Transient development of perturbations in stratified shear flow

Journal Article · Thu Jul 15 04:00:00 EDT 1993 · Journal of the Atmospheric Sciences; (United States)

DOI:https://doi.org/10.1175/1520-0469(1993)050<2201:TDOPIS>2.0.CO;2· OSTI ID:5899611

Farrell, B F ^[1]; Ioannou, P J ^[2]

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1. Harvard Univ., Cambridge, MA (United States)
2. Massachusetts Institute of Technology, Cambridge (United States)

Transient development of perturbations in inviscid stratified shear flow is investigated. Use is made of closed form analytical solutions that allow concise identification of optimally growing plane-wave solutions for the case of an unbounded flow with constant shear and stratification. For the case of channel flow, variational techniques are employed to determine the optimally growing disturbances. The maximum energy growth attained over a specific time interval decreases continuously with increasing stratification, and no special significance attaches to Ri = 0.25. Indeed, transient growth can be substantial even for Ri = O(1). A general lower bound on the energy growth attained by an optimal perturbation in a stratified flow over a given time interval is the square root of the growth attained by the corresponding perturbation in unstratified flow. Enhanced perturbation persistance is found for mean-flow stratification lying in the range 0.1 < Ri < 0.3. Small but finite perturbations in mean flow with Ri < 0.4 produce regions with locally negative total density gradient, which are expected to overturn. Although the perturbations are of wave form, buoyancy fluxes mediate transfer between perturbation kinetic and potential energy during transient development, thus implying that buoyancy flux is not a determinative diagnostic for distinguishing between waves and turbulence in stratified flows. 44 refs., 14 figs., 2 tabs.

• OSTI ID: 5899611
• Journal Information: Journal of the Atmospheric Sciences; (United States), Journal Name: Journal of the Atmospheric Sciences; (United States) Vol. 50:14; ISSN 0022-4928; ISSN JAHSAK
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
540110*
540310 -- Environment
Aquatic-- Basic Studies-- (1990-)
ATMOSPHERIC CIRCULATION
FLOW MODELS
FLUID FLOW
FLUID MECHANICS
GRAVITY WAVES
HYDROGEN COMPOUNDS
MATHEMATICAL MODELS
MECHANICS
METEOROLOGY
OCEANIC CIRCULATION
OXYGEN COMPOUNDS
RICHARDSON NUMBER
SHEAR
STRATIFICATION
TURBULENT FLOW
WATER
WIND