# Dynamic Response of the Indian Ocean to Onset of the Southwest Monsoon

M. J. Lighthill

## Abstract

The linearized theory of unsteady wind-driven currents in a horizontally stratified ocean is applied to the northern part of the Indian Ocean. This is argued to be a suitable area for detailed application and evaluation of the theory because (i) the theory has certain advantages near the equator (for example, influence of detailed bottom topography is reduced, thermoclines are somewhat less variable in character, and speeds of baroclinic propagation are enhanced relative to current speeds), and (ii) the wind-stress pattern undergoes a well marked change with onset of the Southwest Monsoon, a change to which the pattern of currents shows a more or less identifiable, and rather quick, response which may be compared with theoretical predictions. Response is predicted to be found principally in two modes as far as vertical distribution of current is concerned; to a somewhat lesser extent in the barotropic mode with uniform distribution, and to a somewhat greater extent in the first baroclinic mode with current distribution as in figure 7, concentrated predominantly in the uppermost 200 m (see Appendix for detailed analysis of the modes appropriate to the equatorial Indian Ocean). Of particular interest is the strong Somali Current, that flows northward along the Somali coast only during the northern hemisphere summer (after monsoon onset) but during that time is comparable in volume flow (about 5 $\times$ 10$^{7}$ m$^{3}$/s) to other western boundary currents such as the Gulf Stream. Detailed discussion of the application of linearized theory to equatorial oceans with western boundaries leads the author to conclude, both in the barotropic (section 2) and baroclinic (section 4) cases, that 'wave packets' of current pattern reaching such a boundary deposit the 'flux' they carry (velocity normal to the boundary integrated along it) in a boundary current which rather rapidly takes a rather concentrated form. Linear theory with horizontal transport neglected indicates that such flux requires of the order of 10 days to become concentrated in a current of 100 km width, but that thereafter it continues to become still thinner; however, with horizontal transport included, a steady-state finite thickness of current is reached. In reality, nonlinear effects would play an important additional part in limiting steady-state current thickness to the observed 100 km or thereabouts, but the time scale required to bring the thickness down to this value is probably given reasonably well by linear theory. Calculations for a zonal distribution of winds, which rather rapidly make a reversal of direction and increase of strength somewhat north of the Equator characteristic of the onset of the Southwest Monsoon, predict westward propagation of both barotropic and baroclinic wave energy at comparable speeds of the order of 1 m/s; the marked contrast here with other oceans (in the comparability of speeds) is given particularly detailed study. Calculations indicate that the barotropic signal is considerably distorted (figure 3) by the fact that low-wavenumber components reach the western boundary first. Baroclinic propagation takes the form of special planetary-wave modes concentrated near the equator (section 3), of which perhaps four, delivering flux patterns depicted in figure 5, and possessing wave velocities of 0.9, 0.55, 0.4 and 0.3 m/s towards the west, are specially relevant to generation of the Somali Current. Peak surface flows in that current are predicted to be influenced about three times as much by this baroclinic propagation as by the barotropic. Theory indicates 1 month (of which two-thirds is needed for propagation of current patterns and one-third for their concentration in a boundary current) as characteristic time scale for formation of the Somali Current (see figure 6 in particular for the calculated baroclinic component) in contradistinction to the 'decades' predicted by the same type of theory in mid-latitude oceans (Veronis & Stommel 1956). Observations do, indeed, make clear that the time scale is not significantly more than 1 month, although the possibility that it might be still less cannot yet be decided on the basis of observational evidence. The flow is calculated as reaching 40% of a typical maximum value (observed in August) already within 1 month of monsoon onset (May), even though no effect of wind stress acting within 500 km of the coast has been taken into account. The linearized theory predicts the current as reaching as far north as 6 degrees N or 7 degrees N, but nonlinear terms are generally found in computational studies (Bryan 1963; Veronis 1966) to bring about some 'inertial overshoot' in concentrated boundary currents, which may explain why the current does not in fact separate until about 9 degrees N.