GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS BEYOND THE TRADITIONAL APPROXIMATION T. Gerkema, 1 J. T. F. Zimmerman, 1,2 L. R. M. Maas, 1,2 and H. van Haren 1 Received 7 November 2006; revised 6 June 2007; accepted 28 September 2007; published 16 May 2008. [1] In studies on geophysical fluid dynamics, it is common practice to take the Coriolis force only partially into account by neglecting the components proportional to the cosine of latitude, the so-called traditional approximation (TA). This review deals with the consequences of abandoning the TA, based on evidence from numerical and theoretical studies and laboratory and field experiments. The phenomena most affected by the TA include mesoscale flows (Ekman spirals, deep convection, and equatorial jets) and internal waves. Abandoning the TA produces a tilt in convective plumes, produces a dependence on wind direction in Ekman spirals, and gives rise to a plethora of changes in internal wave behavior in weakly stratified layers, such as the existence of trapped short low-frequency waves, and a poleward extension of their habitat. In the astrophysical context of stars and gas giant planets, the TA affects the rate of tidal dissipation and also the patterns of thermal convection. Citation: Gerkema, T., J. T. F. Zimmerman, L. R. M. Maas, and H. van Haren (2008), Geophysical and astrophysical fluid dynamics beyond the traditional approximation, Rev. Geophys., 46, RG2004, doi:10.1029/2006RG000220. 1. INTRODUCTION [2] In a now famous memoir, Coriolis [1835] derived the equations of motion for rotating devices, in which he identified a deflecting force that he called ‘‘force centrifuge compose ´e,’’ now known as the Coriolis force. It acts on particles moving in the frame of reference of the rotating system, is proportional to their velocity, and produces a deflection in a direction perpendicular to velocity. The rotating ‘‘device’’ we are primarily concerned with in this paper is, of course, the Earth. The notion that the Earth’s diurnal rotation produces a deflecting force had, in fact, been recognized before Coriolis, albeit initially in rudimen- tary form; in the 18th century, G. Hadley thus provided a qualitative explanation of the trade winds [Burstyn, 1966]. In a preamble to his dynamic theory of tides, Laplace [1798] derived the exact mathematical form of the deflect- ing force. Adopting a geographical coordinate system, he showed that there are four ‘‘Coriolis’’ terms, whose roles are indicated in Table 1 (an elementary derivation of each of these terms is provided in Appendix A). [3] Of these four terms, two are proportional to the sine of latitude; the other two are proportional to the cosine. This distinction has a deeper, dynamical significance. The force associated with the sine terms is due to, and induces, only horizontal movements. In the cosine terms, on the other hand, the vertical direction is always involved: the associ- ated force either is due to a vertical velocity or induces a vertical acceleration. (These effects are perhaps most readily appreciated by means of the following simple mechanical examples: (1) the eastward deflection of a stone dropped from a tower and (2) the upward force undergone by an eastward moving object, reducing its weight, the so-called Eo ¨tvo ¨s effect.) Exploiting this distinction, Laplace devel- oped a chain of arguments which led him to conclude that while the sine terms are to be retained, the cosine terms can be neglected (see Laplace [1878, Livre I, sections 35 and 36]; for a valuable summary of this and other aspects of Laplace’s tidal theory, see Dubois [1885]). In this, he has been followed almost universally in later studies on geo- physical fluid dynamics (GFD), which inspired Eckart [1960] to coin the apt name ‘‘traditional approximation’’ (TA) to refer to the neglect of the cosine terms, i.e., the terms with ~ f in Table 1. The TA’s widespread adoption notwithstanding, studies devoted to the role of ~ f have occasionally appeared since the late 1920s and more fre- quently so in recent years. As the interest in the topic has waxed and waned repeatedly, the literature is scattered, and much of it has slipped into oblivion. The principal goals of this review are to give a coherent overview of the existing literature, to pinpoint the kinds of motion in which ~ f is plausibly significant, and to outline the unresolved issues. Click Here for Full Articl e 1 Royal Netherlands Institute for Sea Research, Texel, Netherlands. 2 Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands. Copyright 2008 by the American Geophysical Union. 8755-1209/08/2006RG000220$15.00 Reviews of Geophysics, 46, RG2004 / 2008 1 of 33 Paper number 2006RG000220 RG2004