One-dimensional bispectra are computed from the statistical theory of turbulence (using the Test Field Model) and are compared with experiments. For an inertial range, we obtain B(k1, p1) = εk−3F(θ), where B is the two-dimensional Fourier transform of $\langle u({\bf x})u({\bf x}+\hat{\imath}\xi_1)u({\bf x}+\hat{\imath}\xi_2)\rangle $ with respect to (ξ1, ξ2), ε is the energy dissipation and F(θ) (θ = tan−1(k1/p1) is an angular distribution of order unity, which is compared to measurements of planetary boundary-layer turbulence. We also compare theory to wind tunnel data, as reported by Helland et al. (1978). Finally, we discuss to what extent the bispectra give insight into the dynamics of the flow.

This note summarizes a detailed numerical computation of bispectra arising from weak nonlinear resonant interactions of internal waves whose energies are represented by the Garrett & Munk (1975) model spectrum. Two spectra are computed – the bispectrum of power and the auto-bispectrum of vertical displacement. These are chosen because the first is the most informative and the second is easy to observe. The numerical computations indicate that the level of the bispectral signal is much too low to be detected by any reasonable observational programme. Even more disturbing, bispectra of Eulerian variables are subject to a kinematic contamination causing a significant bispectral level which can easily be misinterpreted as a nonlinear interaction.

The energy transfer in a finite-depth gravity-wave spectrum is investigated in the approximation of a narrow spectrum. It is shown that for ocean depths larger than approximately one tenth of the wavelength (kh [ges ] 0·7) the finite-depth case can be reduced to Longuet-Higgins’ (1976) result for an infinitely deep ocean by a similarity transformation involving changes in scale of the angular spreading function and the transfer rate. For shallower water (kh < 0·7) Longuet-Higgins’ expansion technique is no longer applicable without modification, as the nonlinear coupling coefficient develops a discontinuity at the origin of the expansion. In the range kh [ges ] 0·7 both the magnitude and the two-dimensional frequency-directional distribution of the energy transfer are found not to differ significantly (to within variations by a factor of 2) from the case of an infinitely deep ocean. The transformation rules relating the infinite-depth and finite-depth cases may provide a useful guide for constructing parametrizations of the nonlinear transfer for finite-depth wave prediction models.