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\begin{document}

\title{Evolution of bottom boundary layers on three dimensional topography --
Buoyancy adjustment and instabilities}



\author[1]{Arjun Jagannathan}%
\author[2]{Kaushik Srinivasan}%
\author[2]{James C. McWilliams}%
\author[2]{Jeroen Molemaker}%
\author[2]{Andrew Stewart}%
\affil[1]{Indian Institute of Technology Madras}%
\affil[2]{University of California Los Angeles}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
A current along a sloping bottom gives rise to upwelling, or downwelling
Ekman transport within the stratified bottom boundary layer (BBL), also
known as the bottom Ekman layer. In 1D models of slope currents,
geostrophic vertical shear resulting from horizontal buoyancy gradients
within the BBL is predicted to eventually bring the bottom stress to
zero, leading to a shutdown, or
\textbackslash{}change\{\textbackslash{}lq arrest \textbackslash{}rq
\textbackslash{},,\}\{\textbackslash{}lq arrest \textbackslash{}rq,\} of
the BBL. Using 3D ROMS simulations, we explore how the dynamics of
buoyancy adjustment in a current-ridge encounter problem differs from 1D
and 2D temporal spin up problems. We show that in a downwelling BBL, the
destruction of the ageostrophic BBL shear, and hence the bottom stress,
is accomplished primarily by nonlinear straining effects during the
initial topographic \textbackslash{}change\{counter\}\{encounter\}. As
the current advects along the ridge slopes, the BBL deepens and evolves
toward thermal wind balance. The onset of negative potential vorticity
(NPV) modes of instability and their subsequent dissipation partially
offsets the reduction of the BBL dissipation during the ridge-current
interaction. On the upwelling side, although the bottom stress weakens
substantially during the encounter, the BBL experiences a horizontal
inflectional point instability and separates from the slopes before
sustained along-slope stress reduction can
\textbackslash{}change\{occured\}\{occur\}. In all our solutions, both
the upwelling and downwelling BBLs are in a partially arrested state
when the current separates from the ridge slope, characterized by a
reduced, but non-zero bottom stress on the slopes.%
\end{abstract}%



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