Abstract
AbstractWe consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow $$v=(y,0)$$
v
=
(
y
,
0
)
and a stratified temperature $$\theta =\alpha y$$
θ
=
α
y
with $$\alpha >\frac{1}{4}$$
α
>
1
4
. We show that for any $$\epsilon >0$$
ϵ
>
0
there exist non-trivial explicit solutions, which are initially perturbations of size $$\epsilon $$
ϵ
, and grow to size 1 on a time scale $$\epsilon ^{-2}$$
ϵ
-
2
. Moreover, the (simplified) linearized problem around these non-trivial states exhibits improved upper bounds on the possible size of norm inflation for frequencies larger and smaller than $$\epsilon ^{-4}$$
ϵ
-
4
.
Funder
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering,Modeling and Simulation
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