A three-dimensional fluid description of nonlinear lower hybrid waves is investigated in the context of plasma density depletions. The objective is a basic understanding of lower hybrid solitary structures associated with transverse ion acceleration in the topside auroral ionosphere. The equations are linearized about a parabolic density depletion and solved. The solution consists of potential structures (eigenfunctions) which rotate in angle about the center of the density depletion. The eigenfrequencies are discrete for |&ohgr;|&ohgr;LH and kz≠0 but become discrete for kz=0 in agreement with previous two-dimensional results [Seyler, 1994>. Simulations of the full nonlinear system are performed, and rotating eigenmodes are extracted from the spectrum. The results agree with the analytic results obtained from the linearized equations. The spectral properties of a lower hybrid solitary structure from the TOPAZ III sounding rocket are reexamined and found to be consistent with theoretical predictions for lower hybrid waves trapped within a density depletion as presented herein. A local wavelet frequency-wavenumber spectrum is constructed from data taken by moving an interferometer through a simulation at a typical rocket velocity. The results compare favorably with the local frequency-wavenumber spectrum of a lower hybrid solitary structure observed by the TOPAZ III sounding rocket. ¿ 1998 American Geophysical Union