Direct numerical simulation of square vortex flows

includes bibliographical references and index

M.Tech (Res); 2023; Mechanical Engineering

Atmospheric and oceanic flows are often modeled as two-dimensional due to their large
planar extents (∼ 1000 km) and small vertical extent (∼ 10 km). Most phenomena in
these systems are governed by the theory of two-dimensional turbulence. Rather than
truncating the third dimension, its effect is modeled using additional friction term in
the 2D Navier-Stokes equations. These equations are said to be applied to a class of
flows called quasi-two-dimensional (Q2D) flows, which are essentially three-dimensional
but almost planar flows. The approximation of Q2D-ness is widely applied for shallow
fluid layers in laboratory experiments.
We study Q2D flows generated by electromagnetically driving a shallow electrolyte
layer. The specific form of forcing mimics that of a chessboard, where the laminar
flow is composed of counter rotating square vortices arranged in a chessboard like
array. The forcing function is carefully chosen to mimic experimental measurements
of a laboratory realization, which is not purely sinusoidal as in the well-known Taylor
Green vortex flow. The steadily forced flow leads to a statistically stationary state
which is analyzed over a wide Reynolds number range. We analyze how the dynamics
and flow structures change with increasing Reynolds number. We illustrate methods
to discuss when and how the Q2D model ceases to accurately represent experiments.