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Instability and diapycnal momentum transport in a double-diffusive ...

Instability and diapycnal momentum transport in a double-diffusive ...

Instability and diapycnal momentum transport in a double-diffusive

Instability and diapycnal momentum transport in a double-diffusive, stratified shear layer William D. Smyth ∗ and Satoshi Kimura College of Oceanic and Atmospheric Sciences Oregon State University, Corvallis OR Submitted to J. Phys. Oceanogr. August 31, 2006 ∗ Corresponding author. Telephone: (541) 737-3029; email: smyth@coas.oregonstate.edu Abstract We investigate the linear stability of a double-diffusively stratified, inflectional shear flow. Double-diffusive stratification has little effect on shear instability except when the density ratio R ρ is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest growing mode even in the presence of inflectionally unstable shear with low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wavevector. The converse is not true: doublediffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Sc s . In the oceanic parameter regime, Sc s is less than unity and can be parameterized as Sc s =0.08 ln[R ρ /(R ρ −1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism. 1 Introduction Thermohaline stratification is double-diffusively unstable for nearly half of the ocean interior (You, 2002). The instability often results in layering, which may occur through two mechanisms that have been seen as distinct, though their relationship is poorly understood. When temperature and salinity vary only in the vertical, the fluid becomes organized into staircases of vigorously convecting layers separated by thin interfaces Radko (2003). When temperature and salinity vary in the horizontal, buoyancy fluxes may drive interleaving motions that have the potential to effect significant lateral transport between watermasses. Effects of shear (i.e. vertically sheared horizontal currents) may be important in both scenarios. In the interleaving case, shear is clearly present between adjacent intruding layers (Mueller et al. 2005, in preparation). In a staircase, shear is not intrinsic, but the ubiquitous presence of gravity waves in the ocean means that such layers will be subjected to shear nonetheless (e.g. Kunze, 1994). While the last few decades have seen many studies of double diffusive instability, the effects of shear on those instabilities have received relatively little attention. Linden (1974) showed both theoretically and experimentally that a uniform shear favors convection rolls whose axes are parallel to the background flow. Analogous results have been found for ordinary convection in the presence of shear (Deardorff, 1965). Thangham et al. (1984) conducted detailed numerical studies of shear effects, but ex- 1

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