Fig. Schematic of the domain used for DNS: the hot plate temperature is TH ( T = 1) on the left half of the base (0 < x <1/2) and the cold plate temperature is TC ( T = 0) on the right half of the base (1/2 < x <1). Superposed is a snapshot of the dimensionless vertical velocity field w in the x-z plane from the first thermally-equilibrated numerical simulation. Colour scale shows velocity relative to the scale L2/k.
Horizontal convection is driven by differential thermal forcing which is applied at the bottom boundary over two equal regions. The steady-state circulation is achieved after the net heat flux from the boundary becomes zero. A stable thermocline forms above the cooled base and is advected over the heated part of the base, con.ning small-scale three-dimensional convection to the heated base and end wall region. At the end wall a narrow turbulent plume rises through the full depth of the channel. The less energetic return flow is downward in the interior, upon which eddy motions are imposed (see Fig. 1).
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Ref. B. Gayen, R. W. Griffiths, G. O. Hughes and J. A. Saenz (2013) Energetics of horizontal convection, J. Fluid Mech., 716, pp-716 R10-1-716 R10-11
B. Gayen, R. W. Griffiths and G. O. Hughes (2014) Stability transitions and turbulence in horizontal convection. J. Fluid Mech., 751, 698-724