Jupiter’s moon Europa likely hosts a saltwater ocean beneath its icy surface. Geothermal heating and rotating convection in the ocean may drive a global overturning circulation that redistributes heat vertically and meridionally, preferentially warming the ice shell at the equator. Here we assess the previously unconstrained influence of ocean‐ice coupling on Europa’s ocean stratification and heat transport. We demonstrate that a relatively fresh layer can form at the ice‐ocean interface due to a meridional ice transport forced by the differential ice shell heating between the equator and the poles. We provide analytical and numerical solutions for the layer’s characteristics, highlighting their sensitivity to critical ocean parameters. For a weakly turbulent and highly saline ocean, a strong buoyancy gradient at the base of the freshwater layer can suppress vertical tracer exchange with the deeper ocean. As a result, the freshwater layer permits relatively warm deep ocean temperatures.Key PointsCoupling of Europa’s ocean circulation and the ice shell impacts global stratificationA low‐latitude freshwater layer may suppress vertical heat and tracer transportParameter space is explored based on properties observed by future missionsPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137725/1/grl56051.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137725/2/grl56051-sup-0001-TextS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137725/3/grl56051_am.pd

Goodman, Jason C.

Manucharyan, Georgy E.

Thompson, Andrew F.

Vance, Steven D.

Zhu, Peiyun

Geophysical Research Letters

English

Jupiter's moon Europa likely hosts a saltwater ocean beneath its icy surface. Geothermal heating and rotating convection in the ocean may drive a global overturning circulation that redistributes heat vertically and meridionally, preferentially warming the ice shell at the equator. Here we assess the previously unconstrained influence of ocean-ice coupling on Europa's ocean stratification and heat transport. We demonstrate that a relatively fresh layer can form at the ice-ocean interface due to a meridional ice transport forced by the differential ice shell heating between the equator and the poles. We provide analytical and numerical solutions for the layer's characteristics, highlighting their sensitivity to critical ocean parameters. For a weakly turbulent and highly saline ocean, a strong buoyancy gradient at the base of the freshwater layer can suppress vertical tracer exchange with the deeper ocean. As a result, the freshwater layer permits relatively warm deep ocean temperatures

Caltech Authors - Main

Confidential manuscript submitted to Geophysical Research Letters
Supporting Information for1
“The influence of meridional ice transport on Europa’s ocean stratifica-2
tion and heat content”3
Peiyun Zhu,1Georgy E. Manucharyan,2Andrew F. Thompson,2Jason C. Goodman, 3and4
Steven D. Vance 45
1Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Michigan, USA.6
2Department of Environmental Science and Engineering, California Institute of Technology, Pasadena, California, USA.7
3Department of Physics, Wheaton College, Norton, Massachusetts, USA8
4Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA.9
Contents10
1. Text S1: Derivation of dmin11
2. Text S2: Other parameterization for turbulence at the freshwater layer base12
3. Figures S1: Solutions of freshwater layer salinity balance for a magnesium sulfate13
ocean14
4. Figures S2: Sensitivity of temperature and salinity contrast at the freshwater layer15
base to Fb , S0 and Fh (via ∆Focn) for a magnesium sulfate ocean16
Introduction17
Text S1: Derivation of dmin.18
Here we describe derivation details of the analytical solution of the minimum fresh-19
water layer depth dmin. The salinity balance of the freshwater layer and parameterization of20
entrainment rate c are given by21
(cu∗ + κ
d
)∆S = (S0 − ∆S)
ρi
ρ
Fh, (1)
22
c = 1.5Ri−3/2, Ri =
dgβ∆S
u∗2,
, ∆S = S0 − Se . (2)
Using (2), we can express c with the following relationship:23
c = 1.5(dgβ∆S
u∗2
)−2/3. (3)
Corresponding author: Peiyun Zhu, zhpeiyun@umich.edu
–1–
Confidential manuscript submitted to Geophysical Research Letters
Assuming cu∗  κd , and thus neglecting the κ term, substituting (3) into (1) results in a cubic24
equation for (∆S)1/2:25
(∆S)3/2 − S0(∆S)1/2 + A = 0, where A =
3u∗4
2 ρiρ Fh (dgβ)
3/2 . (4)
This cubic equation (4) always has one negative root, which is not a physical solution be-26
cause we require ∆S > 0. The two other roots are either both positive real roots or com-27
plex numbers. The transition between real and complex roots occurs when the two real roots28
are identical. This occurs when the derivative of (4) with respect to ∆S is equal to zero, i.e.29
when ∆S = S0/3. Substituting ∆S in (4) leads to30
dmin =
0.84u∗8/3
( ρiρ Fh)
2/3
gβS0
. (5)
Any value of d smaller than dmin is not a solution because (4) does not have real roots. Phys-31
ically, only the smaller of the two real roots can be a solution for ∆S. The root with a larger32
magnitude gives a value of Ri that suppresses c and breaks the assumption that turbulent33
mixing dominates over diffusion at the base of the freshwater layer, i.e. cu∗  κd .34
Text S2: Other parameterization for turbulence at the freshwater layer base35
The parameterization for turbulent entrainment (see equations in (2)) applies to a tur-36
bulence induced by the vertical shear of horizontal velocities at the interface between the37
freshwater layer and the deep ocean, assuming a significant circulation in the latter. We esti-38
mate the entrainment rate at the ice-ocean interface on Europa, cice, to be 10−3 in our study39
because calculations based on a formula from Jenkins [1991] suggests cice to be o(10−4), and40
McPhee et al. [1999] suggests cice = 0.0058 based on sea ice observations in the Arctic41
Ocean. cice = 10−3 is within the uncertainty range for this parameter based on terrestrial42
studies.43
However, turbulence may also arise from other mechanisms, such as plumes rising44
from the seafloor and impinging the interface. Entrainment rates of plume-induced turbu-45
lence can be parameterized by an interfacial Froude number Fr = wi/
√
bi
g∆ρ
ρ0
[Bains, 1975]46
where wi is the characteristic center-line vertical velocity of the plume, bi is the local plume47
radius, ∆ρ is the density difference across the interface and ρ0 is a reference density. Entrain-48
ment rate is given by c = AFnr , coefficient A and exponent n varying with different ranges of49
Fr [Shrinivas and Hunt, 2014]. Theoretical models [Shrinivas and Hunt, 2014] and labora-50
tory experiments [Bains, 1975; Kumagai, 1984] support n ranging from 2 to 3.5 for Fr < 1.5.51
–2–
Confidential manuscript submitted to Geophysical Research Letters
As Fr is equivalent to Ri−1/2, these values of n show no significant deviation from our pa-52
rameterization of c in (2). The range of Ri in our results is 100 to 1000, corresponding to53
Fr < 0.1. The coefficient A varies by less than one order of magnitude under different ex-54
perimental conditions [Kit et al., 1980], but this variation can be incorporated into the uncer-55
tainty of u∗.56
–3–
Confidential manuscript submitted to Geophysical Research Letters
Figure S1: Solutions of freshwater layer salinity balance for a magnesium sulfate (MgSO4) ocean.
Salinity contrast ∆S (color-filled contours) and temperature contrast ∆T (dashed contours) be-
tween the deep ocean and the freshwater layer for a MgSO4 ocean at an average salinity of 100 psu,
Fh = 1.76 × 10−11 m s−1 and Fb = 0.01 Wm−2. The black and red contours indicate dmin and dmax
respectively. All ∆T and ∆S values are in log10 space; u∗ and d axes are logarithmic.
–4–
Confidential manuscript submitted to Geophysical Research Letters
Figure S2: Sensitivity of temperature and salinity contrast at the freshwater layer base to Fb , S0
and Fh (via ∆Focn) for a magnesium sulfate ocean (a) Temperature contrast ∆T between the fresh-
water layer and the deep ocean corresponding to dmin, at u∗ = 0.01 m s−1 and Fh = 1.76 × 10−11
m s−1, as a function of Fb and S0 for a MgSO4 ocean. The black contour indicates the minimum
permissible salinity. ∆T is plotted in log10 space. (b) Range of freshwater layer depth d, bounded
by dmin and dmax (black and red contours respectively), temperature contrast ∆T (dashed lines) and
salinity contrast ∆S (colors) as a function of ∆Focn (W m−2), for a MgSO4 ocean at S0 = 100 psu,
u∗ = 0.01 m s−1 and Fb = 0.01 Wm−2.
–5–


The influence of meridional ice transport on Europa's ocean stratification and heat content

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The influence of meridional ice transport on Europa’s ocean stratification and heat content

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The influence of meridional ice transport on Europa’s ocean stratification and heat content

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