tokens: aspects of the influence of rotation on the convective flows. Therefore, the impact of the Coriolis force on the stochastic excitation of GIWs can be evaluated. In this context, recent work has established an estimate of the GIW energy flux (André et al. 2017 ). It can be used to estimate the rotational scaling of the amplitude of the wave energy flux arising from the modified properties of the convective driving. From Equation (61) of André et al. ( 2017 ), the vertical GIW energy flux can be computed from the horizontal average of the product of the vertical velocity and pressure perturbation that, given the linearization of the Boussinesq equations for monochromatic waves propagating in a selected horizontal direction, can be evaluated to bewhere v w is the magnitude of the vertical velocity of the wave. Moreover, the solution for the vertical velocity implies that the dispersion relationship iswhere f and f ss are defined above in Equation ( 20 ). Note that a reference table is given to help identify the many parameters in this section (Table 2 ). Table 2 Frequently Used Symbols in the Models of Interfacially Excited and Reynolds-stress-induced Wave Excitation Note. The abbreviations used in the table are V for vertical, H for horizontal, and PH for projected horizontal. Following P81 , further assumptions are necessary to complete the estimate of the wave energy flux. The convection is turbulent. So the fluctuating part of the velocity field is of the same order of magnitude as the convective eddy turnover velocity , which implies that convective pressure perturbations are approximately . Assuming that the pressure is continuous across the interface between the convectively stable and unstable regions, the horizontally averaged pressure perturbations of the propagating waves excited at the interface must then be equal to the turbulent pressure on the convective side of the interface. Those pressure perturbations follow from the solution for the vertical velocity and the nondiffusive Boussinesq equations (André et al. 2017 ). For plane wave solutions, the magnitude of those perturbations can then be written asNote however, the pressure matching condition fails for these modes at the pole for sub-inertial waves (). The reason is that the propagation domain of sub-inertial GIWs excludes the pole and it becomes increasingly concentrated toward the equator for faster rotation rates (e.g., Dintrans Rieutord 2000 ; Prat et al. 2016 ). Using the dispersion relationship, and equating the two pressures, yields the following equation for the vertical wave velocity:Therefore, the wave energy flux density becomes Flows in a gravitationally stratified convective medium tend to have an extent in the direction of gravity that is much larger than their extent in the transverse directions. Therefore, the horizontal wavenumber of the convective flows is much greater than the vertical wavenumber. This implies that . For efficient wave excitation, the
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