Goldreich, Peter and Kumar, Pawan (1990) Wave generation by turbulent convection. Astrophysical Journal, 363 (2). pp. 694704. ISSN 0004637X. https://resolver.caltech.edu/CaltechAUTHORS:20130313143153072

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Abstract
We consider wave generation by turbulent convection in a plane parallel, stratified atmosphere that sits in a gravitational field, g. The atmosphere consists of two semiinfinite layers, the lower adiabatic and polytropic and the upper isothermal. The adiabatic layer supports a convective energy flux given by mixing length theory; F_c ~ pv^3_H, where p is mass density and v_H is the velocity of the energy bearing turbulent eddies. Acoustic waves with ω > ω_(ɑc) and gravity waves with ω < 2k_h H_iωb propagate in the isothermal layer whose acoustic cutoff frequency, ω_(ac), and BruntVäisälä frequency, ω_b, satisfy ω^2_(ɑc) = yg/4H_i and ω^2_b = (y1)g/yH_i, where y and H_i denote the adiabatic index and scale height. The atmosphere traps acoustic waves in upper part of the adiabatic layer (pmodes) and gravity waves on the interface between the adiabatic and isothermal layers (fmodes). These modes obey the dispersion relation ω^2≈2/m gk_h(n + m/2), for ω < ω_(ɑc). Here, m is the polytropic index, k_h is the magnitude of the horizontal wave vector, and n is the number of nodes in the radial displacement eigenfunction; n = 0 for fmodes. Wave generation is concentrated at the top of the convection zone since the turbulent Mach number, M = v_H/c, peaks there; we assume M_t « 1. The dimensionless efficiency, η, for the conversion of the energy carried by convection into wave energy is calculated to be η~M_t^(5/12) for pmodes,fmodes, and propagating acoustic waves, and η~M, for propagating gravity waves. Most of the energy going into pmodes, fmodes, and propagating acoustic waves is emitted by inertial range eddies of size h ~ M_t^(3/2)H_t, at ω ~ ω_(ɑc) and k_h ~ 1/H_t. The energy emission into propagating gravity waves is dominated by energy bearing eddies of size ~ H_t and is concentrated at ω ~ v_t/H_t ~ M_t ω_(ɑc) and k_h ~ 1/H_t. We find the power input to individual pmodes, E_p, to vary as ω<^(2m^2+7m3)/(m+3) at frequencies ω « v_t/H_t. Libbrecht has shown that the amplitudes and linewidths of the solar pmodes imply E_p ∝ ω^8 for ω « 2 x 10^(2) s^(1). The theoretical exponent matches the observational one for m ≈ 4, a value obtained from the density profile in the upper part of the solar convection zone. This agreement supports the hypothesis that the solar pmodes are stochastically excited by turbulent convection.
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Additional Information:  © 1990 American Astronomical Society. Received 1990 January 29; accepted 1990 May 9. The authors are indebted to T. Bogdan, A. Ingersoll, N. Murray, and R. Stein for much helpful advice. This research was supported by NSF grants AST 8913664 and PHY 8604396 and NASA grants NAGW 1303, 1568, and 5951. Part of it was performed while P. G. and P. K. held visiting appointments at the HarvardSmithsonian Center for Astrophysics. P. G. thanks the Smithsonian Institution for a Regents Fellowship and P. K. thanks W. Press, W. Kalkofen, and R. Noyes for financial support.  
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Subject Keywords:  convection, Sun: atmosphere, Sun: oscillations, turbulence, wave motions  
Issue or Number:  2  
Record Number:  CaltechAUTHORS:20130313143153072  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:20130313143153072  
Official Citation:  Wave generation by turbulent convection Goldreich, Peter; Kumar, Pawan Astrophysical Journal, Part 1, vol. 363, Nov. 10, 1990, p. 694704.  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  37506  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  13 Mar 2013 22:50  
Last Modified:  03 Oct 2019 04:48 
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