Space-Time scales of internal waves

Abstract We have contrived a model E(αω) α μ−1ω−p+1(ω 2−ω i 2)−+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω r-1 (ω 2−ω i 2)½, and frequency ω extending from the inertial frequency ω i to the local Vaisala frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α1, α2, ω), with α1, α2 designating components of α. Certain moments of E(α1, α2, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F (u,η,…)(ω) = ∫∫ (U 2, Z 2,…)E(α1, ∞2, ω) dα1 dα2, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F (…)(α1) = ∫∫… dα2 dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is ...