In literature there is no mathematical proof of the experimentally trivial stability of the rest state for a layer of compressible fluid heated from above. In the case of layer heated from below it is known that the system shows a threshold in the temperature gradient below which the fluid is not sensible to the imposed difference of temperature. Only semi empirical justifications are available for this phenomenon, see [6]. Neglecting the thermal conductivity, we are able to prove that for a layer of compressible fluid between two rigid planes kept at constant temperature, the rest state is linearly stable for every values of the parameters involved in two cases: a) the layer is heated from above (see section 3); b) the layer is heated from below and the gradient of temperature imposed is less then a precise quantity, namely g=cp, where g is the gravity constant, and cp is the specific heat at constant pressure, known as adiabatic gradient , the same that we find in Jeffreys’ pape
On the Benard problem
GUIDOBONI, Giovanna;PADULA, Mariarosaria
2005
Abstract
In literature there is no mathematical proof of the experimentally trivial stability of the rest state for a layer of compressible fluid heated from above. In the case of layer heated from below it is known that the system shows a threshold in the temperature gradient below which the fluid is not sensible to the imposed difference of temperature. Only semi empirical justifications are available for this phenomenon, see [6]. Neglecting the thermal conductivity, we are able to prove that for a layer of compressible fluid between two rigid planes kept at constant temperature, the rest state is linearly stable for every values of the parameters involved in two cases: a) the layer is heated from above (see section 3); b) the layer is heated from below and the gradient of temperature imposed is less then a precise quantity, namely g=cp, where g is the gravity constant, and cp is the specific heat at constant pressure, known as adiabatic gradient , the same that we find in Jeffreys’ papeI documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.