Persistent clock of turbulent thermal convection

The large-scale circulation (LSC) of turbulent convection is a prominent feature of its dynamics and forms the basis for descriptive theories. We show, using experimental and numerical results from thermal convection in a cylindrical cell, that the LSC possesses a persistent internal “clock”: its pulsating velocity as a function of time is described by a constant value of the parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>U</a:mi> <a:mo>/</a:mo> <a:mo>(</a:mo> <a:mi>l</a:mi> <a:mi>f</a:mi> <a:mo>)</a:mo> </a:mrow> </a:math> , where <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>U</b:mi> </b:math> is the mean velocity, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>f</c:mi> </c:math> is the pulsation frequency, and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>l</d:mi> </d:math> is the characteristic length scale. By introducing a narrow sidewall barrier, we can trip the LSC, forming a pair of interconnected rolls stacked above and below the barrier. They independently exhibit the same value for the ratio <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>U</e:mi> <e:mo>/</e:mo> <e:mo>(</e:mo> <e:mi>l</e:mi> <e:mi>f</e:mi> <e:mo>)</e:mo> </e:mrow> </e:math> , even for vertically asymmetric pairs, indicating signs of synchrony. Thus, this parameter establishes a direct connection between plume-shedding dynamics and the flow topology.