Continuous dynamical modes in straits having arbitrary cross sections, with applications to the Bab al Mandab

The continuous dynamical modes of the exchange flow in the Bab al Mandab ar e computed in an attempt to assess the hydraulic character of the Row at th e sill. First, an extended version of the Taylor-Goldstein equation for lon g waves that accounts for cross-channel topographic variations, is develope d. A series of calculations using idealized background velocity U(z) and bu oyancy frequency N(z) are presented to illustrate the effects of simple top ographic cross sections on the internal modes and their speeds. Next, hydro graphic and direct velocity measurements from April to November 1996 using moored CTDs and a bottom-mounted ADCP are utilized to construct monthly mea n vertical profiles of N-2(z) and at the U(z) sill. An analytical approxima tion of the true topography across the strait is also constructed. The obse rved monthly mean profiles are then used to solve for the phase speeds of t he first and second internal modes. Additional calculations are carried out using a selection of "instantaneous" (2-h average) profiles measured durin g extremes of the semidiurnal tide. The results are compared with a three-l ayer analysis of data from the previous year. Many of the authors' conclusions follow from an intriguing observation conc erning the long-wave phase speeds. Specifically, it was nearly always obser ved that the calculated speeds c(-1) and c(1) of the two waves belonging to the first internal mode obey c(-1) < U-min < U-max < c(1), where U-min and U-max are the minimum and maximum of the velocity profile. An immediate co nsequence is that neither wave has a critical level. For monthly mean profi les, each of which have U-min < 0 < U-max, the how is therefore subcritical (the phase speeds of the two waves have opposite signs). For instantaneous profiles this relationship continues to hold, although the velocity profil e can be unidirectional. Thus the flow can be critical (c(-1) = 0 and/or c( 1) = 0) or even supercritical (c(-1) and c(1) have the same sign) with resp ect to the first mode. Similar findings follow for the second baroclinic mo de phase speeds (c(-2) and c(2)). The authors conclude that hydraulically c ritical flow is an intermittent feature, influenced to a great extent by th e tides. It is noted that the phase speed pairs for each mode lie very clos e to U-min and U-max. As suggested by the analysis of idealized profiles, t his behavior is characteristic of flows that are marginally stable, perhaps as a result of prior mixing. This suggestion is supported by Richardson nu mber (Ri) profiles calculated from the monthly mean and instantaneous data. Middepth values of Ri were frequently found to be O(1) and sometimes <1/4, a result consistent with the presence of mixing over portions of the water column.