#!/usr/bin/env python
# coding: utf-8

# # Steady interface flow towards the coast
# Mark Bakker, TU Delft, The Netherlands

# In[1]:


# these are needed so that the notebook can also be run on Python 2
from __future__ import division, print_function
from pylab import *
get_ipython().run_line_magic('matplotlib', 'notebook')
from semi_interface import *


# ### Interface flow towards the coast
# Flow is confined below the land and semi-confined below the sea. The leaky sea bottom extends a distance $L$ below the sea. The freshwater is moving and the saltwater is at rest.
# ![](semi_coast_layout.png)
# Input variables:
# * `k`: hydraulic conductivity [m/d]
# * `H`: aquifer thickness [m]
# * `c`: resistance of leaky layer [d]
# * `grad`: absolute value of head gradient towards coast upstream of interface toe
# * `rhof`: density of fresh water [kg/m3]
# * `rhos`: density of salt water [kg/m3]
# * `Ls`: length of leaky sea bottom below sea (may also be `inf`) [m]
# * `ztop`: elevation of top of aquifer with respect to datum [m]
# * `sealevel`: elevation of sealevel with respect to datum [m]

# ### Case I of Bakker (2006)

# In[2]:


sc1 = SemiCoast(k=10, H=10, c=100, grad=0.0005, 
                rhof=1000, rhos=1025, Ls=inf, 
                ztop=0, sealevel=0)
print('toe of interface at:', sc1.toe())
print('tip of interface at:', sc1.tip())
sc1.plot(xmin=-300, xmax=300);


# ### Case II of Bakker (2006)

# In[3]:


sc2 = SemiCoast(k=10, H=10, c=100, grad=0.00375, 
                rhof=1000, rhos=1025, Ls=inf, 
                ztop=0, sealevel=0)
print('toe of interface at:', sc2.toe())
print('tip of interface at:', sc2.tip())
sc2.plot(xmin=-300, xmax=300);


# ### Case III of Bakker (2006)

# In[4]:


sc3 = SemiCoast(k=10, H=10, c=100, grad=0.0005, 
                rhof=1000, rhos=1025, Ls=80, 
                ztop=0, sealevel=0)
print('toe of interface at:', sc3.toe())
print('tip of interface at:', sc3.tip())
sc3.plot(xmin=-300, xmax=300);


# ### Case IV of Bakker (2006)

# In[5]:


sc4 = SemiCoast(k=10, H=10, c=100, grad=0.00375, 
                rhof=1000, rhos=1025, Ls=150, 
                ztop=0, sealevel=0)
print('toe of interface at:', sc4.toe())
print('tip of interface at:', sc4.tip())
sc4.plot(xmin=-300, xmax=300);


# ### Specification of upstream head (onshore, so $x<0$)
# Rather than specifying the gradient upstream of the toe, the head `h` is specified at some point `x` in the aquifer below the land (so `x` is negative).

# In[6]:


schead = SemiCoastHead(k=10, H=10, c=100, x=-1000, h=1, 
                       rhof=1000, rhos=1025, Ls=1000, 
                       ztop=0, sealevel=0)
print('toe of interface at:', schead.toe())
print('tip of interface at:', schead.tip())
print('location of h=1 (should be -1000)', schead.onshorex(h=1))
print('computed gradient:', schead.grad)
schead.plot();


# ### Figure for three different sealevels

# In[7]:


schead = SemiCoastHead(k=10, H=10, c=100, x=-1000, h=0.25, 
                       rhof=1000, rhos=1025, Ls=1000, 
                       ztop=0, sealevel=0, label='h=0.25')
schead.plot(xmin=-500, xmax=200)
schead = SemiCoastHead(k=10, H=10, c=100, x=-1000, h=0.5, 
                       rhof=1000, rhos=1025, Ls=1000, 
                       ztop=0, sealevel=0, label='h=0.5')
schead.plot(newfig=False);
schead = SemiCoastHead(k=10, H=10, c=100, x=-1000, h=1, 
                       rhof=1000, rhos=1025, Ls=1000, 
                       ztop=0, sealevel=0, label='h=1')
schead.plot(newfig=False);
legend(loc='best');


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