## 1 Introduction  
It is well known that internal waves (IWs) play an important role in ocean dynamics, in particular in energy fluxes, mixing processes, the exchange of nutrients and gases, etc., and the detection and characterization of IW remains a challenging problem. Remote sensing methods, particularly using satellites, are the most promising techniques for investigations of IWs using IW signatures on the sea surface (see, e.g., [1; 2; 3; 4; 5] and references therein). Orbital surface currents caused by IWs modulate the spectrum of small-scale wind waves, thus resulting in significant variations of microwave radar return. Different mechanisms by which IWs can be observed on the sea surface as bands with reduced and/or increased intensity of small-scale, gravity-capillary waves (GCWs) have been described in the literature. The most often discussed are hydrodynamic modulation (so-called straining or kinematic mechanism) of short wind waves due to non-uniform orbital velocities of the IW (see, e.g., [1; 6; 7; 8; 9; 10]), and a \"film modulation mechanism\" associated with the redistribution of surfactants on the sea surface and with corresponding modulation of the surface wave damping rate (see, e.g., [11; 12; 13; 14]). The straining mechanism is shown to be effective for those GCWs for which group velocities are close to the IW phase velocity--a resonance between IWs and surface waves. For typical oceanic IWs,this mechanism can be realized for the dm-/m-scale wavelength range of the wind wave spectrum [8; 9; 10]. Short cm-mm-scale surface waves are far from the resonance with oceanic IW, and this mechanism is unable to explain observations in this wavelength range, in particular, radar signatures of oceanic IWs in X- and K-band radar images. Instead, cm-mm-scale waves are very sensitive to the presence of surface films, and variations in their spectrum can be rather significant when the surfactant concentration is modulated by non-uniform IW orbital currents. This mechanism was illustrated by some laboratory [11] and field observations [10; 13] indicating the intensification of IW signatures in the presence of surfactant films, but rigorous quantitative explanations have not yet been given to this effect. There has been another modulation mechanism--a \"cascade\" modulation associated with so-called bound waves (see, [15; 16]), in particular with parasitic capillary ripples [10; 17; 18; 19; 20; 21] generated by steep cm-dm-scale GCW when the latter are modulated, even if weakly, by IW. This \"cascade\" mechanism was proposed in [10] to explain the strong modulation of mm-scale parasitic ripples under the action of IW in a wave tank experiment and some of its manifestations in field observations. The capillary ripple modulations can be much stronger than that of the carrying steep short gravity waves because the intensity of the ripples grows very fast with the amplitude of the gravity waves. The experimental studies described in [10] were, however, mostly qualitative; thus, more detailed quantitative experiments and their theoretical analyses were needed. The difficulty of such analysis is some shortcomings of the model of the wind wave spectrum, because the sources, sinks and nonlinear effects affecting the formation of the wind wave spectrum are still poorly known. In [22; 23], some phenomenological terms describing the generation of bound waves were introduced into the kinetic equation for the spectrum of the wind wave action. Bound waves in [22; 23] were described as if they were quasi-linear and weakly interacting waves with their intrinsic dispersion relationship: this is not completely true. This model has difficulty explaining some phenomena observed in the experiments; in particular, an increase in capillary ripple modulation over internal and long surface waves in the presence of surfactant films [24; 25].