Abstract
Abstract. We discuss here the evolution of vorticity and potential vorticity (PV) for a bottom current crossing a marine channel in shallow-water approximation, focusing on the effect of friction and mixing. The purpose of this research is indeed to investigate the role of friction and vertical entrainment on vorticity and PV spatial evolution in channels or straits when along-channel morphology variations are significant. To pursue this investigation, we pose the vorticity and PV equations for a homogeneous bottom water vein and we calculate these two quantities as an integral form. Our theoretical findings are considered in the context of in situ hydrographic data related to the Eastern Mediterranean Deep Water (EMDW), i.e., a dense, bottom water vein that flows northwestward, along the Sicily Channel (Mediterranean Sea). Indeed, the narrow sill of this channel implies that friction and entrainment need to be considered. Small tidal effects in the Sicily Channel allow for a steady theoretical approach. We argue that bottom current vorticity is prone to significant sign changes and oscillations due to topographic effects when, in particular, the current flows over the sill of a channel. These vorticity variations are, however, modulated by frictional effects due to seafloor roughness and morphology. Such behavior is also reflected in the PV spatial evolution, which shows an abrupt peak around the sill region. Our diagnoses on vorticity and PV allow us to obtain general insights about the effect of mixing and friction on the pathway and internal structure of bottom-trapped currents flowing through channels and straits, and to discuss spatial variability of the frictional coefficient. Our approach significantly differs from other PV-constant approaches previously used in studying the dynamics of bottom currents flowing through rotating channels.
Highlights
An ongoing debate in diagnostic models for currents that flow over a sill in a rotating channel with varying cross sections concerns the effect of friction and mixing, which clearly plays an important role in the presence of morphological constraints (Pratt et al, 2008; Pratt and Whitehead, 2008)
Our theoretical findings are considered in the context of in situ hydrographic data related to the Eastern Mediterranean Deep Water (EMDW), i.e., a dense, bottom water vein that flows northwestward, along the Sicily Channel (Mediterranean Sea)
We introduce the hydrographic settings of the Sicily Channel (Fig. 1) (Astraldi et al, 2001; A01 hereafter) and employ interpolated, cross-averaged flow velocity (u) and thickness (h) data related to the Eastern Mediterranean Deep Water (EMDW; a bottom vein flowing northwestward through the Sicily Channel) in order to diagnose our vorticity and potential vorticity (PV) equations
Summary
An ongoing debate in diagnostic models for currents that flow over a sill in a rotating channel with varying cross sections concerns the effect of friction and mixing, which clearly plays an important role in the presence of morphological constraints (Pratt et al, 2008; Pratt and Whitehead, 2008). Experimental data have shown complicated dynamics that suggest a strong effect of both interfacial and bottom friction that may induce a secondary circulation (Johnson et al, 1976) These considerations are at the base of our interest for a more realistic analysis of bottom currents that cross a narrow marine channel, in the presence of an irregular morphology, and flow underneath upper layers that have different dynamics. To pursue such an investigation, we derive vorticity and PV equations from the classic stream-tube model (Smith, 1975; Killworth, 1977), which describes the steady properties of a homogeneous, viscous bottom water vein, considering entrainment in the mass conservation equation (Turner, 1986) We discuss these equations in order to figure out the role of seafloor morphology, friction, and mixing in marine channel dynamics. The usual inviscid quasi-geostrophic approach does not seem adequate in the Sicily Channel
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