ERTEL, HANS

(b. Berlin, Germany, 24 March 1904; d. Berlin, German Democratic Republic, 2 July 1971)

meteorology, geophysics, physics, hydrography, oceanography.

Ertel studied mathematics, physics, and meteorology at the University of Berlin, where he received the doctorate in 1932. In 1935 he was appointed observer, and in 1938 lecturer, in theoretical meteorology at Berlin. He was professor at the Central Institute of Meteorology and Geodynamics at Vienna in 1942, and from 1943 to 1945 he was professor of geophysics at the University of Innsbruck. Ertel was professor of geophysics at the University of Berlin (German Democratic Republic) and director of its Institute of Meteorology and Geophysics from 1946 to 1969, and was director of the Institute of Physical Hydrography of the German Academy of Sciences, also in Berlin, from 1949 to 1969.

Ertel is a seminal figure in the development of modern meteorology and geophysics. His research, culminating in his general vorticity theorem (Ertel’s potential vorticity theorem), was a key element in the transition from classical to modern meteorology.

Through Ertel’s work Humboldt University and the Academy of Sciences at Berlin, with its Institute of Meteorology and Geophysics and Institute of Physical Hydrography, became international centers of meteorology, geophysics, and fluid dynamics. Ertel’s special field was theoretical meteorology and the application of fluid dynamics to meteorological and geophysical problems. In his earlier years he published on Guilbert’s rule (1930) and the curvature of the surface of discontinuity in the atmosphere and ocean (1931). After 1931 he worked on geostrophy, barotropy, fronts and cyclones, and the role of midlatitude disturbances. In 1936 Ertel developed his advective-dynamic theory of air pressure and its periodicities (1936). Later he investigated the instability of the wind field at the troposphere (1936). He analyzed energy content, friction, and turbulence in the atmosphere and obtained a thermodynamic basis for the turbulence criteria (1939).

In 1939 Ertel reduced the equations of state to Hamilton’s general dynamic principle. In 1942 he found the most important result, establishing the general vorticity theorem (see Table I) that contained the Bjerknes circulation theorem as a particular case. In 1955 he published a generalization that included the Helmholtz vorticity theorem.

From 1949 to 1971, Ertel derived from the vorticity equations a symmetrical deformation tensor that made possible linear transformation of the vorticity components into their total time derivatives (1962). His other work (some with Carl-Gustav Rossby at Cambridge and Hilding Koehler at Uppsala) included differential equations of fluid dynamics and description of steady convection (1949). Ertel’s further studies included his hydrodynamic commutation

formula (1964, 1965) In 1971 he proved that the Jacobian functional determinant of the Eulerian components’ velocity with respect to the Langrangian initial coordinates must remain invariant following the motion of a fluid element in inertial currents.

Ertel was a member of several scientific societies and academies, including the academies of sciences at Berlin, Halle, Uppsala, and Vienna. He was editor or coeditor of many scientific journals, including Gerland’s Beitrage zurGeophysik, Acta hydrophysica, Zeitschrift für Meteorologie, Forschungen und Fortschritte, Idöjárás, and Geofisica pura e applicada.

BIBLIOGRAPHY

1. Original Works. Ertel’s papers are listed in Idöjárás 75 (1971). 263–270; Poggendorff, VIIa; and Zeitschrift für Meteorologie, 22 (1971), 319–328. His chief books are Methoden und Probleme der dynamischen Meteorologie, (Berlin, 1938; repr. 1972); and Elemente der Operatorenrechnung mit geophysikalischen Anwendungen. (Berli, 1940).

Among his articles are “The oretische Begründung einiger Guilbertscher Regeln,” in Berichte über die Tätigkeit der Preussisches Meteorologisches Institut Berlin (1930). 114–118; “Die Krümmung der Diskontinuitätsflächen in der Atmosphäre und im Ozean,” ibid. (1931), 147–152; “Advektiv-dynamische Theorie der Luftdruckschwankungen und ihrer Periodizitäten,” in Veröffentlichungen der Meteorologisches Institut Berlin, 1. no. 1 (1936);“die Arten der Unstetigkeiten des Windfeldes an der Tropopause.” in Meteorologische Zeitschrift, 53 (1936). 450–455; “Ein allgemeines Variationsprinzip der atmosphärischen Dynamik,” ibid., 169–171; “Thermodynamische Begründung des Richardsonschen Turbulenzkriteriums,” ibid., 56 (1939), 109–111; “Über ein allgemeines Variationsprinzip der Hydrodynamik.” in Abhandlungen der Preussische Akademie der Wissenschaften, Physikalischmathematische Klasse (1939), no.7;“Ein neuer hydrodynamischer Wirbelsatz,” in Meteorologische Zeitschrift, 59 (1942), 277–281: “Über das Verhältnis des neuen hydrodynamischen Wirbelsatzes zum Zirkulationssatz von V.Bjerknes,” ibid., 385–387; “Über hydrodynamische Wirbelsätze,” in Physikalische Zeitschrift, 43 (1942), 526–529: “Über stationäre oszillatorische Luftströmungen auf der rotierenden Erde,” in Meteorologische Zeitschrift, 60 (1943), 332–334.

“Ein neuer Erhaltungs-Satz der Hydrodynamik,” in Sitzungsberichte der Deutsche Akademie der Wissenschaften zu Berlin, Mathematisch-naturwissenschaftliche Klasse (1949), no. 1. with Carl Gustaf Rossby, “Ein Theorem über die stationäre Wirbelbewegung kompressibler Flüssigkeiten,” Zeitschrift für angewandte Mathematik und Mechanik, 29 (1949), 109–113 , with Hilding Köehler; “ANew Conservation-Theorem of Hydrodynamics,” in Geofisica pura e applicada. 14 fasc. 3–4 (1949), with Carl-Gustaf Rossby; “Ein Theorem über asynchron-periodische Wirbelbewegungen kompressibler Flüssigkeiten.” in Miscellanea Academica Berolinensia (1950). 62–68; “Ein Theorem über die Feldstärke in Potentialfeldern, in Sitzungsberichte der Deutsche Akademie der Wissenschaften zu Berlin. Klasse fur Mathematik und allgemeine Naturwissenschaften (1954); no. 2; “Kanonischer Algorithmus hydrodynamischer Wirbelgleichungen,” ibid. (1995), no. 4; “Ein neues Wirbel-Theorem der Hydrodynamik,” ibid., no. 5; “Teorema sobre invariantes sustanciales de la hidrodinámica.” in Gerlands Beiträge zur Geophysik, 69 (1960). 290–293; “Relación entre la derivada individual y una cierta divergencia espacial en hidrodinámica,” ibid., 357–361; “Ein System von Identitäten und seine Anwendung zur Transformation von Wirbelgleichungen der Hydrodynamik.” in Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin. 4 (1962). 292–296.

“Vertauschungs-Relationen der Hydrodynamik.” in Monatsberichte der Akademie der Wissenschaften zu Berlin, 6 (1964), 838–841: “Hydrodynamische Vertauschungs-Relationen.” in Acta hydrophysica. 9 (1965). 115–123: “theorie der Stroömung um Seebuhnen.” in Gerlands Beiträge zur Geophysik. 77 (1968). 251–256: “Hydrodynamische Theorie der litoralen Sandriffe.” ibid., 78 (1969). 245–250: “Eine Differenzengleichung der Hydrodynamik autobarotroper Wirbelströmungen.” ibid., 414–418; “Ein Satz zur Kinematik nichtstationärer Stromfelder.” ibid., 79 (1970). 147–151: “Transformation der Differentialform der Weberschen hydrodynamischen Gleichungen unter Ber¨cksichtigung der Erdrotation.” ibid., 421–424: “Eine Relation zwischen kinematischen Parametern horizontaler Strömungsfelder in der Atmosphäre.” in Idöjás, 74 (1970), 98–102: “Analytische Approximation der bodennahen Advektion.” ibid., spec. iss., 497–499: “Eine Betrachtung zur geomorphologisch wirksamen. Arbeit der Brandungswellen an Flachk¨sten.” in Acta hydropyusica, 16 (1971), 5–10: “Eine Differentialinvariante der Trägheitsbewegungen in der Atmosphäre und im Ozean.” in Zeitschrift f¨r Meteorologie. 22 (1971). 339–314; and “Quellen und Senken des universellen Schwerefeldes,” in Annalen der Physik, 26 . (1971), 23–28, with Hans-Jürgen Treder.

II. Secondary Literature, Obituary notices include F. Dési, in Idöj´r´s, 75 (1971), 261;P. Mauersberger, in Zeitschrift f¨r Meteorologie, 22 (1971), 651–317: Wilfried Schröder, in Wetter und Leben, 23 (1971), 244: and Heinz Stiller. in Gerlands Beiträge zur Geophysik, 81 (1972). 161–163. See also P.kahlig. in Archives of Geophysics. Bioklimatoligie. A19 (1970). 125; H. Pichler, in Pure and Applied Geophysics. 65 (1966), 180: and C. Truesdell. “Recent Advances in Rational Mechanics.” in Science. 127 (1958). 729–739.

Wilfried SchrÖder