P r o g r e s s i n
E a r t h S c i e n c e ? New Ideas / Hypotheses New Observations New Simulations E 5 r 0 jUj p ðN/jUj jfj/jUj P 1D (k) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi N2 2 jUj2k2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jUj2k2 2 f2 q dk, (3) where k 5 (k, l) is now the wavenumber in the reference frame along and across the mean flow U and P 1D (k) 5 1 2p ð1‘ 2‘ jkj jkj P 2D (k, l) dl (4) is the effective one-dimensional (1D) topographic spectrum. Hence, the wave radiation from 2D topogra- phy reduces to an equivalent problem of wave radiation from 1D topography with the effective spectrum given by P1D (k). The effective 1D spectrum captures the effects of 2D c. Bottom topography Simulations are configured with multiscale topogra- phy characterized by small-scale abyssal hills a few ki- lometers wide based on multibeam observations from Drake Passage. The topographic spectrum associated with abyssal hills is well described by an anisotropic parametric representation proposed by Goff and Jordan (1988): P 2D (k, l) 5 2pH2(m 2 2) k 0 l 0 1 1 k2 k2 0 1 l2 l2 0 !2m/2 , (5) where k0 and l0 set the wavenumbers of the large hills, m is the high-wavenumber spectral slope, related to the pa- FIG. 3. Averaged profiles of (left) stratification (s21) and (right) flow speed (m s21) in the bottom 2 km from observations (gray), initial condition in the simulations (black), and final state in 2D (blue) and 3D (red) simulations.