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Spectra of Internal Waves and Turbulence in Stratified Fluids: 1. General Discussion and Indications from Measurements in Stably Stratified Atmosphere and Ocean
Author(s) -
Pao YihHo
Publication year - 1969
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs004i012p01315
Subject(s) - internal wave , turbulence , wavenumber , physics , atmosphere (unit) , buoyancy , gravity wave , stratified flow , spectral line , computational physics , stratified flows , mesoscale meteorology , stratification (seeds) , scalar (mathematics) , geophysics , mechanics , meteorology , wave propagation , optics , astronomy , geometry , seed dormancy , germination , botany , mathematics , dormancy , biology
A unified spectral description of internal waves and turbulence in a stably stratified atmosphere or ocean is proposed. We envisage that the fluctuating motions in a free atmosphere with scales smaller than the synoptic scale consist of internal waves and turbulence. At low wavenumbers, internal waves predominate; this range of wavenumbers may be called the internal wave subrange. The internal waves can be identified from the characteristics of velocity‐scalar cospectra and quadrature spectra, as shown recently by Pao [1969b] in a laboratory experiment. When the internal waves are sufficiently strong and distinct, the different harmonics of internal waves may appear in the autospectra of velocity and temperature where the peaks and valleys are clearly identifiable. This, we believe, explains the presence of peaks and valleys in some velocity autospectra of clear air turbulence measured in strongly stratified regions of the atmosphere. At intermediate wavenumbers (buoyant subrange) the buoyancy effect is still strong but the turbulent scrambling process also becomes important; the higher‐order harmonics of internal waves are no longer distinct and cannot be detected in the autospectra; the velocity autospectra are steeper than k −5/3 . At high wavenumbers (inertial and viscous subranges) turbulence predominates. The characteristics of fluctuating motion in this range of wavenumbers can be described well with Kolmogorov's concept of local isotropy and are not affected by the stratification. The proposed spectral behavior for the free atmosphere is described in detail and supported with existing measurements in stably stratified regions of the atmosphere and ocean in part 1. It will be further supported by our laboratory experiments on the breaking of internal waves in a two‐fluid system [ Hall and Pao , 1969] in part 2.