipative flow induced by the Rayleigh quotient of a positive self-adjoint operator. The nonlinear term acts as a global feedback that projects the dissipation onto a fixed-norm sphere, allowing the dynamics to be interpreted as a constrained gradient flow (continuous spectral normalization). In the typical engineering regime (after finite element discretization, finite volume schemes, or modal truncation), we establish global well-posedness, norm preservation, monotonicity of the Rayleigh quotient, and characterization of stationary states as eigenvectors. We further show that the flow selects the smallest eigenvalue compatible with the initial condition, corresponding to dynamic selection of the fundamental mode (low-frequency / low effective energy). As an applied example, we discuss vibration mode filtering in one-dimensional structures, interpreting the flow as a continuous algorithm for modal shape extraction and stabilization in discretized systems.