At any frequency between the Brunt-Vaisala frequency, and 

 the low-frequency cut-off at the inertial period, there are an 

 infinite number of gravity modes, each having a different vertical 

 structure and a different horizontal wavelength. It can be shown 

 that the horizontal wave number k, in the case of no rotation, is 

 very nearly 



V 



.2 -2 j_ (1) 



N ' rf 



where N is the Brunt-Vaisala frequency, d is the depth, crthe 

 wave frequency, and n the vertical mode number. The horizontal 

 wavelength goes to zero ascr ->-N, and grows rapidly away from 

 this limit. 



With a limited aperture array, we are thus restricted to high 

 frequencies, or high vertical mode numbers if the array is to 

 have an antenna property. Very high wave numbers, above the 

 Nyquist wave number, will be aliased, but this can be suppressed 

 by rapid time sampling. High wave numbers at low-frequencies 

 will cause an alias, but its magnitude is unknown. The use of the 

 array depends upon concepts that are now very familiar from seis- 

 mology, radar, and a few oceanographic applications. 



Consider a simple example. With a pilot project aperture of 

 2000 m., we have a theoretical wave number resolution of: 



AK -- 3 — - io " ^ 



Z- lO 

 where the wavenumber is that component lying along the array. 

 (See Figure 2-1). We have no direct resolution perpendicular to the 

 array. With 3 instruments equally spaced out along the line, we 

 have a wave -number alias frequency of 



Kh = \0 ^ 

 also. In principle, therefore, we can unambiguously observe only 

 one wave-length. However, there is considerable additional infor- 

 mation available to us from the dispersion relation for internal 

 waves. ■ 



Consider a plane-wave: i ( K x +1^ - cr-t) 



w ( x^ t^^ t] = A e 



197 



