This paper proposes a joint analysis of variations of global sea-level pressure (SLP) and of Earth's rotation (RP), expressed as the coordinates of the rotation pole (m1, m2) and length of day (lod). We retain iterative singular spectrum analysis (iSSA) as the main tool to extract the trend, periods, and quasi periods in the data time series. SLP components are a weak trend, seven quasi-periodic or periodic components (∼130, 90, 50, 22, 15, 4, 1.8 years), an annual cycle, and its first three harmonics. These periods are characteristic of the space-time evolution of the Earth's rotation axis and are present in many characteristic features of solar and terrestrial physics. The amplitudes of the annual SLP component and its three first harmonics decrease from 93 hPa for the annual to 21 hPa for the third harmonic. In contrast, the components with pseudo-periods longer than a year range between 0.2 and 0.5 hPa. We focus mainly on the annual and, to a lesser extent, the semi-annual components. The annual RP and SLP components have a phase lag of 152 days (half the Euler period). Maps of the first three components of SLP (that together comprise 85% of the data variance) reveal interesting symmetries. The trend is very stable and forms a triskeles structure that can be modeled as Taylor–Couette flow of mode 3. The annual component is characterized by a large negative anomaly extending over Eurasia in the NH summer (and the opposite in the NH winter) and three large positive anomalies over Australia and the southern tips of South America and South Africa in the SH spring (and the opposite in the SH autumn), forming a triskeles. The semi-annual component is characterized by three positive anomalies (an irregular triskeles) in the NH spring and autumn (and the opposite in the NH summer and winter), and in the SH spring and autumn by a strong stable pattern consisting of three large negative anomalies forming a clear triskeles within the 40–60∘ annulus formed by the southern oceans. A large positive anomaly centered over Antarctica, with its maximum displaced toward Australia, and a smaller one centered over Southern Africa, complement the pattern. Analysis of iSSA components of global sea level pressure shows a rather simple spatial distribution with the principal forcing factor being changes in parameters of the Earth's rotation pole and velocity. The flow can probably best be modeled as a set of coaxial cylinders arranged in groups of three (triskeles) or four and controlled by Earth topography and continent/ocean boundaries. Flow patterns suggested by maps of the three main iSSA components of SLP (trend, annual, and semi-annual) are suggestive of Taylor–Couette flow. The envelopes of the annual components of SLP and RP are offset by four decades, and there are indications that causality is present in that changes in Earth rotation axis lead force pressure variations.