a reduced model for internal waves interacting with submarine ...

V Flat bottom Rough bottom
Linear u 1 − √ β ρ [ ]
2
ρ 1
T [0,2l] u1 ξ u 1 − √ β ρ 2 1
T [ ]
ρ 1 M(ξ) [0,2l] u1 ξ
Weakly
Nonlinear
Strongly
Nonlinear
u 1 − √ β ρ [ ]
2
ρ 1
T [0,2l] u1 ξ u 1 − √ β ρ 2 1
T [ ]
ρ 1 M(ξ) [0,2l] u1 ξ
u 1 − √ β ρ [ ]
2
ρ 1
T [0,2l] (1−η)u1 ξ u 1 − √ β ρ 2 1
T [ ]
ρ 1 M(ξ) [0,2l] (1−η)u1 ξ
Table 4.2: The auxiliary variable V.
(E, F) Flat bottom Rough bottom
( ) ( )
Linear
u1ξ ,η ξ u1ξ ,η ξ
1
M(ξ)
Weakly
Nonlinear
Strongly
Nonlinear
([ (1−αη)u1
]ξ ,η ξ−αu 1 u 1ξ
)
([ (1−η)u1
]ξ ,η ξ− u 1 u 1ξ
)
1
([ (1−αη)u1
M(ξ)
]ξ ,η )
ξ−αu 1 u 1ξ
1
([ (1−η)u1
M(ξ)
]ξ ,η )
ξ− u 1 u 1ξ
Table 4.3: The field (E, F).
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