- #1

joshmccraney

Gold Member

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## Main Question or Discussion Point

Hi PF!

Given a fluid/fluid interface ##F(t,x,y,z) = 0## the kinematic boundary condition states ##DF/Dt = 0##. Given ##y=F## the text states ##v = \partial_tF+u\partial_xF+w\partial_zF##. How is this possible? I thought ##DF/Dt = 0 = \partial_tF+u\partial_xF+v\partial_yF+w\partial_zF## and ##F=y \implies \partial_yF = 1##, thus implying ##-v = \partial_tF+u\partial_xF+w\partial_zF##. What happened to the negative sign?

Given a fluid/fluid interface ##F(t,x,y,z) = 0## the kinematic boundary condition states ##DF/Dt = 0##. Given ##y=F## the text states ##v = \partial_tF+u\partial_xF+w\partial_zF##. How is this possible? I thought ##DF/Dt = 0 = \partial_tF+u\partial_xF+v\partial_yF+w\partial_zF## and ##F=y \implies \partial_yF = 1##, thus implying ##-v = \partial_tF+u\partial_xF+w\partial_zF##. What happened to the negative sign?