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A Note on the Role of Mean Flows in Doppler-Shifted Frequencies

Theo GerkemaNIOZ Royal Netherlands Institute for Sea Research, Texel, Netherlands

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Leo R. M. MaasNIOZ Royal Netherlands Institute for Sea Research, Texel, Netherlands

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Hans van HarenNIOZ Royal Netherlands Institute for Sea Research, Texel, Netherlands

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Abstract

The purpose of this paper is to resolve a confusion that may arise from two quite distinct definitions of “Doppler shifts”: both are used in the oceanographic literature but they are sometimes conflated. One refers to the difference in frequencies measured by two observers, one at a fixed position and one moving with the mean flow—here referred to as “quasi-Doppler shifts.” The other definition is the one used in physics, where the frequency measured by an observer is compared to that of the source. In the latter sense, Doppler shifts occur only if the source and observer move with respect to each other; a steady mean flow alone cannot create a Doppler shift. This paper rehashes the classical theory to straighten out some misconceptions. It is also discussed how wave dispersion affects the classical relations and their application.

Corresponding author address: Theo Gerkema, Royal NIOZ, P.O. Box 59, 1790 AB Den Burg, Texel, Netherlands. E-mail: gerk@nioz.nl

Abstract

The purpose of this paper is to resolve a confusion that may arise from two quite distinct definitions of “Doppler shifts”: both are used in the oceanographic literature but they are sometimes conflated. One refers to the difference in frequencies measured by two observers, one at a fixed position and one moving with the mean flow—here referred to as “quasi-Doppler shifts.” The other definition is the one used in physics, where the frequency measured by an observer is compared to that of the source. In the latter sense, Doppler shifts occur only if the source and observer move with respect to each other; a steady mean flow alone cannot create a Doppler shift. This paper rehashes the classical theory to straighten out some misconceptions. It is also discussed how wave dispersion affects the classical relations and their application.

Corresponding author address: Theo Gerkema, Royal NIOZ, P.O. Box 59, 1790 AB Den Burg, Texel, Netherlands. E-mail: gerk@nioz.nl
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