## 1. Introduction

[2] The contribution of breaking internal waves to deep-ocean mixing is largely dependent on the existence of short vertical length scales (high vertical modes) of the motions that induce shear instabilities. Whilst kinetic energy is dominated at semidiurnal (‘D_{2}’) tidal frequencies (most at harmonic frequencies M_{2}, S_{2}, N_{2}), debate is ongoing how motions at these frequencies transfer their energy to small scales such that large vertical current shear is established that induces the breaking of internal waves near the buoyancy frequency N.

[3] Observations [*Leaman and Sanford*, 1975] show that vertical scales at the inertial frequency f = 2Ωsinϕ, the vertical component of **Ω**, the Earth rotational vector, at latitude ϕ, are quite short O(100 m) in the open ocean. A resonant wave-wave interaction model has been proposed [*McComas and Bretherton*, 1977] for the generation of small vertical scales following ‘parametric sub-harmonic instability’ (PSI), a term used for a process in which energy is transferred from energetic large-scale waves to small-scale waves at half the original frequency, until the energy level of the latter is of the same order as that of the former. Although historic estimates of the transfer rate yielded O(100 days) for weak interactions, renewed interest for the importance of strong non-linear transfer was recently aroused following numerical estimates O(10 days) for the transfer rate from a random internal wave field [*Hibiya et al.*, 2002] and ∼5 days for a mode-1 internal tidal wave [*MacKinnon and Winters*, 2005]. The recent models focus on transfer of energetic D_{2}-motions to smaller f-scales, so that e.g. at ∣ϕ∣ ≈ 29° 2f ≈ 1.4·10^{−4}s^{−1} ≈ M_{2}.

[4] As traditionally free internal gravity waves exist at frequencies (σ) in a band between f < σ < N, dominant D_{2}-waves are thought to transfer energy via PSI to free propagating waves only when their diurnal half-frequencies D_{1} fall within the internal wave band; that is at ∣ϕ∣ < 29.91° for S_{2} → S_{1} generation, ∣ϕ∣ < 28.80° for M_{2} → M_{1} and ∣ϕ∣ < 28.21° for N_{2} → N_{1}. As a result, one expects to observe due to PSI across the above ‘critical’ latitudes ϕ_{c} i) a transition in tidal energy with attenuation of D_{2}-energy on the equator-side of ϕ_{c}, ii) a transition in f/D_{1}-shear and associated mixing, with enhanced mixing on the equator-side of ϕ_{c}, iii) largest f-energy and shear around ϕ_{c}.

[5] So far, most of the evidence of PSI comes from numerical modeling, which shows local enhancement of near-inertial energy around ∣ϕ∣ ≈ 29° [*Hibiya et al.*, 2002] and a dramatic decrease in amplitude but only between 27.5° < ∣ϕ∣ < 29.5° [*MacKinnon and Winters*, 2005]. Multi-mode (beam) D_{2}-waves seem to transfer to subharmonic waves as well as to higher harmonics [*Lamb*, 2004].

[6] Open ocean observations of PSI are mainly limited to tethered falling XCP and XBT observations from 0∼1500 m above topographic ridges, notably in the Pacific, from which enhanced mixing by a factor of 2–3 is estimated between 22° < ∣ϕ∣ < 32° compared to poleward observations [*Hibiya and Nagasawa*, 2004]. Short (4.5 days) shipborne ADCP data from 0–800 m above Hawaiian Ridge suggest a very local non-linear coupling between D_{2} and D_{1} at ∼520–580 m [*Carter and Gregg*, 2005], but no conclusions could be drawn on specific individual frequencies within D_{1}, due to the shortness of record.

[7] In this paper, more than half-year long deep-ocean moored current meter records are used to further investigate possible importance of PSI for open-ocean internal wave induced mixing. The focus is on the latitudinal variation of: i) f-energy; ii) D_{2}-energy, and iii) the energy at non-tidal diurnal harmonic frequencies like M_{1} and N_{1} (S_{1} was not distinguishable from astronomically forced K_{1}). Moorings above large topography are avoided when possible because of difficulty of tracking with a few current meters tidal beams that may vary in space and time [*van Haren*, 2004a].

[8] This implies certain assumptions about generation and propagation of near-inertial internal waves in the open-ocean. ‘Global’ models of f-enhancement all account for the beta effect. Ambiguous is the direction of meridional propagation, as some models describe a broadband generation of internal waves that focus their energy at their critical latitude following poleward propagation [*Munk*, 1980; *Fu*, 1981]. [*Garrett*, 2001] discusses near-surface generation and subsequent equatorward propagation, yielding a blue-shift of the spectral f-peak. Local modifications in peak frequency and peak height may occur, with trapping of f-energy in regions of sub-f negative vorticity [*Mooers*, 1975; *Xing and Davies*, 2002].

[9] The critical latitude may be just poleward of the latitude of f when inertio-gravity waves on a spherical shell are considered so that a red-shift of the f-peak can be observed [*Maas*, 2001]. *Gerkema and Shrira* [2005] discuss trapping of poleward propagating sub-f energy beyond the f-latitude in layers of small N (>∼f). This poleward trapping is predicted including the horizontal component of the Earth's rotational vector 2Ωcosϕ that yields inertio-gravity wave band limits σ_{min} < σ < σ_{max}, with σ_{min} < f and N < σ_{max}. These limits substantially extend the traditional internal gravity wave limits when N is small: e.g. around ∣ϕ∣ = 30°, N = 2.5f yields 20% smaller, larger limits than f, N, respectively.