{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Deep Water Bubble Calculations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this Jupyter notebook we perform the calculations for the paper Mark W. Sprague, Michael L. Fine, and Timothy M. Cameron (2022), \"An investigation of bubble resonance and its implications for sound production by deep-water fishes,\" with documentation/explanation of each step. Refer to the paper for the references cited in this notebook. This notebook runs in the Julia programming language. Julia version 1.7.2 was used for all calculations in the paper.\n", "\n", "We use following Julia packages for the calculations in this notebook.\n", "\n", "* CSV - read parameter values stored in CSV files.\n", "\n", "* DataFrames - store parameter values in dataframes.\n", "\n", "* Interpolations - interpolate between parameter values calculated at specific depth. Gas and water parameters were calculated for a range of depths in a different notebook. We import the calculated parameter values and create interpolating functions to provide parameters at any depth in the range. All interpolations use a cubic spline method.\n", "\n", "* SymPy (which calls the SymPy Python package) - symbolic expressions and symbolic calculations. Once each expression is in a form for numerical calculations, a Julia numerical function is generated with the SymPy lambdify function.\n", "\n", "* Roots - numerically solving equations.\n", "\n", "* Optim - find the maximum values of parameters. We used the optimize function to find a constrained minimum of the negative of the parameter using Brent's method.\n", "\n", "* PyPlot - generate figures using the Python Matpoltlib package.\n", "\n", "* PyCall - generate a Python function needed to customize the PyPlot figure format.\n", "\n", "* Statistics - use the mean and max and std functions.\n", "\n", "Some of the symbolic calculations in this notebook produce long symbolic expressions as output. These expressions are many lines long and often do not fit within the page margins or screen size. Output from these expressions has been suppressed using a trailing semicolon (;). To view the output, delete the trailing semicolon before entering the input cell." ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## 2. Initializations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the packages used in the notebook." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [] }, "outputs": [], "source": [ "using CSV, DataFrames, Interpolations\n", "using SymPy, Roots, Optim, PyPlot, PyCall\n", "import Statistics: mean, max, std" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import SymPy symbols into the document." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [], "source": [ "import_from(sympy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function that executes Python code to interface with PyPlot (which also runs in Python) will make it easier to generate subplots with the PyPlot gridspec method." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "slice (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slice(i,j) = pycall(pybuiltin(\"slice\"), PyObject, i,j)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the parameters and value substitutions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First define the imaginary number $i$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$i$" ], "text/plain": [ "ⅈ" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "i = IM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the symbols for use in mathematical expressions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(ρ, pw, μ, σ, c, dd, γ, a, ω)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ρ, pw, μ, σ, c, dd, γ, a, ω = symbols(\"ρ, pw, μ, σ, c, dd, γ, a, ω\", real=true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define $f$ as a variable." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(f,)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@vars f" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "valst" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " vals(gas, depth, temp=\"w\")\n", "\n", "Function to produce a Dictionary with numerical values for each of the \n", "water and gas parameters in a specified environment. The resulting\n", "dictionary can be used to substitute these values for the symbols in a\n", "symbolic expression.\n", "\n", "# Arguments\n", "gas - type of gas in the bubble. Use \"N\", \"N2\", or \"n2\"\n", " for nitrogen. Use \"O\", \"O2\", or \"o2\" for oxygen.\\n\n", "depth - depth of the environment. Use 0, \"S\", \"s\", or \n", " \"surface\" for 0 m. Use 7.2, \"Sh\", \"sh\", or \n", " \"shallow\" for 7.2 m. Use 1000 for 1000 m. Use 2000 \n", " for 2000 m. Use 3500, \"D\", \"d\", or \n", " \"deep\" for 3500 m (deep water). Use 7200, \"dd\",\n", " \"DD\", or \"very deep\" for 7200 m (very deep)\\n\n", "temp - optional parameter for the water temperature (only for \n", " the sueface and shallow water) environments. Use \"w\" or\n", " \"warm\" for the warm water (20 °C) environment. Use \"c\"\n", " or \"cold\" for the cold water environment (1.50 °C). The\n", " default value is \"warm\".\\n\n", "# Output Dictionary Keys\n", "\"ρ\" - water density (kg/m^3)\\n\n", "\"pw\" - ambient pressure (Pa)\\n\n", "\"μ\" - water dynamic viscosity (Pa s)\\n\n", "\"σ\" - water surface tension (N/m)\\n\n", "\"c\" - water sound speed (m/s)\\n\n", "\"dd\" - gas thermal diffusivity (m^2/s)\\n\n", "\"γ\" - gas ratio of specific heats\n", "\n", "\"\"\"\n", "function vals(gas, depth; temp=\"w\")\n", " if (gas == \"N\") | (gas == 1) | (gas == \"N2\") | (gas == \"n2\")\n", " if (depth == 0) | (depth == \"s\") | (depth == \"S\") | (depth == \"surface\") \n", " if (temp == \"w\") | (temp == \"warm\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1028, 1.01325e5, 1.077e-3, 7.352e-2, 1522, 2.100e-5, 1.401)\n", " )\n", " elseif (temp == \"c\") | (temp == \"cold\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1027, 1.01325e5, 1.812e-3, 7.601e-2, 1456, 1.862e-5, 1.402)\n", " )\n", " end\n", " elseif depth == 1000\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1032, 1.019e7, 1.812e-3, 7.601e-2, 1473, 1.914e-7, 1.612)\n", " )\n", " elseif depth == 2000\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1036, 2.033e7, 1.812e-3, 7.601e-2, 1490, 1.143e-7, 1.738)\n", " )\n", " elseif (depth == 3500) | (depth == \"d\") | (depth == \"D\") | (depth == \"deep\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1043, 3.562e7, 1.812e-3, 7.601e-2, 1516, 9.538e-8, 1.760)\n", " )\n", " end\n", " elseif (gas == \"O\") | (gas == 2) | (gas == \"O2\") | (gas == \"o2\")\n", " if (depth == 0) | (depth == \"s\") | (depth == \"S\") | (depth == \"surface\")\n", " if (temp == \"w\") | (temp == \"warm\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1028, 1.01325e5, 1.077e-3, 7.352e-2, 1522, 2.1210e-5, 1.397)\n", " )\n", " elseif (temp == \"c\") | (temp == \"cold\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1027, 1.01325e5, 1.812e-3, 7.601e-2, 1456, 1.878e-5, 1.400)\n", " )\n", " end\n", " elseif depth == 1000\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1032, 1.019e7, 1.812e-3, 7.601e-2, 1473, 1.720e-7, 1.668)\n", " )\n", " elseif depth == 2000\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1036, 2.033e7, 1.812e-3, 7.601e-2, 1490, 9.264e-8, 1.897)\n", " )\n", " elseif (depth == 3500) | (depth == \"d\") | (depth == \"D\") | (depth == \"deep\")\n", " return (\n", " [ρ, pw, μ, σ, c, dd, γ] .=> \n", " (1043, 3.562e7, 1.812e-3, 7.601e-2, 1516, 7.487e-8, 1.950)\n", " )\n", " end\n", " end\n", " error(\"Values not found.\")\n", "end \n", "\n", "\"\"\"\n", " ρ, pw, μ, σ, c, dd, γ = valst(gas, depth[, temp])\n", "\n", "Function to call vals and return the parameters values in an Array. This function is useful for supplying the parameters to a \n", "Julia function.\n", "\n", "# Arguments\n", "gas - type of gas in the bubble. Use \"N\", \"N2\", or \"n2\"\n", " for nitrogen. Use \"O\", \"O2\", or \"o2\" for oxygen.\\n\n", "depth - depth of the environment. Use 0, \"S\", \"s\", or \n", " \"surface\" for 0 m. Use 7.2, \"Sh\", \"sh\", or \n", " \"shallow\" for 7.2 m. Use 1000 for 1000 m. Use 2000 \n", " for 2000 m. Use 3500, \"D\", \"d\", or \n", " \"deep\" for 3500 m (deep water). Use 7200, \"dd\",\n", " \"DD\", or \"very deep\" for 7200 m (very deep)\\n\n", "temp - optional parameter for the water temperature (only for \n", " the sueface and shallow water) environments. Use \"w\" or\n", " \"warm\" for the warm water (20 °C) environment. Use \"c\"\n", " or \"cold\" for the cold water environment (1.50 °C). The\n", " default value is \"warm\".\\n\n", "# Output\n", "ρ - water density (kg/m^3)\\n\n", "pw - ambient pressure (Pa)\\n\n", "μ - water dynamic viscosity (Pa s)\\n\n", "σ - water surface tension (N/m)\\n\n", "c - water sound speed (m/s)\\n\n", "dd - gas thermal diffusivity (m^2/s)\\n\n", "γ - gas ratio of specific heats\n", " \n", "\"\"\"\n", "function valst(gas, depth; temp=\"w\")\n", " v1 = Dict(vals(gas, depth, temp=temp))\n", " return v1[ρ], v1[pw], v1[μ], v1[σ], v1[c], v1[dd], v1[γ]\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a list of the symbols in the same order as the output of values in the valst function." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(ρ, pw, μ, σ, c, dd, γ)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vlist = (ρ, pw, μ, σ, c, dd, γ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Property interpolation with depth" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1. Oxygen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read calculated parameter values for oxygen bubbles into a dataframe. This data file was produced by the S1 Notebook in Section 5.1.9." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "valso2 = CSV.read(\"DeepWaterPropertiesO2.csv\", DataFrame);" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8-element Vector{String}:\n", " \"depth\"\n", " \"water_density\"\n", " \"pressure\"\n", " \"water_dyn_viscosity\"\n", " \"water_surface_tension\"\n", " \"water_sound_speed\"\n", " \"thermal_diffusivity\"\n", " \"gamma\"" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "names(valso2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define an array containing interpolation functions for each column of the dataframe." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "ivalo2 = Array{ScaledInterpolation}(undef,7)\n", "for n in 1:7\n", " itp = Interpolations.interpolate(valso2[:,n+1], BSpline(Cubic(Line(OnGrid()))))\n", " ivalo2[n] = scale(itp, (valso2[1,1]:valso2[end,1]))\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a function that returns a Dictionary of parameter values for a given depth. This dictionary is useful for substituting into symbolic expressions." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "valsfo2" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " valsfo2(d)\n", "Return a Dictionary of interpolated parameter values for oxygen bubbles at depth d.\n", "\"\"\"\n", "function valsfo2(d)\n", " flist = (ivalo2[n](d) for n in 1:7)\n", " vlist .=> flist\n", "end" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "Define a function that returns an array of parameter values for a given depth. This array is useful for providing values to functions." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "valso2list" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " valsfo2list(d)\n", "Return an Array of interpolated parameter values for oxygen bubbles at depth d.\n", "\"\"\"\n", "function valso2list(d)\n", " collect(ivalo2[n](d) for n in 1:7)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2. Nitrogen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read calculated parameter values for nitrogen bubbles into a dataframe. This data file was produced by the S1 Notebook in Section 5.2.9." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "valsn2 = CSV.read(\"../GasParameters/ValsN2.csv\", DataFrame, header=false, transpose=true);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define an array containing interpolation functions for each column of the dataframe." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ivaln2 = Array{ScaledInterpolation}(undef,7)\n", "for n in 1:7\n", " itp = Interpolations.interpolate(valsn2[:,n+1], BSpline(Cubic(Line(OnGrid()))))\n", " ivaln2[n] = scale(itp, (valsn2[1,1]:valsn2[end,1]))\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a function that returns a Dictionary of parameter values for a given depth. This dictionary is useful for substituting into symbolic expressions." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "valsfn2" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " valsfn2(d)\n", "Return a Dictionary of interpolated parameter values for nitrogen bubbles at depth d.\n", "\"\"\"\n", "function valsfn2(d)\n", " flist = (ivaln2[n](d) for n in 1:7)\n", " vlist .=> flist\n", "end" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "Define a function that returns an array of parameter values for a given depth. This array is useful for providing values to functions." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "valsn2list" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " valsfn2list(d)\n", "Return an Array of interpolated parameter values for nitrogen bubbles at depth d.\n", "\"\"\"\n", "function valsn2list(d)\n", " collect(ivaln2[n](d) for n in 1:7)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Bubble Size and Resonance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1. Definitions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equation numbers given here are those in Ainslie and Leighton [1]. Note: We use dd to represent the thermal diffusivity, $D_p$ in Ainslie and Leighton [1]. \n", "\n", "The following expression is Eq. (8)." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\frac{\\sqrt{2} \\sqrt{\\frac{dd}{ω}}}{2}$" ], "text/plain": [ " ____\n", " ╱ dd \n", "√2⋅ ╱ ── \n", " ╲╱ ω \n", "───────────\n", " 2 " ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lth = sqrt(dd / (2ω))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following expression for the bubble Laplace radius is Eq. (11). The parameter σ is $\\tau$ in Ainslie and Leighton [1] is , and pw is $P_{\\mathrm{liq}}$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\frac{2 σ}{pw}$" ], "text/plain": [ "2⋅σ\n", "───\n", " pw" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "RLap = 2σ / pw" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, use the dictionary generated by the vals function to generate a numerical value." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.267827063447501e-9" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(RLap(vals(\"n2\", 3500)...))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following equation is Eq. (12) for the natural angular frequency. This is the Minnaert angular frequency." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\frac{\\sqrt{3} \\sqrt{pw} \\sqrt{γ} \\sqrt{\\frac{1}{ρ}}}{a}$" ], "text/plain": [ " ___\n", " ____ ╱ 1 \n", "√3⋅╲╱ pw ⋅√γ⋅ ╱ ─ \n", " ╲╱ ρ \n", "────────────────────\n", " a " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ωM = expand_power_base(1/a * sqrt(3γ * pw / ρ), force=true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for ωM using vals." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "42464.08442394073539373615396379947556004437812655596490962434667038011121324344" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(ωM(vals(\"n2\", 3500)..., a=>0.01))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a Julia function for the Minneart frequency." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "#118 (generic function with 1 method)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fMjl = lambdify(ωM/(2*π), (a, vlist...))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "42464.08442394074" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2*π * fMjl(0.01, valst(\"n2\", 3500)...)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following is Eq. (14) for the thermal diffusion ratio. The parameter a is $R_0$, the bubble radius, in Ainslie and Leighton [1]." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\frac{\\sqrt{2} a}{\\sqrt{dd} \\sqrt{\\frac{1}{ω}}}$" ], "text/plain": [ " √2⋅a \n", "──────────────\n", " ___\n", " ____ ╱ 1 \n", "╲╱ dd ⋅ ╱ ─ \n", " ╲╱ ω " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = expand_power_base(a / lth, force=true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for X using vals." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2566.618233025503586652631289132593889747080961471964214565849780904802650517199" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(X(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following is Eq. (16) for the complex polytropic index." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "Γ = simplify(γ / \n", " (1 - \n", " (((1 + i) * X/2) / (tanh((1 + i) * X/2)) - 1) * \n", " (6 * i * (γ - 1)) / (X^2)\n", " )\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for Γ using vals." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.7584365465467842 + 0.001559466675711914im" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(Γ(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We solve Eq. (15) for $\\omega$ to get the resonant frequency $\\omega_{\\mathrm{res}}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First enter an expression for Eq. (15). Each defined parameter is expanded in the resulting expression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "eq15 = Eq(\n", " γ * ω^2 / ωM^2,\n", " (1 + RLap/a) * re(Γ) - RLap / (3a)\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use vals and enter numerical values for a and ω to evaluate the left and right sides of the equation. We will use this below to find numerical solutions." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.009633162446505897, 1.758437154756190352918898161325051116620666094925326833635863147467430535808923)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(N(lhs(eq15)(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500)), N(rhs(eq15)(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that if we enter values for a and the parameters supplied by the vals function, both sides of Eq. (15) become functions of ω only. We will use this to solve numerically for frequency values." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "eq15(a=>0.1, vals(\"n2\", 0)...);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following is Eq. (34) for the dimensionless frequency." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/latex": [ "$\\frac{a ω}{c}$" ], "text/plain": [ "a⋅ω\n", "───\n", " c " ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ϵ = ω * a / c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for ϵ using vals." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.020722906685948502" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(ϵ(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (46) for the equilibrium pressure inside the bubble." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$pw + \\frac{2 σ}{a}$" ], "text/plain": [ " 2⋅σ\n", "pw + ───\n", " a " ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pgas = pw + 2σ/a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for pgas using vals." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.5620015202e7" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(pgas(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (93) for a frequency-dependent parameter related to the resonant frequency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "ω0 = simplify(sqrt(3 * re(Γ) * pgas / (ρ * a^2) - 2 * σ / (ρ * a^3)));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for ω0 using vals." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "42445.22660247035756165512249712223906496083819417985503674056170985506937390732" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(ω0(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (87) for the stiffness parameter K." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "K = simplify(ω0^2 + ϵ^2 / (1 + ϵ^2) * ω^2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for K using vals." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.801601497907386526890443524370992964559564711017030564728345747037665056562364e+09" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(K(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (91) for the viscous damping factor. The parameter μ is $\\eta_s$, the shear viscosity coefficient of the liquid, in Ainslie and Leighton [1]." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\frac{2 μ}{a^{2} ρ}$" ], "text/plain": [ "2⋅μ \n", "────\n", " 2 \n", "a ⋅ρ" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "βvis = 2μ / (ρ * a^2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for βvis using vals." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.03474592521572387" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(βvis(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (92) for the thermal damping factor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "βth = simplify((3 * pgas) / (2ρ * a^2 * ω) * imag(Γ));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for βvth using vals." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "254.2888262311701877290558552074788321531971508530733444014724842977070258107796" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(βth(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (90) for the non-acoustic damping factor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "β0 = βvis + βth;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for β0 using vals." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "254.3235721563859116022697906983456204669212514428255416670974842977070258107796" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(β0(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (88) for the (total) damping factor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "β = β0 + ϵ / (1 + ϵ^2) * ω/2;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, generate a numerical value for β using vals." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "286.8610649953059419810940236955492009199818188218233444014724842977070258107819" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N(β(vals(\"n2\", 3500)..., a=>0.01, ω=>2*π*500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2. Resonant Frequency" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert the symbolic expression eq15 to a Julia function so we can find a numerical solution (right side - left side = 0)." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "#118 (generic function with 1 method)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq15jl = lambdify((lhs(eq15) - rhs(eq15))(ω=>2*pi*f),(a, vlist..., f))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now define a function to find frequencies for the zeros of eq15jl with supplied parameters." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fres (generic function with 2 methods)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " fres(a1, v1[, f0])\n", "Find the resonance frequency that is a numerical solution eq15jl. \n", "The argment f0 is the optional starting value for the numerical \n", "solution with default value 200 Hz.\n", "\"\"\"\n", "fres(a1, v1, f0=200) = find_zero(eq15jl(a1, v1..., f), f0)\n", "fres(a1, v1; f0=200) = find_zero(eq15jl(a1, v1..., f), f0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.3. Natural Frequency" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve Eq. (124) for the natural oscillation frequency we subtract the right side from the left side so we can find the root numerically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "eq124z = ω^2 - (K - β^2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert the symbolic expression eq124z to a Julia function so we can find a numerical solution (right side - left side = 0)." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "#118 (generic function with 1 method)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq124zjl = lambdify(eq124z(ω=>2*pi*f),(a,vlist...,f))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now define a function to find frequencies for the zeros of eq124zjl with supplied parameters." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fnat (generic function with 2 methods)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " fnat(a1, v1[, f0])\n", "Find the natural frequency of oscillation that is a numerical solution\n", "eq124zjl. The argment f0 is the optional starting value for the\n", "numerical solution with default value 200 Hz.\n", "\"\"\"\n", "fnat(a1, v1, f0) = find_zero(eq124zjl(a1, v1..., f), f0)\n", "fnat(a1, v1; f0=200) = find_zero(eq124zjl(a1, v1..., f), f0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a check, evaluate the function for some parameters." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "32.35148197122246" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fnat(0.1, valst(\"n2\", 0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.4. Far-Field Resonance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Eq. (85) for the scattering cross section. This relationship is from Eq. (43) in a previous study by Ainslie and Leighton [42]. Equation (149) in Ainslie and Leighton [1] is based on this with $\\omega_0$ and $\\beta_0$ held constant." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Symbolic output from the expression below has been suppressed. To show the output, delete the trailing semicolon before entering the entering the expression.*" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "σs = 4 * pi * a^2 / ((ω0^2/ω^2 - 1 - 2 * β0 * ϵ / ω)^2 + (2 * β0/ω + ω0^2 * ϵ/ω^2)^2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert the symbolic expression σs to a Julia function so we can find a numerical solution for the maximum value." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "#118 (generic function with 1 method)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "σsjl = lambdify(σs(ω=>2*pi*f),(a, vlist..., f))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now define a set of functions that maximizes σsjl returning the frequency of the maximum and the maximum value." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "σres (generic function with 2 methods)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " fff(a1, v1[, f1, f2])\n", "Numerically determine the resonance frequency that maximizes the value\n", "of σsjl between frequencies f1 and f2. f1 and f2 are optional\n", "arguments with default values 0 Hz and 10000 Hz respectively.\n", "\"\"\"\n", "fff(a1, v1, f1, f2) = optimize(fin -> -σsjl(a1, v1..., fin), f1, f2).minimizer\n", "fff(a1, v1; f1=0.0, f2=10000.0) = optimize(fin -> -σsjl(a1, v1..., fin), f1, f2).minimizer\n", "\n", "\"\"\"\n", " σres(a1, v1[, f1, f2])\n", "Numerically determine the maximum value of σsjl between frequencies \n", "f1 and f2. f1 and f2 are optional arguments with default \n", "values 0 Hz and 10000 Hz respectively.\n", "\"\"\"\n", "σres(a1, v1, f1, f2) = -optimize(fin -> -σsjl(a1, v1..., fin), f1, f2).minimum\n", "σres(a1, v1; f1=0.0, f2=10000.0) = -optimize(fin -> -σsjl(a1, v1..., fin), f1, f2).minimum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.5. Far-field pressure resonance plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a range of bubble radii for evaluation of radius dependencies and for plotting." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "0.01:0.005:0.2" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "avals = 0.01:0.005:0.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.5.1. Calculation of far-field resonance frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Arrays of fff values are calculated below for the bubble radii in avals." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "fffns = map(a1 -> fff(a1, valst(\"n2\", 0)), avals);" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "fffncs = map(a1 -> fff(a1, valst(\"n2\", 0, temp=\"c\")), avals);" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "fffn1k = map(a1 -> fff(a1, valst(\"n2\", 1000)), avals);" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "fffn2k = map(a1 -> fff(a1, valst(\"n2\", 2000)), avals);" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "fffnd = map(a1 -> fff(a1, valst(\"n2\", 3500)), avals);" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "fffos = map(a1 -> fff(a1, valst(\"o2\", 0)), avals);" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "fffocs = map(a1 -> fff(a1, valst(\"o2\", 0, temp=\"c\")), avals);" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "fffo1k = map(a1 -> fff(a1, valst(\"o2\", 1000)), avals);" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "fffo2k = map(a1 -> fff(a1, valst(\"o2\", 2000)), avals);" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "fffod = map(a1 -> fff(a1, valst(\"o2\", 3500)), avals);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5.5.2. Plotting far-field resonance frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the far-field resonance frequencies vs. bubble radius. This is Fig 1B." ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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