Table A.1: Values of the outgoing wave amplitude (km s^-1) imposed at the top of the atmosphere which, once integrated backward, give rms velocity field fluctuations values at the base between $20{\rm ~km~s^{-1}}$ and $30{\rm ~km~s^{-1}}$ . L(r) signifies that an expanding turbulent lengthscale has been used. Except where indicated a flat spectrum is imposed at the top boundary.
Frequencies or $\vert{\bf z^+_c}\vert$ ( ${\rm km~s^{-1}}$ ) giving $u_0=[20{-}30]~{\rm km~s^{-1}}$ for

couplings $\alpha =4$ $\alpha =6$ $\alpha=8$ $\alpha =10$

$10^{-6}~{\rm Hz}$ 54 - 80 85 - 126 131 - 191 187 - 272

$10^{-4}~{\rm Hz}$ 54 - 80 86 - 126 131 - 191 187 - 272

$10^{-3}~{\rm Hz}$ 58 - 83 89 - 129 135 - 195 192 - 278

$10^{-2}~{\rm Hz}$ 76 - 110 126 - 178 215 - 293 353 - 464

$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ ; $\rightarrow~\rm I$ 43- 63 70- 102 114- 163 177- 248

$10^{-6}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ ; $\rightarrow~\rm II$ 43- 64 70- 104 118- 173 192- 280

$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ ; $\rightarrow~\rm III$ 37- 55 61- 90 104- 150 171- 242

$10^{-6}~{\rm Hz}$ - $10^{-4}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ ; $\rightarrow~\rm IV$ 34 - 50 54 - 79 86 - 125 131 - 186

$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ , L(r); $\rightarrow~\rm V$ 38 - 56 63 - 92 110 - 160 191 - 276

$10^{-6}~{\rm Hz}$ - $10^{-4}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ , L(r); $\rightarrow~\rm VI$ 35 - 51 56 - 82 92 - 133 146 - 208

I and II, Power-law 54 - 80 85 - 126 130 - 191 187 - 272

III and IV, Power-law 54- 80 85- 126 131- 191 187 - 271

V and VI, Power-law 56 - 82 89 - 129 139 - 200 204 - 289

**Table A.1:** Values of the outgoing wave amplitude (km s^-1) imposed at the top of the atmosphere which, once integrated backward, give rms velocity field fluctuations values at the base between $20{\rm ~km~s^{-1}}$ and $30{\rm ~km~s^{-1}}$ . L(r) signifies that an expanding turbulent lengthscale has been used. Except where indicated a flat spectrum is imposed at the top boundary.
Frequencies or	$\vert{\bf z^+_c}\vert$ ( ${\rm km~s^{-1}}$ ) giving $u_0=[20{-}30]~{\rm km~s^{-1}}$ for
couplings	$\alpha =4$	$\alpha =6$	$\alpha=8$	$\alpha =10$
$10^{-6}~{\rm Hz}$	54 - 80	85 - 126	131 - 191	187 - 272
$10^{-4}~{\rm Hz}$	54 - 80	86 - 126	131 - 191	187 - 272
$10^{-3}~{\rm Hz}$	58 - 83	89 - 129	135 - 195	192 - 278
$10^{-2}~{\rm Hz}$	76 - 110	126 - 178	215 - 293	353 - 464
$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ ; $\rightarrow~\rm I$	43- 63	70- 102	114- 163	177- 248
$10^{-6}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ ; $\rightarrow~\rm II$	43- 64	70- 104	118- 173	192- 280
$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ ; $\rightarrow~\rm III$	37- 55	61- 90	104- 150	171- 242
$10^{-6}~{\rm Hz}$ - $10^{-4}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ ; $\rightarrow~\rm IV$	34 - 50	54 - 79	86 - 125	131 - 186
$10^{-6}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ - $10^{-1}~{\rm Hz}$ , L(r); $\rightarrow~\rm V$	38 - 56	63 - 92	110 - 160	191 - 276
$10^{-6}~{\rm Hz}$ - $10^{-4}~{\rm Hz}$ - $10^{-2}~{\rm Hz}$ , L(r); $\rightarrow~\rm VI$	35 - 51	56 - 82	92 - 133	146 - 208
I and II, Power-law	54 - 80	85 - 126	130 - 191	187 - 272
III and IV, Power-law	54- 80	85- 126	131- 191	187 - 271
V and VI, Power-law	56 - 82	89 - 129	139 - 200	204 - 289

Source LaTeX | All tables | In the text

	1 Introduction
	2 The model
	3 Results
	4 Conclusions
	References
	Online Material
	Appendix A: Realistic wave amplitudes