Near-wall velocity field in turbulent Rayleigh-Bénard convection with rough surface

We present measurements of the near-wall velocity field in turbulent Rayleigh-Bénard convection with a partially rough horizontal surface. These measurements cover Rayleigh numbers ranging from <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>R</a:mi> <a:mi>a</a:mi> <a:mo>=</a:mo> <a:mn>5.8</a:mn> <a:mo>×</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>10</a:mn> </a:msup> </a:mrow> </a:math> to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>R</b:mi> <b:mi>a</b:mi> <b:mo>=</b:mo> <b:mn>8.0</b:mn> <b:mo>×</b:mo> <b:msup> <b:mn>10</b:mn> <b:mn>11</b:mn> </b:msup> </b:mrow> </b:math> , while the Prandtl number was fixed at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>P</c:mi> <c:mi>r</c:mi> <c:mo>=</c:mo> <c:mn>0.7</c:mn> </c:mrow> </c:math> . The measurements have been undertaken in the large-scale convection experiment “Barrel of Ilmenau,” which provides a very high resolution in space and time. The measurements confirm the prominent role of the ratio between the thickness of the boundary layer <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>δ</d:mi> <d:mrow> <d:mi>t</d:mi> <d:mi>h</d:mi> </d:mrow> </d:msub> </d:math> and the height of the roughness elements <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>h</e:mi> </e:math> , although transition effects only appear below <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>δ</f:mi> <f:mrow> <f:mi>t</f:mi> <f:mi>h</f:mi> </f:mrow> </f:msub> <f:mo>/</f:mo> <f:mi>h</f:mi> <f:mo>≈</f:mo> <f:mn>0.6</f:mn> </f:mrow> </f:math> in our experiments. In addition, we calculated the ratio between the turbulent kinetic energy and the average kinetic energy in the boundary layer. This ratio remains virtually constant up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>R</g:mi> <g:mi>a</g:mi> <g:mo>=</g:mo> <g:mn>4.2</g:mn> <g:mo>×</g:mo> <g:msup> <g:mn>10</g:mn> <g:mn>11</g:mn> </g:msup> </g:mrow> </g:math> and increases beyond this value. This is another indication of a qualitative transition of the boundary layer flow field. We observed this transition above both the TOP and above the VALLEY regions of the rough surface, concluding that both regions may contribute similarly to an increase in heat flux. The transition in the flow field is purely induced by viscous effects. The Richardson number, based on the thickness of the boundary layer and the velocity of the mean wind, is much smaller than one for all Rayleigh numbers investigated. This indicates that viscous effects dominate the near-wall flow field, and buoyancy does not play any role in the variation of the flow field here. We have also analysed time series of the wall-normal velocity component <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>w</h:mi> </h:math> in the plane where the temperature fluctuates at its maximum. The distribution of the fluctuations of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>w</i:mi> </i:math> deviates from a normal distribution for all investigated Rayleigh numbers. In particular, the distributions exhibit broader tails on both sides. However, the distributions show just a little asymmetry, which we would expect as a signature of thermal plumes.