Low-gravity sideways double-diffusive instabilities: Small wave number asymptotics

Abstract

When a stable salinity gradient in a vertical slot undergoes lateral heating, instabilities can arise. The level of heating required for instability can be several orders of magnitude smaller than is required in the absence of a salinity gradient. Previously it has been found that the portion of the stability boundary corresponding to this most unstable region could be derived using small wave number asymptotics. Although the leading order asymptotics are unaffected by consideration of vibration or g-jitter, it has been observed that the region of the stability boundary given by these asymptotics could be reduced or eliminated by increasing the level of vibration. Here we look at the higher order asymptotics and determine how vibration affects the stability boundary in the region of maximum instability.